Basic Electronics College Algebra Course Manual

Introduction to Electronics

CHAPTER

Section 1.1 Electronics Safety

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1-1 Electronics Safety

Safety is everyone’s responsibility. Everyone must cooperate to create the safest possible working conditions. Where your personal life and good health are concerned, safety becomes your responsibility whether you step in front of a speeding truck, or expose yourself to a lethal shock, are matters over which you, as an individual have more control than anyone else.

1-2 Applications of Electronics 1-3 Digital Number Systems 1-4 Representing Binary Quantities

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Safety is simply a matter of applying common sense precautions. The rules of safety are concerned with the prevention of accidental injuries sustained when an accident occurs. The general rules for shop safety apply equally to the electricalelectronics laboratory. The following important shop rules should be observed at all times.

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1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

Don’t clown around or engage in horseplay. Many painful injuries are caused by the carelessness and thoughtless antics of the clown. Get your teacher’s approval before starting your work. This will save your time and help prevent accidents. Remember your teacher is there to help you. Report all injuries at once, even the slightest. A small cut can develop serious complications if not properly treated. Wear safety glasses- when grinding or working in areas where sparks or chips of metals are flying. Remember that your eyes is a priceless possession. Keep the floors around your work area clean and free of litter which might cause someone to slip or stumble. Use tools correctly and do not use them if they are not in proper working condition. Observe the proper methods of handling and lifting objects. Get help to lift heavy objects. Do not talk nor disturb a fellow student when he is operating a machine. Never leave the machine while it is running down. Stay with it until it stops completely. Obtain permission before you use power tools.

Students and teachers who work with electricity face hazard of electrical shock and should make every effort to understand the danger. Electricity can cause fatal burns or cause vital organs to malfunction. In general, a current of 5 mA or less will cause a sensation of shock, but rarely any damage. Larger currents can cause hand muscles to contract. Currents on the order of 100 mA are often fatal if they pass through the body for even a few seconds. The Electronics Workshop is primarily concerned with low-voltage electronics. The chance of injury due to electric shock is very, very, low. Experiments for younger students have been designed to be easily completed without the use of soldering. Nonetheless, as in all laboratory situations, there are safety rules that must be followed. The two most important safety rules are: 1. Always have a knowledgeable adult to supervise work. Ask a teacher or parent to help you. 2. Always use common sense and pay attention to the job you are working on. Doing so can prevent most laboratory accidents.

Electricity-electronics is a tremendous field and most of us do well to understand small segments of it. Ask questions when in doubt. Be humble! Every possible precaution has been taken to ensure the safety of experiments and the correctness of information. The study of electronics is interesting and exciting. Enjoy yourself and be safe.

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Introduction to Electronics

Section 1.2 Applications of Electronics In addition to use in radio and television, Electronics is used to almost all industries for control functions, automation, and computing. There are so many applications that the broad field of electronics must be considered in smaller areas. Three logical groupings of electronics applications are defined here. Also included is a brief description of some important divisions with some typical job titles for working in the electronic business. Communications Electronics. This field includes AM and FM radio with stereo, and television with color. The equipment is divided between transmitters and receivers. Also, transmitters can be divided between radio frequency equipment to produce the carrier wave radiated from the antenna and the audio and video equipment in the studio that supplies the modulating signal with the desired information. High-fidelity audio equipment can be considered with radio receivers. The receiver itself has audio amplifiers to drive the loudspeaker that reproduce the sound. Satellite communications is also a transmit-receive system using electro-magnetic radio waves. The satellite just happens to be orbiting around the earth at a height of about 22,300 miles order to maintain a stationary position relative to the earth. Actually, the satellite is a relay station for transmitter and receiver earth stations. Electric Power. These applications are in the generation and distribution if 60-Hz AC power, as the source of energy for electrical equipment. Included are lighting, heating, motors, and generators. Electronics plays an important role in the control and monitoring of electrical equipments. Digital Electronics. We see the digits 0 to 9 on an electronic calculator or digital watch, but digital electronics has a much broader meaning. The circuits for digital applications operate with pulses of voltage or current, as shown in the diagram below. A pulse waveform is either completely ON or OFF because of the sudden changes in amplitude. In-between values have no function. Note that ON and OFF stage can also be labeled as HIGH and LOW, or 1 and 0 in binary notation. Effectively the digital pulses correspond to the action of switching circuits that are either on or off.

Voltage or current variations with a continuous set of values form an analog waveform, as shown below. The 60-Hz power line and audio and video signals are common examples. Note that the values between 0 and 10 V are marked to indicate that all the in-between values are an essential part of a waveform. Actually, all the possible applications in the types of electronic circuits can be divided into two just two types- digital circuits that recognize pulses when they are HIGH or LOW, and analog circuits that use all values in the waveform. The applications of digital electronics, including calculators, computers, data processing and data communications, possibly form the largest branch of electronics. In addition many other applications, including radio and television, use both analog and digital circuits. In addition to all the general applications in communications, digital equipment, and electric services, several fields that could be of specific interest include automotive electronics, industrial electronics, and medical electronics. Both digital and analog techniques are used. In automotive electronics, more and more electronic equipment is used in cars for charging the battery, power assist functions, measuring gages, and monitoring and control of engine performance. Perhaps the most important application is the electronic ignition. This method provides better timing

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Introduction to Electronics

of the ignition spark, especially at high speeds. On-board computer monitor and control a wide auto functions. Industrial electronics includes control of welding and heating processes, the use of elevator control, operation of copying machines. Metal detectors and smoke detectors, moisture control, and computer-controlled machinery. In addition there are many types of remote control-functions, such as automatic garage door openers and burglar alarms. Closed-circuit television is often used for surveillance. Medical electronics combines electronics with biology. Medical research diagnosis, and treatment all use electronic equipment. Examples are the electron microscope and electrocardiograph machine. In hospitals, oscilloscopes are commonly used as the display to monitor the heartbeat of patients in extensive care.

Job titles Different specialties in electronics are indicated by the following titles for engineers: antenna, audio, computer, digital, illumination, information theory, magnetic, microwave, motors and generators, packaging, power distribution, radio, semiconductor, television, and test equipment. Many of these fields combine physics and chemistry, especially for semiconductors. The types of jobs in these fields include engineer for research, development, production, sales, or management, teacher, technician, technical writer, computer programmer, drafter, service worker, tester and inspector. Technicians and service workers are needed for testing, maintenance and repair of all the different types of electronic equipments.

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Introduction to Electronics Score: Instructor’s signature: Date: Remarks:

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Exercise 1. Electronics safety comprehension exam 1. In your own words, enumerate five electronics safety tips that you understand in this lesson. (2 points each) a.

b.

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d.

e.

2. What field of electronics interests you most? Why? (5 points)

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Resistors

2

CHAPTER

The resistor's function is to reduce the flow of electric current. This symbol is used to indicate a resistor in a circuit diagram, known as a schematic.

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2-1 Types of Resistors

Resistance value is designated in units called the "Ohm." A 1000 Ohm resistor is typically shown as 1K-Ohm ( kilo Ohm ), and 1000 KOhms is written as 1M-Ohm ( mega ohm ).

2-2 Resistor Color Codes 2-3 The Ohmmeter

There are two classes of resistors; fixed resistors and the variable resistors. They are also classified according to the material from which they are made. The typical resistor is made of either carbon film or metal film. There are other types as well, but these are the most common.

2-4 The Ohmeter 2-5 The Multimeter 2-6 Variable Resistors 2 -7 Rating of Resistors

The resistance value of the resistor is not the only thing to consider when selecting a resistor for use in a circuit. The "tolerance" and the electric power ratings of the resistor are also important.

2-8 Resistor Troubles

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The tolerance of a resistor denotes how close it is to the actual rated résistance value. For example, a ±5% tolerance would indicate a resistor that is within ±5% of the specified resistance value. The power rating indicates how much power the resistor can safely tolerate. Just like you wouldn't use a 6 volt flashlight lamp to replace a burned out light in your house, you wouldn't use a 1/8 watt resistor when you should be using a 1/2 watt resistor. The maximum rated power of the resistor is specified in Watts. Power is calculated using the square of the current ( I2 ) x the resistance value ( R ) of the resistor. If the maximum rating of the resistor is exceeded, it will become extremely hot, and even burn. Resistors in electronic circuits are typically rated 1/8W, 1/4W, and 1/2W. 1/8W is almost always used in signal circuit applications. When powering a light emitting diode, comparatively large current flows through the resistor, so you need to consider the power rating of the resistor you choose.

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Section 2.1 Types of Resistors A fixed resistor is one in which the value of its resistance cannot change.

Carbon film resistors This is the most general purpose, cheap resistor. Usually the tolerance of the resistance value is ±5%. Power ratings of 1/8W, 1/4W and 1/2W are frequently used. Carbon film resistors have a disadvantage; they tend to be electrically noisy. Metal film resistors are recommended for use in analog circuits. However, I have never experienced any problems with this noise. The physical size of the different resistors are as follows.

Rough size Rating power Thickness Length (W) (mm) (mm) From the top of the photograph 1/8W 1/4W 1/2W

1/8

2

3

1/4

2

6

1/2

3

9

This resistor is called a Single-In-Line(SIL) resistor network. It is made with many resistors of the same value, all in one package. One side of each resistor is connected with one side of all the other resistors inside. One example of its use would be to control the current in a circuit powering many light emitting diodes (LEDs). In the photograph on the left, 8 resistors are housed in the package. Each of the leads on the package is one resistor. The ninth lead on the left side is the common lead. The face value of the resistance is printed. ( It depends on the supplier. ) Some resistor networks have a "4S" printed on the top of the resistor network. The 4S indicates that the package contains 4 independent resistors that are not wired together inside. The housing has eight leads instead of nine. The internal wiring of these typical resistor networks has been illustrated below. The size (black part) of the resistor network which I have is as follows: For the type with 9 leads, the thickness is 1.8 mm, the height 5mm, and the width 23 mm. For the types with 8 component leads, the thickness is 1.8 mm, the height 5 mm, and the width 20 mm.

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Metal film resistors Metal film resistors are used when a higher tolerance (more accurate value) is needed. They are much more accurate in value than carbon film resistors. They have about ±0.05% tolerance. They have about ±0.05% tolerance. I don't use any high tolerance resistors in my circuits. Resistors that are about ±1% are more than sufficient. Ni-Cr (Nichrome) seems to be used for the material of resistor. The metal film resistor is used for bridge circuits, filter circuits, and low-noise analog signal circuits.

Rough size Rating power Thickness Length (W) (mm) (mm) From the top of the photograph 1/8W (tolerance ±1%) 1/4W (tolerance ±1%) 1W (tolerance ±5%) 2W (tolerance ±5%)

1/8

2

3

1/4

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6

1

3.5

12

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CDS Elements Some components can change resistance value by changes in the amount of light hitting them. One type is the Cadmium Sulfide Photocell. (Cd) The more light that hits it, the smaller its resistance value becomes. There are many types of these devices. They vary according to light sensitivity, size, resistance value etc. Pictured at the left is a typical CDS photocell. Its diameter is 8 mm, 4 mm high, with a cylinder form. When bright light is hitting it, the value is about 200 ohms, and when in the dark, the resistance value is about 2M ohms. This device is using for the head lamp illumination confirmation device of the car.

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Other Resistors There is another type of resistor other than the carbon-film type and the metal film resistors. It is the wirewound resistor. A wirewound resistor is made of metal resistance wire, and because of this, they can be manufactured to precise values. Also, high-wattage resistors can be made by using a thick wire material. Wirewound resistors cannot be used for high-frequency circuits. Coils are used in high frequency circuits. Since a wirewound resistor is a wire wrapped around an insulator, it is also a coil, in a manner of speaking. Using one could change the behavior of the circuit. Still another type of resistor is the Ceramic resistor. These are wirewound resistors in a ceramic case, strengthened with a special cement. They have very high power ratings, from 1 or 2 watts to dozens of watts. These resistors can become extremely hot when used for high power applications, and this must be taken into account when designing the circuit. These devices can easily get hot enough to burn you if you touch one. The photograph on the left is of wirewound resistors. The upper one is 10W and is the length of 45 mm, 13 mm thickness. The lower one is 50W and is the length of 75 mm, 29 mm thickness. The upper one is has metal fittings attached. These devices are insulated with a ceramic coating.

The photograph on the left is a ceramic (or cement) resistor of 5W and is the height of 9 mm, 9 mm depth, 22 mm width.

Thermistor ( Thermally sensitive resistor ) The resistance value of the thermistor changes according to temperature. This part is used as a temperature sensor.There are mainly three types of thermistor. NTC(Negative Temperature Coefficient Thermistor) : With this type, the resistance value decreases continuously as the temperature rises. PTC(Positive Temperature Coefficient Thermistor) : With this type, the resistance value increases suddenly when the temperature rises above a specific point. CTR(Critical Temperature Resister Thermistor) : With this type, the resistance value decreases suddenly when the temperature rises above a specific point. The NTC type is used for the temperature control.

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The relation between the temperature and the resistance value of the NTC type can be calculated using the following formula.

R T R0 T0 B

: The resistance value at the temperature T : The temperature [K] : The resistance value at the reference temperature T0 : The reference temperature [K] : The coefficient

As the reference temperature, typically, 25°C is used. The unit with the temperature is the absolute temperature(Value of which 0 was -273°C) in K(Kelvin). 25°C are the 298 Kelvins.

Section 2.2 Resistor color code Because carbon resistors are small physically, they are color-coded to mark their value in ohms. The basis of this system is the use of colors for numerical values as listed in the table below. In memorizing the colors note that the darkest colors, black and brown, are for the lowest numbers, zero and one, whereas white is for nine. The color coding is standardized by the Electronic Industries Association (EIA). These colors are also used for small capacitors.

Example 1 (Brown=1),(Black=0),(Orange=3) 3 10 x 10 = 10k ohm Tolerance(Gold) = ±5%

Example 2 (Yellow=4),(Violet=7),(Black=0),(Red=2) 2 470 x 10 = 47k ohm Tolerance(Brown) = ±1%

Color

Value

Multiplier

Tolerance (%)

Black

0

0

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Brown

1

1

±1

Red

2

2

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Orange

3

3

±0.05

Yellow

4

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Green

5

5

±0.5

Blue

6

6

±0.25

Violet

7

7

±0.1

Gray

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8

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White

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9

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Gold

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Silver

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±10

None

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As illustrated in the diagram above, silver in the fourth band indicates a tolerance of 10 %, gold indicates 5%. If there is no color band for tolerance, it is 20%. The inexact value of carbon resistor is a disadvantage of their economical construction. They usually cost only a few cents, or less in larger quantities. In most circuits, though, a small difference in resistance can be tolerated. It should be noted that some resistors have five stripes, instead of four. In this case, the first three stripes give three digits, followed by the decimal multiplier in the fourth stripe and the tolerance in the fifth stripe. These resistors have more precise values, with tolerances of 0.1 to 2 percent. Resistance Color Stripes. The use of bands or stripes is the most common system for color-coding carbon resistors as shown in the diagram above right. Color stripes are printed at one end of the insulating body, which is usually tan. Reading from left to right, the first band close to the edge gives the first digit in numerical value of R. The next band marks the second digit. The third band is the decimal multiplier, which gives the number of zeroes after the two digits. Resistors under 10Ω Ω. For these values the third stripe is either gold or silver, indicating a fractional decimal multiplier. When the third digit is gold, multiply the first two digits by 0.1. Example, if the first two digits are 25 then, 25 X 0.1 = 2.5 Ω. Silver means a mult4iplier of 0.01 . If the first two digits is still 25 then, 25 X 0.01 = .25 Ω. It is important to realize that the gold and silver colors are used as decimal multipliers only in the third stripe. However, gold and silver are used most often in the fourth stripe to indicate how accurate the R value is. Resistor Tolerance. The amount by which the actual R can be different from the color-coded value is the tolerance, usually given in percent. For instance, a 2000Ω resistor with 10 percent tolerance can have resistance 10 percent above or below the coded value. This R, therefore, is between 1800Ω to 2200Ω. The calculation are as follows: 10 percent of 2000 is .1 X 2000 = 200 For + 10 percent, the value is 2000 + 200 = 2200Ω For – 10 percent, the value is 2000 – 200 = 1800Ω

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Score: Instructor’s signature: Date: Remarks:

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Exercise 2. Resistor Color Codes I.

Fill up the table below for the expected value of the resistors in ohms and in kilo-ohms given its color codes below. (2 points per number) Value in Ohms

Value in K-ohms

1. Grey, Blue, Red, Silver 2. Yellow, Green, Gold, Gold 3. Violet, Brown, Black, Silver, Gold 4. Brown, Black, Red, Gold 5. Blue, Yellow, Orange, Silver 6. Brown, Black, Silver, Silver 7. Red, Red, Red, Gold 8. Green, Orange, Brown, Silver 9. Brown, Violet, Yellow, Gold 10. Blue, Black, Red, Orange, Gold II.

Compute for the tolerance value of each resistor given its color codes.(2 points per number)

1. Red, Brown, Orange, Gold a. Upper Limit b. Lower Limit 2. Orange, Violet, Brown, Silver a. Upper Limit b. Lower Limit 3. Grey, White, Violet, Gold, Silver a. Upper Limit b. Lower Limit 4. Blue, Green, Silver, Gold a. Upper Limit b. Lower Limit 5. Brown, Black, Gold, Silver a. Upper Limit b. Lower Limit

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Section 2.3 The Ohmmeter The two instruments most commonly used to check the continuity (a complete circuit), or to measure the resistance of a circuit or circuit element, are the OHMMETER and the MEGGER (megohm meter). The ohmmeter is widely used to measure resistance and check the continuity of electrical circuits and devices. Its range usually extends to only a few megohms. The megger is widely used for measuring insulation resistance, such as between a wire and the outer surface of the insulation, and insulation resistance of cables and insulators. The range of a megger may extend to more than 1,000 megohms. The ohmmeter consists of a dc ammeter, with a few added features. The added features are: A dc source of potential (usually a 3-volt battery) One or more resistors (one of which is variable) A simple ohmmeter circuit is shown in figure 2-1. The ohmmeter's pointer deflection is controlled by the amount of battery current passing through the moving coil. Before measuring the resistance of an unknown resistor or electrical circuit, the test leads of the ohmmeter are first shorted together, as shown in figure 1-31. With the leads shorted, the meter is calibrated for proper operation on the selected range. While the leads are shorted, meter current is maximum and the pointer deflects a maximum amount, somewhere near the zero position on the ohms scale. Because of this current through the meter with the leads shorted, it is necessary to remove the test leads when you are finished using the ohmmeter. If the leads were left connected, they could come in contact with each other and discharge the ohmmeter battery. When the variable resistor (rheostat) is adjusted properly, with the leads shorted, the pointer of the meter will come to rest exactly on the zero position. This indicates

Zero Resistance Between the test leads, which, in fact, are shorted together. The zero reading of a series-type ohmmeter is on the righthand side of the scale, where as the zero reading for an ammeter or a voltmeter is generally to the left-hand side of the scale. (There is another type of ohmmeter which is discussed a little later on in this chapter.) When the test leads of an ohmmeter are separated, the pointer of the meter will return to the left side of the scale. The interruption of current and the spring tension act on the movable coil assembly, moving the pointer to the left side (∞) of the scale. Figure 1-31. - A simple ohmmeter circuit.

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Using the Ohmmeter After the ohmmeter is adjusted for zero reading, it is ready to be connected in a circuit to measure resistance. A typical circuit and ohmmeter arrangement is shown in figure 2-2 Figure 2-2. - Measuring circuit resistance with an ohmmeter.

The power switch of the circuit to be measured should always be in the OFF position. This prevents the source voltage of the circuit from being applied across the meter, which could cause damage to the meter movement. The test leads of the ohmmeter are connected in series with the circuit to be measured (fig. 1-32). This causes the current produced by the 3-volt battery of the meter to flow through the circuit being tested. Assume that the meter test leads are connected at points a and b of figure 1-32. The amount of current that flows through the meter coil will depend on the total resistance of resistors R1 and R2, and the resistance of the meter. Since the meter has been preadjusted (zeroed), the amount of coil movement now depends solely on the resistance of R1and R2. The inclusion of R1 and R2 raises the total series resistance, decreasing the current, and thus decreasing the pointer deflection. The pointer will now come to rest at a scale figure indicating the combined resistance of R1 and R2. If R1 or R2, or both, were replaced with a resistor(s) having a larger value, the current flow in the moving coil of the meter would be decreased further. The deflection would also be further decreased, and the scale indication would read a still higher circuit resistance. Movement of the moving coil is proportional to the amount of current flow.

Ohmmeter Ranges The amount of circuit resistance to be measured may vary over a wide range. In some cases it may be only a few ohms, and in others it may be as great as 1,000,000 ohms (1 megohm). To enable the meter to indicate any value being measured, with the least error, scale multiplication features are used in most ohmmeters. For example, a typical meter will have four test lead jacksCOMMON, R X 1, R X 10, and R X 100. The jack marked COMMON is connected internally through the battery to one side of the moving coil of the ohmmeter. The jacks marked R X 1, R X 10, and R X 100 are connected to three different size resistors located within the ohmmeter. This is shown in figure 2-3. Figure 1-33. - An ohmmeter with multiplication jacks.

Some ohmmeters are equipped with a selector switch for selecting the multiplication scale desired, so only two test lead jacks are necessary.

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Other meters have a separate jack for each range, as shown in figure 1-33. The range to be used in measuring any particular unknown resistance (Rx in figure 1-33) depends on the approximate value of the unknown resistance. For instance, assume the ohmmeter in figure 1-33 is calibrated in divisions from 0 to 1,000. If Rx is greater than 1,000 ohms, and the R x 1 range is being used, the ohmmeter cannot measure it. This occurs because the combined series resistance of resistor R X 1 and Rx is too great to allow sufficient battery current to flow to deflect the pointer away from infinity (∞). (Infinity is a quantity larger than the largest quantity you can measure.) The test lead would have to be plugged into the next range, R X 10. With this done, assume the pointer deflects to indicate 375 ohms. This would indicate that Rx has 375 ohms X 10, or 3,750 ohms resistance. The change of range caused the deflection because resistor R X 10 has about 1/10 the resistance of resistor R X 1. Thus, selecting the smaller series resistance permitted a battery current of sufficient amount to cause a useful pointer deflection. If the R X 100 range were used to measure the same 3,750-ohm resistor, the pointer would deflect still further, to the 37.5-ohm position. This increased deflection would occur because resistor R X 100 has about 1/10 the resistance of resistor R X 10. The foregoing circuit arrangement allows the same amount of current to flow through the meter's moving coil whether the meter measures 10,000 ohms on the R X 10 scale, or 100,000 ohms on the R X 100 scale. It always takes the same amount of current to deflect the pointer to a certain position on the scale (midscale position for example), regardless of the multiplication factor being used. Since the multiplier resistors are of different values, it is necessary to ALWAYS "zero" adjust the meter for each multiplication fact or selected. You should select the multiplication factor (range) that will result in the pointer coming to rest as near as possible to the midpoint of the scale. This enables you to read the resistance more accurately, because the scale readings are more easily interpreted at or near midpoint.

Ohmmeter Safety Precautions The following safety precautions and operating procedures for ohmmeters are the MINIMUM necessary to prevent injury and damage.





Be certain the circuit is deenergized and discharged before connecting an ohmmeter. Do not apply power to a circuit while measuring resistance. When you are finished using an ohmmeter, switch it to the OFF position if one is provided and remove the leads from the meter. Always adjust the ohmmeter for 0 (or ∞ in shunt ohmmeter) after you change ranges before making the resistance measurement.

Section 2.4 The Multimeter A MULTIMETER is the most common measuring device used in the Navy. The name multimeter comes from MULTIple METER, and that is exactly what a multimeter is. It is a dc ammeter, a dc voltmeter, an ac voltmeter, and an ohmmeter, all in one package. Figure 1-37 is a picture of a typical multimeter.

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Figure 1-37. - A typical multimeter.

The multimeter shown in figure 1-37 may look complicated, but it is very easy to use. You have already learned about ammeters, voltmeters, and ohmmeters; the multimeter is simply a combination of these meters. Most multimeters use a d'Arsonval meter movement and have a built-in rectifier for ac measurement. The lower portion of the meter shown in figure 1-37 contains the function switches and jacks (for the meter leads). The use of the jacks will be discussed first. The COMMON or -jack is used in all functions is plugged into the COMMON jack. The +jack is used for the second meter lead for any of the functions printed in large letters beside the FUNCTION SWITCH (the large switch in the center). The other jacks have specific functions printed above or below them and are self-explanatory (the output jack is used with the dB scale, which will not be explained in this chapter). To use one of the special function jacks, except +10 amps, one lead is plugged into the COMMON jack, and the FUNCTION SWITCH is positioned to point to the special function (small letters). For example, to measure a very small current (20 microamperes), one meter lead would be plugged into the COMMON jack, the other meter lead would be plugged into the 50A AMPS jack, and the FUNCTION SWITCH would be placed in the 50V/IA AMPS position. To measure currents above 500 milliamperes, the +10A and -10A jacks would be used on the meter with one exception. One meter lead and the FUNCTION SWITCH would be placed in the 10MA/AMPS position.

Multimeter Controls As described above, the FUNCTION SWITCH is used to select the function desired; the -DC, +DC, AC switch selects dc or ac (the rectifier), and changes the polarity of the dc functions. To measure resistance, this switch should be in the +DC position. The ZERO OHMS control is a potentiometer for adjusting the 0 reading on ohmmeter functions. Notice that this is a series ohmmeter. The RESET is a circuit breaker used to protect the meter movement (circuit breakers will be discussed in chapter 2 of this module). Not all multimeters have this protection but most have some sort of protection, such as a fuse. When the multimeter is not in use, it should have the leads disconnected and be switched to the highest voltage scale and AC. These switch positions are the ones most likely to prevent damage if the next person using the meter plugs in the meter leads and connects the meter leads to a circuit without checking the function switch and the dc/ac selector.

Multimeter Scales The numbers above the uppermost scale in figure 1-38 are used for resistance measurement. If the multimeter was set to the R x 1 function, the meter reading would be approximately 12.7 ohms.

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Figure 1-38. - A multimeter scale and reading.

The numbers below the uppermost scale are used with the uppermost scale for dc voltage and direct current, and the same numbers are used with the scale just below the numbers for ac voltage and alternating current. Notice the difference in the dc and ac scales. This is because the ac scale must indicate effective ac voltage and current. The third scale from the top and the numbers just below the scale are used for the 2.5-volt ac function only. The lowest scale (labeled DB) will not be discussed. The manufacturer's technical manual will explain the use of this scale. The table in figure 1-38 shows how the given needle position should be interpreted with various functions selected. As you can see, a multimeter is a very versatile measuring device and is much easier to use than several separate meters.

Parallax Error Most multimeters (and some other meters) have a mirror built into the scale. Figure 1-39 shows the arrangement of the scale and mirror. Figure 1-39. - A multimeter scale with mirror.

The purpose of the mirror on the scale of a meter is to aid in reducing PARALLAX ERROR. Figure 140 will help you understand the idea of parallax. Figure 1-40(A) shows a section of barbed wire fence as you would see it from one side of the fence. Figure 1-40(B) shows the fence as it would appear if you were to look down the fine of fence posts and were directly in line with the posts. You see only one post because the other posts, being in line,

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are hidden behind the post you can see. Figure 1-40(C) shows the way the fence would appear if you moved to the right of the line of posts. Now the fence posts appear to the right of the post closest to you. Figure 1-40(D) shows the line of fence posts as you would see them if you moved to the left of the front post. This apparent change in position of the fence posts is called PARALLAX. Parallax can be a problem when you are reading a meter. Since the pointer is slightly above the scale (to allow the pointer to move freely), you must look straight at the pointer to have a correct meter reading. In other words, you must be in line with the pointer and the scale. Figure 1-41 shows the effect of parallax error. Figure 1-41. - A parallax error in a meter reading. (A) shows a meter viewed correctly.

The meter reading is 5 units. Figure 1-41(B) shows the same meter as it would appear if you were to look at it from the right. The correct reading (5) appears to the right of the pointer because of parallax. The mirror on the scale of a meter, shown in figure 1-39, helps get rid of parallax error. If there is any parallax, you will be able to see the image of the pointer in the mirror. If you are looking at the meter correctly (no parallax error) you will not be able to see the image of the pointer in the mirror because the image will be directly behind the pointer. Figure 1-42 shows how a mirror added to the meter in figure 1-41 shows parallax error. Figure 1-42(A) is a meter with an indication of 5 units. There is no parallax error in this reading and no image of the pointer is seen in the mirror. Figure 1-42(B) shows the same meter as viewed from the right. The parallax error is shown and the image of the pointer is shown in the mirror.

Figure 1-42. - A parallax error on a meter with a mirrored scale.

Multimeter Safety Precautions As with other meters, the incorrect use of a multimeter could cause injury or damage. The following safety precautions are the MINIMUM for using a multimeter.












Deenergize and discharge the circuit completely before connecting or disconnecting a multimeter. Never apply power to the circuit while measuring resistance with a multimeter. Connect the multimeter in series with the circuit for current measurements, and in parallel for voltage measurements. Be certain the multimeter is switched to ac before attempting to measure ac circuits. Observe proper dc polarity when measuring dc. When you are finished with a multimeter, switch it to the OFF position, if available. If there is no OFF position, switch the multimeter to the highest ac voltage position. Always start with the highest voltage or current range. Select a final range that allows a reading near the middle of the scale. Adjust the "0 ohms" reading after changing resistance ranges and before making a resistance measurement. Be certain to read ac measurements on the ac scale of a multimeter. Observe the general safety precautions for electrical and electronic devices.

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Resistors Score: Instructor’s signature: Date: Remarks:

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Laboratory Experiment 1 Using the Ohmmeter 3. Before connecting the resistors as shown in the diagram below, measure first the values of each resistors and write down their values in the table below. Then connect the resistors as follows.

4.

Complete the table below. Resistor Number R1

Color- Code Value

Expected Value

Measured Value

R2 R3 R4 R5 R6 R7 R2 & R3

n.a.

Nodes A - B

n.a.

Nodes C - D

n.a.

Nodes A - D

n.a.

From arrow arrow

n.a.

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Variable Resistors Variable resistors can be wire-wound or the carbon type. Inside the metal case, the control has a circular disk that is carbon composition resistance element. It can be a thin coating pressed o a paper or a molded carbon disk. Joined to the two ends are the external solderinglug terminals 1 and 3. The middle terminal is connected to the variable arm that contacts the resistor element by a metal spring wiper. As the shaft of the control is turned, the variable arm moves the wiper to make contact at different points in the resistor element. The same idea applies to the slide control, except that the resistor element is straight instead of circular. When the contact moves closer to the end, the R decreases between this terminal and the variable arm. Between the two ends, however, the R is not variable but always has the maximum resistance of the control. Carbon controls are available with a total R from 1000 Ω to 5 MΩ, approximately. Their power rating is usually ½ to 2 W.

Rheostats and Potentiometers These are variable resistances, either carbon or wire-wound, used to vary the amount of current or voltage in a circuit. The controls can be used in either DC or AC applications. A rheostat is a variable R with two terminals connected in series with a load. The purpose is to vary the amount of current. A potentiometer, generally called a pot for short, has three terminals. The fixed maximum R across the two ends is connected across a voltage source. The variable arm is used to vary the voltage division between the center terminal and the ends. This function of a potentiometer is compared with a rheostat in the table below. Rheostat Two terminals In series with load and V source Varies the I

Potentiometer Three terminals Ends are connected across V source Taps off part of V

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There are two general ways in which variable resistors are used. One is the variable resistor which value is easily changed, like the volume adjustment of Radio. The other is semi-fixed resistor that is not meant to be adjusted by anyone but a technician. It is used to adjust the operating condition of the circuit by the technician. Semi-fixed resistors are used to compensate for the inaccuracies of the resistors, and to fine-tune a circuit. The rotation angle of the variable resistor is usually about 300 degrees. Some variable resistors must be turned many times to use the whole range of resistance they offer. This allows for very precise adjustments of their value. These are called "Potentiometers" or "Trimmer Potentiometers." In the photograph to the left, the variable resistor typically used for volume controls can be seen on the far right. Its value is very easy to adjust. The four resistors at the center of the photograph are the semi-fixed type. These ones are mounted on the printed circuit board. The two resistors on the left are the trimmer potentiometers.

This symbol is used to indicate a variable resistor in a circuit diagram. There are three ways in which a variable resistor's value can change according to the rotation angle of its axis. When type "A" rotates clockwise, at first, the resistance value changes slowly and then in the second half of its axis, it changes very quickly. The "A" type variable resistor is typically used for the volume control of a radio, for example. It is well suited to adjust a low sound subtly. It suits the characteristics of the ear. The ear hears low sound changes well, but isn't as sensitive to small changes in loud sounds. A larger change is needed as the volume is increased. These "A" type variable resistors are sometimes called "audio taper" potentiometers.

As for type "B", the rotation of the axis and the change of the resistance value are directly related. The rate of change is the same, or linear, throughout the sweep of the axis. This type suits a resistance value adjustment in a circuit, a balance circuit and so on. They are sometimes called "linear taper" potentiometers. Type "C" changes exactly the opposite way to type "A". In the early stages of the rotation of the axis, the resistance value changes rapidly, and in the second half, the change occurs more slowly. This type isn't too much used. It is a special use. As for the variable resistor, most are type "A" or type "B".

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Section 2.6 Rating of Resistors In addition to having the required ohms value, a resistor should have a wattage rating high enough to dissipate the power produced by the current flowing through the resistance, without becoming too hot. Carbon resistors in normal operation are quite warm, up to a maximum temperature of 85°C, which is close to 100°C boiling point of water. Carbon resistors should not be so hot, however that they “sweat” beads of liquid on the insulating case. Wire-wound resistors operate at very high temperatures, a typical value being 300°C for the maximum temperature. If a resistor becomes too hot because of excessive power dissipation, it can change appreciably in resistance value or burn open. The power rating is a physical property that depends on the resistor construction. Note the following:

1. A larger physical size indicates a higher power rating. 2. Higher-wattage resistors can operate at higher temperatures. 3. Wire-wound resistors are physically larger with higher wattage ratings than carbon resistors.

Section 2.7 Resistor Troubles The most common trouble in resistors is an open circuit. When the open resistor is a series component, there is no current in the entire path. Noisy controls. In applications such as volume and tone control, carbon controls are preferred because the smoother change in resistance results in less noise when the variable arm is rotated. With use, however, the resistance element becomes worn by the wiper contact, making the control noisy. When a volume or tone control makes a scratchy noise as the shaft is rotated, it indicates a worn out resistance element. Checking resistors with ohmmeter. Resistance measurements are made with an ohmmeter. The ohmmeter has its own voltage source so that it is always used without any external power applied to the resistance being measured. Separate the resistance from the circuit by disconnecting one lead of the resistor. Then connect the ohmmeter lead across the resistance to be measured An open resistor reads indefinitely high ohms. For some reason, an infinite ohm is often confused with zero ohms. Remember, though, that an infinite ohm means an open circuit. The current is zero, but the resistance is infinitely high. Furthermore it is practically impossible for a resistor to become short-circuited in itself. The resistor may be short-circuited by some other part of the circuit. However, he construction of resistors such that the trouble they develop is an open circuit with infinitely high ohms. The ohmmeter must have an ohms scale capable of reading the resistance value, or the resistor cannot be checked. In checking a 10 MΩ resistor, for instance, if the highest R the ohmmeter can read is 1 MΩ, it will indicate infinite resistance, even if the resistors’ normal value is 10 MΩ. An ohms scale of 100 MΩ or more should be used for checking such resistances. To check resistors of less than 10 Ω, a low ohms scale of about 100 Ω or less is necessary. Center scale should be 6 Ω or less. Otherwise, the ohmmeter can read a normally low resistance value as zero ohms.

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When checking resistance in a circuit, it is important to be sure there are no parallel paths across the resistor being measured. Otherwise, the measured resistance can be much lower than the actual resistor value.

Section 2.8 Resistor Connections The total resistance depends on the series or parallel connections. However, the combination has a power rating equal to the sum of the individual values. Weather resistors are in series or parallel. The reason is that the total physical size increases with each added resistor. Equal resistors are generally used in order to have equal distribution of I, V and P. In general, series resistors add for a higher RT. With parallel resistors, REQ is reduced.

Series Combinations of Resistors Two elements are said to be in series whenever the same current physically flows through both of the elements. The critical point is that the same current flows through both resistors when two are in series. The particular configuration does not matter. The only thing that matters is that exactly the same current flows through both resistors. Current flows into one element, through the element, out of the element into the other element, through the second element and out of the second element. No part of the current that flows through one resistor "escapes" and none is added. This figure shows several different ways that two resistors in series might appear as part of a larger circuit diagram.

You might wonder just how often you actually find resistors in series. The answer is that you find resistors in series all the time. An example of series resistors is in house wiring. The leads from the service entrance enter a distribution box, and then wires are strung throughout the house. The current flows out of the distribution box, through one of the wires, then perhaps through a light bulb, back through the other wire. We might model that situation with the circuit diagram shown below.

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In many electronic circuits series resistors are used to get a different voltage across one of the resistors. We'll look at those circuits, called voltage dividers, in a short while. Here's the circuit diagram for a voltage divider. Besides resistors in series, we can also have other elements in series - capacitors, inductors, diodes. These elements can be in series with other elements. For example, the simplest form of filter, for filtering low frequency noise out of a signal, can be built just by putting a resistor in series with a capacitor, and taking the output as the capacitor voltage. As we go along you'll have lots of opportunity to use and to expand what you learn about series combinations as you study resistors in series.

Let's look at the model again. We see that the wires are actually small resistors (small value of resistance, not necessarily physically small) in series with the light bulb, which is also a resistor. We have three resistors in series although two of the resistors are small. We know that the resistors are in series because all of the current that flows out of the distribution box through the first wire also flows through the light bulb and back through the second wire, thus meeting our condition for a series connection. Trace that out in the circuit diagram and the pictorial representation above. Let us consider the simplest case of a series resistor connection, the case of just two resistors in series. We can perform a thought experiment on these two resistors. Here is the circuit diagram for the situation we're interested in. Imagine that they are embedded in an opaque piece of plastic, so that we only have access to the two nodes at the ends of the series connection, and the middle node is inaccessible. If we measured the resistance of the combination, what would we find? To answer that question we need to define voltage and current variables for the resistors. If we take advantage of the fact that the current through them is the same (Apply KCL at the interior node if you are unconvinced!) then we have the situation below.

Note that we have defined a voltage across each resistor (Va and Vb) and current that flows through both resistors (Is) and a voltage variable, Vs, for the voltage that appears across the series combination.

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Let's list what we know: The current through the two resistors is the same. The voltage across the series combination is given by: Vs= Va + Vb The voltages across the two resistors are given by Ohm's Law: Va = Is Ra We can combine all of these relations, and when we do that we find the following. Vs= Va + Vb Vs= Is Ra + Is Rb Vs= Is (Ra + Rb) Vs= Is Rseries Here, we take Rseries to be the series equivalent of the two resistors in series, and the expression for Rseries is: Rseries = Ra + Rb What do we mean by series equivalent? Here are some points to observe. If current and voltage are proportional, then the device is a resistor. We have shown that Vs= Is X Rseries, so that voltage is proportional to current, and the constant of proportionality is a resistance. We will call that the equivalent series resistance. There is also a mental picture to use when considering equivalent series resistance. Imagine that you have two globs of black plastic. Each of the globs of black plasic has two wires coming out. Inside these two black plastic globs you have the following. In the first glob you have two resistors in series. Only the leads of the series combination are available for measurement externally. You have no way to penetrate the box and measure things at the interior node. In the second box you have a single resistor that is equal to the series equivalent. Only the leads of this resistor are available for measurement externally. Then, if you measured the resistance using the two available leads in the two different cases you would not be able to tell which black plastic glob had the single resistor and which one had the series combination. Here are two resistors. At the top are two 2000W resistors. At the bottom is single 4000W resistors. (Note, these are not exactly standard sizes so it took a lot of hunting to find a supply store that sold them!). You can click the green button to grow blobs around them.

After you have grown the blobs around the resistors there is no electrical measurement you can make that will allow you to tell which one has two resistors and which one has one resistor. They are electrically indistinguishable! (Or, in other words, they are equivalent!)

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Resistors Score: Instructor’s signature: Date: Remarks:

_______

Exercise 4 Resistors in Series Here is a circuit you may have seen before. Answer the questions below for this circuit.

1.Are elements #3 and #4 in series? (Yes or No) 2.Are elements #1 and #2 in series? (Yes or No) 3.Is the battery in series with any element?

° ° ° °

Element 1 Element 2 Element 3 Element 4

4.Is the series equivalent resistor larger than either resistor, or is it smaller? (Larger or Smaller) 5. What is the series equivalent of two 1000 W resistors in series? 6. What is the series equivalent of a 1000 W resistor and a 2700 W resistor in series? 7. What is the series equivalent of three 1000 W resistors in series? You may want to do this problem in two steps. 8. Imagine that you have a 100 W resistor. You want to add a resistor in series with this 100 W resistor in order to limit the current to 0.5 amps when 110 volts is placed across the two resistors in series. How much resistance should you use?

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Parallel Resistors The other common connection is two elements in parallel. Two resistors or any two devices are said to be in parallel when the same voltage physically appears across the two resistors. Schematically, the situation is as shown below.

Note that we have defined the voltage across both resistor (Vp) and the current that flows through each resistor (Ia and Ib) and a voltage variable, Vp, for the voltage that appears across the parallel combination. Let's list what we know. The voltage across the two resistors is the same. The current through the parallel combination is given by: Ip= Ia + Ib The currents through the two resistors are given by Ohm's Law: Ia = Vp /Ra Ib = Vp /Rb We can combine all of these relations, and when we do that we find the following. Ip= Ia + Ib Ip= Vp /Ra + Vp /Rb Ip= Vp[ 1/Ra + 1/Rb] Ip= Vp/Rparallel Here, we take Rparallel to be the parallel equivalent of the two resistors in parallel, and the expression for Rparallel is: 1/Rparallel = 1/Ra + 1/Rb There may be times when it is better to rearrange the expression for Rparallel. The expression can be rearranged to get: Rparallel = (Ra*Rb)/(Ra + Rb) Either of these expressions could be used to compute a parallel equivalent resistance. The first has a certain symmetry with the expression for a series equivalent resistance.

Parallel Resistors - A Point to Remember It is important to note that the equivalent resistance of two resistors in parallel is always smaller than either of the two resistors.

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Score: Instructor’s signature: Date: Remarks:

_______

Exercise 5 Resistors in Parallel 1. Is the parallel equivalent resistor larger than either resistor, or is it smaller? 2. What is the parallel equivalent of two 1000 W resistors in parallel? 3. What is the parallel equivalent of a 1000 W resistor and a 1500 W resistor in parallel? 4. What is the equivalent of three 1000 W resistors in parallel? You may want to do this problem in two steps. 5.What is the equivalent resistance of this resistance combination?

6. What is the equivalent resistance of this resistance combination?

7. What is the equivalent resistance of this resistance combination? Here all three resistors are 33 kW. Remember to input your answer in ohms.

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Combinations of Resistors - Series/Parallel Circuits Resistors do not occur in isolation. They are almost always part of a larger circuit, and frequently that larger circuit contains many resistors. It is often the case that resistors occur in combinations that repeat. Here's a circuit with resistors that has them connected in a different way. For a short while we're going to work on the question of how to analyze this circuit. For a start we're going to assume that this is a resistor. It has two leads at the left (marked here with red dots) and we'll assume that we want to find the equivalent resistance you would have at those leads.

We will use the following numerical values for the resistors in this example, and we will work through using these values. Ra = 1500 W Rb = 3000 W Rc = 2000 W Rd = 1000 W Vs = 12 v We need to figure out where we can start. We can start by trying to find any of the combinations we've learned about. So let's think about whether there are any series or parallel combinations and if there are let's see if we can identify them. Then we can apply what we know about series and parallel combinations. There's no guarantee that approach will work, but it is worth a try. Let's look at two resistors at a time. Now, we should be able to replace the two resistors in series with their series equivalent. If we do that, there's a node in the middle with a voltage, and we'll lose information about that voltage. Right now, we're not interested in that voltage, and we'll willing to lose that information. Let's just replace the two resistors with their series equivalent. Click the red button to make that replacement. Depressing the button will remove the two resistors in series, and releasing the button will insert the replacement. Now you should have the circuit with the two resistors in series replaced by their series equivalent. Now, we can see that there is another replacement we can make. What's that replacement?

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Ok, you see how it goes. Let's take a numerical example using the values mentioned above. Ra = 1500 W Rb = 3000 W Rc = 2000 W Rd = 1000 W Vs = 12 v Here is the circuit.

1. What is the equivalent resistance of the two resistors in series - 1000W and 2000W? 2. Next you should have two resistors in parallel. What is the parallel equivalent? 3. Now you should have two resistors in series attached to the source. What is the value of the series equivalent? 4. With a 12v source - as shown in the figure - what is the current that is drawn from the source? Give your answer in amperes here. Give your answer in milliamperes here, if that's what you want.

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Score: Instructor’s signature: Date: Remarks:

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Exercise 5 Resistors in Parallel Please answer what is asked. 1.) If a current of 3 A is divided by the following circuit, the current flowing through the 4 Ohm resistor is a. b. c. d.

3 2 1 1.5

2.) The diagram at the right shows part of a circuit into which a current I is flowing. Which ammeter shows the highest reading? a. b. c. d.

A1 A2 A3 All three ammeters give the same reading

3.) The diagram to the right represents a part of a circuit containing an ohmic resistor, a voltmeter and an ammeter. If the reading on the ammeter A increases the reading on voltmeter V … a. b. c. d.

increases in the same ratio increases but not in the same ratio remains unchanged decreases in the same ratio

4.) A battery is connected to two identical light bulbs in parallel as well as another identical bulb in series. An ammeter and a voltmeter are also connected as shown in the circuit diagram below.

a b c d

Voltmeter reading increases increases increases decreases

Ammeter reading increases decreases unchanged decreases

5.) A learner connects a circuit as shown in the diagram to the right. He/she uses a source of electricity with an electromotive force (emf) of 12 V. Which one of the following best gives the ammeter and voltmeter readings which the learner is most likely to get with this circuit?

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a b c d

Ammeter reading reads zero reads zero very large reading very large reading

Voltmeter reading reads zero reads 12 V reads zero reads 12 V

6.) Three identical resistors of 4 Ω are connected to give a combined resistance of 6 Ω. Which of the following circuit diagrams illustrates how this was done?

a. b. c. d.

I II III IV

7.) In the circuit to the right B1, B2 and B3 are identical light bulbs. The internal resistance of the battery can be ignored. Which statement is true regarding the relative brightness of the bulbs?

a. b.

The three bulbs glow with the same brightness. B2 and B3 glow with the same brightness but brighter than B1.

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Resistors c. d.

B2 and B3 glow with the same brightness but less brightly than B1. B1 glows brighter than B2 while B2 in turn glows brighter than B3.

8.) Two identical light bulbs, X and Y, are connected in series as shown in the sketch to the right. How will the brightness of the bulbs change if switch S is closed?

a. b. c. d.

X brighter dimmer brighter not lit up

Y brighter dimmer not lit up brighter

9.) A student connects three identical resistors as shown in the sketch to the right. The potential difference across the battery is 12 Volt. What are the readings on V1 and V2 respectively?

a. b. c. d.

V1 4 6 8 9

V2 8 6 4 3

10.) A 9 V battery is composed of six 1,5 V cells, which are connected in series. Each cell has an internal resistance of 0,2 Ω. What is the highest current that can be obtained from such a battery? a. b. c. d.

7.5A 1.5A 1.2A 0.3A

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Exercises on resistor connections. Find total resistance RT given the following circuits 1. Series connection.

a. Solution: RT = R 1 + R2 + R3 = 1KΩ + 5KΩ + 10KΩ = 16KΩ

b. Solution: RT = R 1 + R2 + R3 = 1MΩ + 5KΩ + 100KΩ = 1MΩ + .005MΩ + .1MΩ = 1.101MΩ or RT = R 1 + R2 + R3 = 1MΩ + 5KΩ + 100KΩ = 1000KΩ + 5KΩ + 100KΩ = 1101KΩ

2. Parallel connection.

a.

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b.

c. 3. Simple Series-Parallel

a.

b.

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OHM'S LAW

3

CHAPTER

What is Ohm’s Law? Law?

A

simple relationship exists between voltage, current, and resistance in electrical circuits. Understanding this relationship is important for fast, accurate electrical problem diagnosis and repair. Ohm's Law says: The current in a circuit is directly proportional to the applied voltage and inversely proportional to the amount of resistance. This means that if the voltage goes up, the current flow will go up, and vice versa. Also, as the resistance goes up, the current goes down, and vice versa. Ohm's Law can be put to good use in electrical troubleshooting. But calculating precise values for voltage, current, and resistance is not always practical ... nor, really needed. A more practical, less time-consuming use of Ohm's Law would be to simply apply the concepts involved:

+

RESISTANCE is not affected by either voltage or current. It is either too low, okay, or too high. If resistance is too low, current will be high at any voltage. If resistance is too high, current will be low if voltage is okay. NOTE: When the voltage stays the same, such as in an Automotive Circuit... current goes up as resistance goes down, and current goes down as resistance goes up. Bypassed devices reduce resistance, causing high current. Loose connections increase resistance, causing low current.

+

+

3-1 Ohm’s Law Formula 3-2 Applications of Ohm’s Law

Current, Voltage and Resistance Calculations in: 3-3 Series Circuits 3-4 Parallel Circuits

SOURCE VOLTAGE is not affected by either current or resistance. It is either too low, normal, or too high. If it is too low, current will be low. If it is normal, current will be high if resistance is low, or current will be low if resistance is high. If voltage is too high, current will be high. CURRENT is affected by either voltage or resistance. If the voltage is high or the resistance is low, current will be high. If the voltage is low or the resistance is high, current will be low.

+

3-5 Series Parallel Circuits 3-6 Voltmeters 3-7 Ammeters 3-8 Problem Sets on Ohm’s Law

+

+

+

+

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Ohm’s Law

Section 3.1 Ohm’s Law Formula When voltage is applied to an electrical circuit, current flows in the circuit. The following special relationship exists among the voltage, current and resistance within the circuit: the size of the current that flows in a circuit varies in proportion to the voltage which is applied to the circuit, and in inverse proportion to the resistance through which it must pass. This relationship is called Ohm's law, and can be expressed as follows: E=IR Voltage = Current x Resistance E Voltage applied to the circuit, in volts (V) I Current flowing in the circuit, in amperes (A) R Resistance in the circuit, in ohms In practical terms "V = I x R" which means "Voltage = Current x Resistance". 1 volt will push one amp through 1 ohm of resistance. NOTE: E = IR, V=AR, or V=IR are all variations of the same formula. How you learned Ohm's law will determine which one you will use. Personal preference is the only difference; anyone will get you the correct answer.

OHM'S LAW SYMBOL SHORTCUT Mathematical formulas can be difficult for many who don't use them regularly. Most people can remember a picture easier than a mathematical formula. By using the Ohms law symbol below, anyone can remember the correct formula to use. By knowing any two values you can figure out the third. Simply put your finger over the portion of the symbol you are trying to figure out and you have your formula.

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Ohm’s Law

Section 3.2 Application of Ohm’s Law As an application of Ohm's law, any voltage V, current I or resistance R in an electrical circuit can be determined without actually measuring it if the two others values are known. This law can be used to determine the amount of current I flowing in the circuit when voltage V is applied to resistance R. As stated previously, Ohm's law is:

Current = Voltage / Resistance. In the following circuit, assume that resistance R is 2 and voltage V that is applied to it is 12 V. Then, current I flowing in the circuit can be determined as follows:

This law can also be used to determine the voltage V that is needed to permit current I to pass through resistance R: V = I x R (Voltage= Current x Resistance). In the following circuit, assume that resistance R is 4 ohms. The voltage V that is necessary to permit a current I of 3 A to pass through the resistance can be determined as follows:

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Still another application of the law can be used to determine the resistance R when the voltage V which is applied to the circuit and current I flowing in the circuit are already known:

In the following circuit, assume that a voltage V of 12 V is applied to the circuit and current I of 4 A flows in it. Then, the resistance value R of the resistance or load can be determined as follows:

TYPES OF CIRCUITS Individual electrical circuits normally combine one or more resistance or load devices. The design of the automotive electrical circuit will determine which type of circuit is used. There are three basic types of circuits:




Series Circuit Parallel Circuit Series-Parallel Circuit

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Ohm’s Law

Section 3.3 Series Circuits A series circuit is the simplest circuit. The conductors, control and protection devices, loads, and power source are connected with only one path to ground for current flow. The resistance of each device can be different. The same amount of current will flow through each. The voltage across each will be different. If the path is broken, no current flows and no part of the circuit works. Christmas tree lights are a good example; when one light goes out the entire string stops working.

A Series Circuit has only one path to ground, so electrons must go through each component to get back to ground. All loads are placed in series. Therefore: 1. An open in the circuit will disable the entire circuit. 2. The voltage divides (shared) between the loads. 3. The current flow is the same throughout the circuit. 4. The resistance of each load can be different.

SERIES CIRCUIT CALCULATIONS If, for example, two or more lamps (resistances R1 and R2, etc.) are connected in a circuit as follows, there is only one route that the current can take. This type of connection is called a series connection. The value of current I is always the same at any point in a series circuit.

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Ohm’s Law

The combined resistance RO in this circuit is equal to the sum of individual resistance R1 and R2. In other words: The total resistance(RO) is equal to the sum of all resistances (R1 + R2 + R3 + .......)

Therefore, the strength of current (I) flowing in the circuit can be found as follows:

Resistance R0 (a combination of resistances R1 and R2, which are connected in series in the circuit as illustrated) and current I flowing in this circuit can be determined as follows:

VOLTAGE DROP A voltage drop is the amount of voltage or electrical pressure that is used or given up as electrons pass through a resistance (load). All voltage will be used up in the circuit. The sum of the voltage drops will equal source voltage. A voltage drop measurement is done by measuring the voltage

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before entering the load and the voltage as it leaves the load. The difference between these two voltage readings is the voltage drop.

VOLTAGE DROP TOTAL When more than one load exists in a circuit, the voltage divides and will be shared among the loads. The sum of the voltage drops equal source voltage. The higher the resistance the higher the voltage drop. Depending on the resistance, each load will have a different voltage drop. 0V + 5V + 7V + 0V = 12V

VOLTAGE DROP CALCULATION When current flows in a circuit, the presence of a resistance in that circuit will cause the voltage to fall or drop as it passes through the resistance. The resultant difference in the voltage on each side of the resistance is called a voltage drop. When current (I) flows in the following circuit, voltage drops V1 and V2 across resistances R1 and R2 can be determined as follows from Ohm's law. (The value of current I is the same for both R1 and R2 since they are connected in series.)

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The sum of the voltage drops across all resistances is equal to the voltage of the power source (VT):

The voltage drop across resistances R1 and R2 in the following circuit can be determined as follows:

Section 3.4 PARALLEL CIRCUIT A parallel circuit has more than one path for current flow. The same voltage is applied across each branch. If the load resistance in each branch is the same, the current in each branch will be the same. If the load resistance in each branch is different, the current in each branch will be different. If one branch is broken, current will continue flowing to the other branches.

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A Parallel Circuit has multiple paths or branches to ground. Therefore: 1. In the event of an open in the circuit in one of the branches, current will continue to flow through the remaining. 2. Each branch receives source voltage. 3. Current flow through each branch can be different. 4. The resistance of each branch can be different.

In parallel connection, two or more resistances (R1, R2, etc.) are connected in a circuit as follows, with one end of each resistance connected to the high (positive) side of the circuit, and one end connected to the low (negative) side. Full battery voltage is applied to all resistances within a circuit having a parallel connection.

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Resistance R0 (a combination of resistances R1 and R2) in a parallel connection can be determined as follows:

From the above, the total current I flowing in this circuit can be determined from Ohm's law as follows:

The total current I is also equal to the sum of currents I1 and I2 flowing through individual resistances R1 and R2

Since battery voltage V is applied equally to all resistances, the strength of currents I1 and I2 can be determined from Ohm's law as follows:

Resistance RO (a combination of resistances R1 and R2, which are connected in parallel in the circuit as shown below), the total current I flowing in the circuit, and currents I1 and I2 flowing through resistances R1 and R2, can be determined respectively as follows:

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Section 3.5 Series - Parallel Circuits A series-parallel circuit has some components in series and others in parallel. The power source and control or protection devices are usually in series; the loads are usually in parallel. The same current flows in the series portion, different currents in the parallel portion. The same voltage is applied to parallel devices, different voltages to series devices. If the series portion is broken, current stops flowing in the entire circuit. If a parallel branch is broken, current continues flowing in the series portion and the remaining branches.

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A resistance and lamps may be connected in a circuit as illustrated below. This type of connecting method is called series-parallel connection, and is a combination of series and parallel connections. The interior dash board lights are a good example. By adjusting the rheostat, you can increase or decrease the brilliance of the lights.

The combined resistance R02 in this series-parallel connection can be determined in the following order: a. Determine combined resistance R01, which is a combination of resistances R2 and R3 connected in parallel. b. Then, determine resistance R02, which is a combination of resistance R1 and combined resistance R01 connected in series.

Total current I flowing in the circuit can be determined from Ohm's law as follows:

The voltage applied to R2 and R3 can be found by the following formula:

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Currents I1, I2 and I flowing through resistances R1, R2 and R3 in the series-parallel connection, as shown below, can be determined as follows:

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Section 3.6 Voltmeters Voltmeters are perhaps the commonest or most widely used instruments for measuring voltage. While there are still many analog voltmeters, most voltmeters today have digital displays, so that you get an LCD display with several digits of resolution. If an instrument has other capabilities (for example being able to measure current and/or resistance) then it is a multimeter. If it is a digital multimeter it is often referred to as a "DMM". There are several things you will need to worry about when using a voltmeter or DMM.  Voltmeters can often measure either DC or AC voltages. o When measuring AC voltages, a voltmeter will give you values for the RMS value not the peak value of the sine wave. And, if the signal isn't sinusoidal, you may have trouble getting the measured value(s) you want.  IVoltmeters have range settings. Some common range settings are 0-0.3v, 0-3v, 0-30v, etc. On lower ranges you will get more accuracy. On digital voltmeters, for example these ranges are really: o 0-3.0000 v o 0-30.000 v o As you go to higher ranges you will get as many significant digits in the measured value. o If you want more significant digits in a meter the cost will go up, and each additional digit is more expensive.  Voltmeters measure voltages that are constant or at least do not change rapidly. A typical digital voltmeter will measure voltage and display the results, then hold the results long enough for you to see the number.

How to Use a Voltmeter As its name implies, a voltmeter measures voltage. Some models also measure ohms and amperage; these are called multimeters. Meters are available in analog and digital styles. Steps: 1. Plug the probes into the meter. Red goes to the positive (+) and black to the negative (-). 2. Turn the selector dial or switch to the type of measurement you want. To measure direct current - a battery, for example - use DCV. To measure alternating current, such as a wall outlet, use ACV. 3. Choose the range setting. The dial may have options from 5 to 1000 on the DCV side and 10 to 1000 on the ACV side. The setting should be the top end of the voltage you are reading. Not all voltmeters have this setting. 4. Turn the meter on. 5. Hold the probes by the insulated handles and touch the red probe to the positive side of a DC circuit or either side of an AC circuit. Touch the other side with the black probe. 6. Read the digital display or analog dial. Tips:  Attach alligator clips to the probes before you turn on the meter. These are useful for hands-free operation and keep fingers out of dangerous areas.  A battery is good if the reading is within 20 percent of the rating on the battery or appliance. In other words, a reading of 7.2 or higher means a 9-volt battery is acceptable.

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Warnings  Don't use a meter with a cracked housing or probes with bare wires showing.  Never use the ohm setting on a multimeter on live voltage. You will damage the meter.  Use a voltage probe or test light if you just want to check if a circuit is live. In this section we'll look at how you use a voltmeter. Here's a representation of a voltmeter.

For our introduction to the voltmeter, we need to be aware of three items on the voltmeter.  The display. This is where the result of the measurement is displayed. You meter might be either analog or digital. If it's analog you need to read a reading off a scale. If it's digital, it will usually have an LED or LCD display panel where you can see what the voltage measurement is.  The positive input terminal, and it's almost always red.  The negative input terminal, and it's almost always black. Next, you need to be aware of what the voltmeter measures. Here it is in a nutshell.  A voltmeter measures the voltage difference between the positive input terminal of the voltmeter and the negative input terminal. That's it. That's what it measures. Nothing more, nothing less - just that voltage difference. That means you can measure voltage differences in a circuit by connecting the positive input terminal and the negative input terminal to locations in a circuit. We'll show a voltmeter connected to the circuit diagram.

This figure shows where you would place the leads if you wanted to measure the voltage across element #4.  Notice that the voltmeter measures the voltage across element #4, +V4.  Notice the polarity definitions for V4, and notice how the red terminal is connected to the "+" end of element #4. If you reversed the leads, by connecting the red lead to the "-" terminal on element #4 and the black lead to the "+" end of element #4, you would be measuring -V4.

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There are some important things to note about taking a voltage measurement. The most important point is this.  Voltage is an across variable. o That means that when you measure voltage you measure a difference between two points in space. o There are other variables of this type. For example, if you use a pressure sensor, you measure the pressure difference between two points, much like you measure a voltage difference. o There are other kinds of variables. For example, there are numerous variables that are flow variables. Current and fluid flow variables are example of flow variables. They usually have units of something per second. (Current is couloumbs/sec, while water flow might be in gallons/sec. - for example.)  When you measure a voltage the two terminals of the voltmeter (in the figure, the red terminal and the black terminal) are connected to the two points where the voltage appears that you want to measure. One terminal - say it is the red terminal - will then be at the same voltage as one of the points, and the other terminal - the black terminal - will be at the same voltage as the other point. The meter then responds to the difference between these two voltages. Let's look at an example. Here are three points. These points could be anything and may be located in a circuit, for example. Wherever they are, there is a voltage difference between any two of these points, and you could theoretically measure the voltage difference between any two of these points. There are actually three different choices for voltage differences. (Red/Green, Green/Blue, Blue/Red) Then, for each difference, there are two different ways you can connect the voltmeter switching red and black leads.

Let's check to see if you understand that. Here are the same three points, but now they are points within a circuit. In this particular circuit, the battery will produce a current that flows through the two resistors in series.

This circuit has a schematic representation shown below.

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And, here is the same circuit with the measurement points (see above) marked.

Now, if you want to measure the voltage across Rb, here is a connection that will do it.

And, the physical circuit would look like this one.

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Now, the reason for taking this so slowly is that students often have trouble moving between circuit diagrams and the physical circuit and understanding how to translate between them. What looks clear on a circuit diagram is not always as clear in the physical situation

Section 3.7 Ammeters An ammeter is a device that measures current. Since all meter movements have resistance, a resistor will be used to represent a meter in the following explanations. Direct current circuits will be used for simplicity of explanation.

Ammeter Connected in Series In figure 1-19(A), R1 and R2 are in series. The total circuit resistance is R2 + R2 and total circuit current flows through both resistors. In figure 1-19(B), R1 and R2 are in parallel. The total circuit resistance is

and total circuit current does not flow through either resistor.

Figure 1-19.—A series and a parallel circuit.

If R1 represents an ammeter, the only way in which total circuit current will flow through the meter (and thus be measured) is to have the meter (R1) in series with the circuit load (R2), as shown in figure 1-19(A). In complex electrical circuits, you are not always concerned with total circuit current. You may be interested in the current through a particular component or group of components. In any case, an ammeter is always connected in series with the circuit you wish to test. Figure 1-20 shows various circuit arrangements with the ammeter(s) properly connected for measuring current in various portions of the circuit.

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Figure 1-20.—Proper ammeter connections.

Connecting an ammeter in parallel would give you not only an incorrect measurement, it would also damage the ammeter, because too much current would pass through the meter.

Effect on the Circuit being Measured The meter affects the circuit resistance and the circuit current. If R is removed from the circuit in figure 1-19(A), the total circuit resistance is R . Circuit current 1

2

with the meter (R ) in the circuit, circuit resistance is R + R and circuit current 1

1

2

The smaller the resistance of the meter (R ), the less it will affect the circuit being measured. (R represents the total resistance of the meter; not just the resistance of the meter movement.) 1

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Ammeter Sensitivity Ammeter sensitivity is the amount of current necessary to cause full scale deflection (maximum reading) of the ammeter. The smaller the amount of current, the more "sensitive" the ammeter. For example, an ammeter with a maximum current reading of 1 milliampere would have a sensitivity of 1 milliampere, and be more sensitive than an ammeter with a maximum reading of 1 ampere and a sensitivity of 1 ampere. Sensitivity can be given for a meter movement, but the term "ammeter sensitivity" usually refers to the entire ammeter and not just the meter movement. An ammeter consists of more than just the meter movement.

Ammeter Ranges If you have a meter movement with a sensitivity of 1 milliampere, you can connect it in series with a circuit and measure currents up to 1 milliampere. But what do you do to measure currents over 1 milliampere? To answer this question, look at figure 1-21. In figure 1-21(A), 10 volts are applied to two resistors in parallel. R1 is a 10-ohm resistor and R2 is a 1.11-ohm resistor. Since voltage in parallel branches is equal-

Figure 1-21.—Current in a parallel circuit.

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In figure 1-21(B), the voltage is increased to 100 volts. Now,

In figure 1-21(C), the voltage is reduced from 100 volts to 50 volts. In this case,

Notice that the relationship (ratio) of IR1 and IR2 remains the same. IR2 is nine times greater than IR1 and IR1 has one-tenth of the total current. If R1 is replaced by a meter movement that has 10 ohms of resistance and a sensitivity of 10 amperes, the reading of the meter will represent one-tenth of the current in the circuit and R 2 will carry nine-tenths of the current. R2 is a SHUNT resistor because it diverts, or shunts, a portion of the current from the meter movement (R1). By this method, a 10-ampere meter movement will measure current up to 100 amperes. By adding a second scale to the face of the meter, the current can be read directly. By adding several shunt resistors in the meter case, with a switch to select the desired resistor, the ammeter will be capable of measuring several different maximum current readings or ranges. Most meter movements in use today have sensitivities of from 5 microamperes to 1 milliampere. Figure 1-22 shows the circuit of meter switched to higher ranges, the shunt an ammeter that uses a meter movement with a sensitivity of 100 microamperes and shunt resistors. This ammeter has five ranges (100 microamperes; 1, 10, and 100 milliamperes; 1 ampere) selected by a switch.

1-21 Figure 1-22.—An ammeter with internal shunt resistors.

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By adding several shunt resistors in the meter case, with a switch to select the desired resistor, the ammeter will be capable of measuring several different maximum current readings or ranges. Most meter movements in use today have sensitivities of from 5 microamperes to 1 milliampere. Figure 1-22 shows the circuit of meter switched to higher ranges, the shunt an ammeter that uses a meter movement with a sensitivity of 100 microamperes and shunt resistors. This ammeter has five ranges (100 microamperes; 1, 10, and 100 milliamperes; 1 ampere) selected by a switch. With the switch in the 100 microampere position, all the current being measured will go through the meter movement. None of the current will go through any of the shunt resistors. If the ammeter is switched to the 1 milliampere position, the current being measured will have parallel paths of the meter movement and all the shunt resistors (R1 , R2, R3, and R4). Now, only a portion of the current will go through the meter movement and the rest of the current will go through the shunt resistors. When the meter is switched to the 10-milliampere position (as shown in fig. 1-22), only resistors R1, R2, and R3 shunt the meter. Since the resistance of the shunting resistance is less than with R4 in the circuit (as was the case in the 1-milliampere position), more current will go through the shunt resistors and less current will go through the meter movement. As the resistance decreases and more current goes through the shunt resistors. As long as the current to be measured does not exceed the range selected, the meter movement will never have more than 100 microamperes of current through it. Shunt resistors are made with close tolerances. That means if a shunt resistor is selected with a resistance of .01 ohms (as R1 in fig. 1-22), the actual resistance of that shunt resistor will not vary from that value by more than 1 percent. Since a shunt resistor is used to protect a meter movement and to allow accurate measurement, it is important that the resistance of the shunt resistor is known very accurately. Figure 1-22 represents an ammeter with internal shunts. The shunt resistors are inside the meter case and selected by a switch. For limited current ranges (below 50 amperes), internal shunts are most often employed

Range Selection Part of the correct use of an ammeter is the proper use of the range selection switch. If the current to be measured is larger than the scale of the meter selected, the meter movement will have excessive current and will be damaged. Therefore, it is important to always start with the highest range when you use an ammeter. If the current can be measured on several ranges, use the range that results in a reading near the middle of the scale. Figure 1-24 illustrates these points.

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Figure 1-24.—Reading an ammeter at various ranges.

Figure 1-24(A) shows the initial reading of a circuit. The highest range (250 milliamperes) has been selected and the meter indication is very small. It would be difficult to properly interpret this reading with any degree of accuracy. Figure 1-24(B) shows the second reading, with the next largest range (50 milliamperes). The meter deflection is a little greater. It is possible to interpret this reading as 5 milliamperes. Since this approximation of the current is less than the next range, the meter is switched as shown in figure 1-24(C). The range of the meter is now 10 milliamperes and it is possible to read the meter indication of 5 milliamperes with the greatest degree of accuracy. Since the current indicated is equal to (or greater than) the next range of the ammeter (5 milliamperes), the meter should NOT be switched to the next range.

Ammeter Safety Precautions When you use an ammeter, certain precautions must be observed to prevent injury to yourself or others and to prevent damage to the ammeter or the equipment on which you are working. The following list contains the MINIMUM precautions to observe when using an ammeter. Ammeters must always be connected in series with the circuit under test. Always start with the highest range of an ammeter. Deenergize and discharge the circuit completely before you connect or disconnect the ammeter. In dc ammeters, observe the proper circuit polarity to prevent the meter from being damaged. Never use a dc ammeter to measure ac. Observe the general safety precautions of electrical and electronic devices.

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Exercise 3. Problem Sets on Ohm’s Law 1. Each resistor is 39 ohms. What is the total resistance between point "A" and point "B"?

2. How much current does the meter read?

3. What is the resistance of R3?

4. How much current does the meter read?

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5..

6. What is the total current in this circuit?

7. What is the voltage to ground at point "B"?

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8. What is the voltage B to D?

9. What is the resistance: A to B? A to C? B to D? C to E? B to E?

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10. What is the voltage "E" to "C"?

11. What is the voltage "A" to "B".

12. What is the total current?

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13. How much current does the meter read?

14. What is the DC voltage at point "A" with respect to ground?

15. How much current does the meter read?

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16. How much current should the meter read?

17. How much current does the meter read?

18. What voltage would you expect to measure at A with respect to B?

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Solutions to Exercise Number 3

1. One end of each resistor connects to point "A" The other end of each resistor connects to point "B"

Total resistance is 13 ohms. 2. When you redraw the diagram in a different form you can see that it is a balanced bridge. Meter current is 0.

3. R3 current is 4 times R2 current. Resistance of R3 must be 1/4 of R2. Or you could use Ohm's Law to calculate R2 voltage.

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4.

5. HINT! Redrawing in a different form helps.

6. When you redraw the circuit in a more conventional form the parallel paths are easier to see.

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7.

8.

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9. A to B A to C Both 5333 ohms B to D 3333 ohms C to E B to E Both 7333 ohms 10.

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11.

12.

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13. HINT! Sometimes when you redraw the circuit it is easier to see the total resistance.

14.

15. Voltage shown are measured with respect to ground.

What is the likely cause of this problem?

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Probably R3 is shorted out. Next you should use an ohmmeter to confirm what the voltage measurements indicate.

16.

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17.

18.

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CHAPTER

Section 4.1 Transformer

+

+

+

4 +

4-1 Transformer

Basic Concepts

4-2 Switch and Fuse

A transformer is a device that allows an AC voltage, usually a sine wave, to pass from the input to the output through magnetism. The voltage, compared to the input, has three different possibilities: 1. The input is higher than the output – step-down transformer. 2. The input is lower than the output – step-up transformer. 3. The input is equal or the same with the output. Because the transformer can be used to change the level of the voltage, it has a very important role in the fields of electronics and electricity. For example, the power company uses a transformer to change the very high voltage used for long distance transmission, to the very low voltage used in the house. Nearly all electronic devices have a cord to plug into the AC line. When AC line voltage enters the device, it enters through a transformer to lower the voltage before it goes to the power supply, where it is then changed to DC voltage.

Construction A transformer is constructed in such a way that magnetism is used to induce voltage in a second wire. The input of the transformer is called the primary winding and the output is called the secondary winding. Both the primary and secondary winding are each a coil of wire (referred to as winding). When the current flows to the wire, magnetism is developed and when magnetic lines of force cross a coil, voltage is developed.

4-3 Semiconductor Diodes 4-4 Meter testing of a diode 4-5 Rectifier Circuits 4-6 Capacitors 4-7 Types of Capacitors 4-8 Transistors 4-9 Meter testing of a transistor

+

+

+

+

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Pictorial Symbol

Schematic Symbol

Transformer Core The purpose of the transformer core is to concentrate the magnetic field. Thus, it allows more complete coupling of the magnetic lines of force (flux) between the primary winding and the secondary winding. The core of the transformer is made of soft iron. Soft iron is used because it is an excellent conductor of magnetic flux, and can magnetize and demagnetize very quickly. In the schematic symbol, the two parallel lines between the windings represent the core.

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Section 4.2 Switch and Fuse Switches are commonly used to open or close a circuit. Closed is the ON or make position; open is the OFF or break position. The switch is connected in series with the voltage source and its load. In the ON position, the closed switch has very little resistance. Then maximum current can flow in the load, with practically zero voltage drop on the switch. Open, the switch has infinite resistance, and no current flows in the circuit. A toggle switch is a generic class of electric switch that uses a mechanical lever, handle or rocking mechanism to actuate it. Toggle switches are available in many different styles and sizes, and are used in countless applications. Many are designed to provide, e.g., the simultaneous actuation of multiple sets of electrical contacts, or the control of large amounts of electric current or mains voltages. The word "toggle" is a reference to a kind of mechanism or joint consisting of two arms, which are almost in line with each other, connected with an elbow-like pivot. In the phrase "toggle switch" it specifically refers to one kind of mechanism that can be used to implement a positive "snap-action." However, the word "toggle switch" has come to mean any kind of switch with a short handle and a positive snap-action, whether it actually contains a toggle mechanism or not. In electronics, the word "toggle" has come to mean circuits that embody an electronic analog of a mechanical snap-action. That is, bistable switching circuits are sometimes called "toggles." In particular, the word can be used for a binary trigger, a circuit in which an impulse causes a transition from whichever state it is in to the alternate state. By further extension, in software, the act of switching from one to the other of two states can be called "toggling."

Fuse Many circuits have a fuse in series as a protection against an overload resulting from a short circuit. Excessive current melts the fuse element, blowing the fuse and opening the series circuit. The purpose is to let the fuse blow before the components are damaged. The blown fuse can be easily replaced after the overload has been eliminated.

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How to select a fuse in a circuit The problem below shows the selection of a fuse as part of a bigger problem. As you'll see when you look at this problem, we break the problem down into steps: determine the level of current we want to avoid apply a margin of comfort to determine the level of current at which we'll normally operate the circuit choose a fuse to blow somewhere between these two levels The following circuits requires fuse problem. We want to choose resistor R1 to ensure that under normal operation the current does not exceed a safe limit. Then the fuses will not normally be operating near the current which would cause it to blow. It will only come into play if something goes gravely wrong and the normal current is exceeded by a large margin. Resistor R2 is a 10 ohm resistor and s capable of dissipating 500mW. The specification calls for a 100% safety margin n the current through R1.

Solution 1. The first step is to use the VIP convention to label all unknown quantities.

2. Next, figure out the maximum tolerable current. This is based on the maximum tolerable power. The only given limitation is that the power dissipated by resistor 2 not to exceed 500mW. How much current would generate that much power?

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Since,

We can compute the axiom permissible current as

For a 100% safety margin, we want half this current or I = 112mA. (The choice of 100% is somewhat arbitrary; other numbers would do more or less well. Also, the decision to apply the safety margin to the current rather than the power is arbitrary. In this case, though the specification made 100% hard equipment) Now that we know the total voltage and the total current we can computer the total resistance needed to ensure that this maximum current is not normally exceeded.

So,

If we use 5% accuracy resistors, we would like the value of R1 never to be less than this computed value in order to guarantee the current never rise above the 112mA we have

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decided is permissible. That is, we want a nominal resistor. The next highest standard value of 5% resistor is 150 ohms, giving us slightly more than the 100% safety margin we sought. How big should our fuse be? It can be close to the actual limit of current, namely 240mA since we’ll normally operate well below this. For example, a fuse is able to handle 200mA to 220mA of current that it won’t blow when it doesn’t need to. In summary, this problem entailed figuring out the maximum current permissible, cutting that by a comfortable margin, computing the resistance necessary to achieve it, selecting a real-world resistor r! to achieve this value, and then selecting a fuse to blow somewhere between the operating level of current and the dangerous level of current.

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_______

Laboratory Experiment 3 Transformer Switch and Fuse Testing 1. Check the resistance of the nodes of the transformer, switch and fuse.

The resistance of the switch in the ON state is ________Ω. The resistance of the switch in the OFF state is ________Ω. The resistance of a good fuse is __________Ω. Fill up the table for the transformer. Use ohmmeter with a range of RX10 ( for the primary winding ) and RX1 ( for the secondary winding ).

Node

Expected Value

A-B

270 – 330 Ω

A-C

540 – 660 Ω

D-E

2–4Ω 1.5 – 3 Ω

E-F

2–4Ω 1.5 – 2.5 Ω

D-F

4–8Ω

Measured Value

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Section 4.3 Semiconductor Diodes Introduction A diode is an electrical device allowing current to move through it in one direction with far greater ease than in the other. The most common type of diode in modern circuit design is the semiconductor diode, although other diode technologies exist. Semiconductor diodes are symbolized in schematic diagrams as such:

When placed in a simple battery-lamp circuit, the diode will either allow or prevent current through the lamp, depending on the polarity of the applied voltage:

When the polarity of the battery is such that electrons are allowed to flow through the diode, the diode is said to be forward-biased. Conversely, when the battery is "backward" and the diode blocks current, the diode is said to be reverse-biased. A diode may be thought of as a kind of switch: "closed" when forward-biased and "open" when reverse-biased. Oddly enough, the direction of the diode symbol's "arrowhead" points against the direction of electron flow. This is because the diode symbol was invented by engineers, who predominantly use conventional flow notation in their schematics, showing current as a flow of charge from the positive (+) side of the voltage source to the negative (-). This convention holds true for all semiconductor symbols possessing "arrowheads:" the arrow points in the permitted direction of conventional flow, and against the permitted direction of electron flow. Diode behavior is analogous to the behavior of a hydraulic device called a check valve. A check valve allows fluid flow through it in one direction only:

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Check valves are essentially pressure-operated devices: they open and allow flow if the pressure across them is of the correct "polarity" to open the gate (in the analogy shown, greater fluid pressure on the right than on the left). If the pressure is of the opposite "polarity," the pressure difference across the check valve will close and hold the gate so that no flow occurs. Like check valves, diodes are essentially "pressure-" operated (voltage-operated) devices. The essential difference between forward-bias and reverse-bias is the polarity of the voltage dropped across the diode. Let's take a closer look at the simple battery-diode-lamp circuit shown earlier, this time investigating voltage drops across the various components:

When the diode is forward-biased and conducting current, there is a small voltage dropped across it, leaving most of the battery voltage dropped across the lamp. When the battery's polarity is reversed and the diode becomes reverse-biased, it drops all of the battery's voltage and leaves none for the lamp. If we consider the diode to be a sort of self-actuating switch (closed in the forward-bias mode

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and open in the reverse-bias mode), this behavior makes sense. The most substantial difference here is that the diode drops a lot more voltage when conducting than the average mechanical switch (0.7 volts versus tens of millivolts). This forward-bias voltage drop exhibited by the diode is due to the action of the depletion region formed by the P-N junction under the influence of an applied voltage. When there is no voltage applied across a semiconductor diode, a thin depletion region exists around the region of the P-N junction, preventing current through it. The depletion region is for the most part devoid of available charge carriers and so acts as an insulator:

If a reverse-biasing voltage is applied across the P-N junction, this depletion region expands, further resisting any current through it:

Conversely, if a forward-biasing voltage is applied across the P-N junction, the depletion region will collapse and become thinner, so that the diode becomes less resistive to current through it. In order for a sustained current to go through the diode, though, the depletion region must be fully collapsed by the applied voltage. This takes a certain minimum voltage to accomplish, called the forward voltage:

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For silicon diodes, the typical forward voltage is 0.7 volts, nominal. For germanium diodes, the forward voltage is only 0.3 volts. The chemical constituency of the P-N junction comprising the diode accounts for its nominal forward voltage figure, which is why silicon and germanium diodes have such different forward voltages. Forward voltage drop remains approximately equal for a wide range of diode currents, meaning that diode voltage drop not like that of a resistor or even a normal (closed) switch. For most purposes of circuit analysis, it may be assumed that the voltage drop across a conducting diode remains constant at the nominal figure and is not related to the amount of current going through it.

REVIEW:  A diode is an electrical component acting as a one-way valve for current.  When voltage is applied across a diode in such a way that the diode allows current, the diode is said to be forward-biased.  When voltage is applied across a diode in such a way that the diode prohibits current, the diode is said to be reverse-biased.  The voltage dropped across a conducting, forward-biased diode is called the forward voltage. Forward voltage for a diode varies only slightly for changes in forward current and temperature, and is fixed principally by the chemical composition of the P-N junction.  Silicon diodes have a forward voltage of approximately 0.7 volts.  Germanium diodes have a forward voltage of approximately 0.3 volts.  The maximum reverse-bias voltage that a diode can withstand without "breaking down" is called the Peak Inverse Voltage, or PIV rating.

Section 4.4 Meter check of a diode Being able to determine the polarity (cathode versus anode) and basic functionality of a diode is a very important skill for the electronics hobbyist or technician to have. Since we know that a diode is essentially nothing more than a one-way valve for electricity, it makes sense we should be able to verify its one-way nature using a DC (battery-powered) ohmmeter. Connected one way across the

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diode, the meter should show a very low resistance. Connected the other way across the diode, it should show a very high resistance ("OL" on some digital meter models):

Of course, in order to determine which end of the diode is the cathode and which is the anode, you must know with certainty which test lead of the meter is positive (+) and which is negative (-) when set to the "resistance" or "Ω" function. With most digital multimeters I've seen, the red lead becomes positive and the black lead negative when set to measure resistance, in accordance with standard electronics color-code convention. However, this is not guaranteed for all meters. Many analog multimeters, for example, actually make their black leads positive (+) and their red leads negative (-) when switched to the "resistance" function, because it is easier to manufacture it that way! One problem with using an ohmmeter to check a diode is that the readings obtained only have qualitative value, not quantitative. In other words, an ohmmeter only tells you which way the diode conducts; the low-value resistance indication obtained while conducting is useless. If an ohmmeter shows a value of "1.73 ohms" while forward-biasing a diode, that figure of 1.73 Ω doesn't represent any real-world quantity useful to us as technicians or circuit designers. It neither represents the forward voltage drop nor any "bulk" resistance in the semiconductor material of the diode itself, but rather is a figure dependent upon both quantities and will vary substantially with the particular ohmmeter used to take the reading. For this reason, some digital multimeter manufacturers equip their meters with a special "diode check" function which displays the actual forward voltage drop of the diode in volts, rather than a "resistance" figure in ohms. These meters work by forcing a small current through the diode and measuring the voltage dropped between the two test leads:

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The forward voltage reading obtained with such a meter will typically be less than the "normal" drop of 0.7 volts for silicon and 0.3 volts for germanium, because the current provided by the meter is of trivial proportions. If a multimeter with diode-check function isn't available, or you would like to measure a diode's forward voltage drop at some non-trivial current, the following circuit may be constructed using nothing but a battery, resistor, and a normal voltmeter:

Connecting the diode backwards to this testing circuit will simply result in the voltmeter indicating the full voltage of the battery. If this circuit were designed so as to provide a constant or nearly constant current through the diode despite changes in forward voltage drop, it could be used as the basis of a temperature-measurement instrument, the voltage measured across the diode being inversely proportional to diode junction temperature. Of course, diode current should be kept to a minimum to avoid self-heating (the diode dissipating substantial amounts of heat energy), which would interfere with temperature measurement. Beware that some digital multimeters equipped with a "diode check" function may output a very low test voltage (less than 0.3 volts) when set to the regular "resistance" (Ω) function: too low to fully collapse the depletion region of a PN junction. The philosophy here is that the "diode check" function is to be used for testing semiconductor devices, and the "resistance" function for anything else. By using a very low test voltage to measure resistance, it is easier for a technician to measure the resistance of non-semiconductor components connected to semiconductor components, since the semiconductor component junctions will not become forward-biased with such low voltages. Consider the example of a resistor and diode connected in parallel, soldered in place on a printed circuit board (PCB). Normally, one would have to unsolder the resistor from the circuit (disconnect it from all other components) before being able to measure its resistance, otherwise any parallel-

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connected components would affect the reading obtained. However, using a multimeter that outputs a very low test voltage to the probes in the "resistance" function mode, the diode's PN junction will not have enough voltage impressed across it to become forward-biased, and as such will pass negligible current. Consequently, the meter "sees" the diode as an open (no continuity), and only registers the resistor's resistance:

If such an ohmmeter were used to test a diode, it would indicate a very high resistance (many megaohms) even if connected to the diode in the "correct" (forward-biased) direction:

Reverse voltage strength of a diode is not as easily tested, because exceeding a normal diode's PIV usually results in destruction of the diode. There are special types of diodes, though, which are designed to "break down" in reverse-bias mode without damage (called Zener diodes), and they are best tested with the same type of voltage source / resistor / voltmeter circuit, provided that the voltage source is of high enough value to force the diode into its breakdown region. More on this subject in a later section of this chapter.

REVIEW:  An ohmmeter may be used to qualitatively check diode function. There should be low resistance measured one way and very high resistance measured the other way. When using an ohmmeter for this purpose, be sure you know which test lead is positive and which is negative! The actual polarity may not follow the colors of the leads as you might expect, depending on the particular design of meter.  Some multimeters provide a "diode check" function that displays the actual forward voltage of the diode when it's conducting current. Such meters typically indicate a slightly lower forward voltage than what is "nominal" for a diode, due to the very small amount of current used during the check.

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Section 4.5 Rectifier circuits Now we come to the most popular application of the diode: rectification. Simply defined, rectification is the conversion of alternating current (AC) to direct current (DC). This almost always involves the use of some device that only allows one-way flow of electrons. As we have seen, this is exactly what a semiconductor diode does. The simplest type of rectifier circuit is the half-wave rectifier, so called because it only allows one half of an AC waveform to pass through to the load:

For most power applications, half-wave rectification is insufficient for the task. The harmonic content of the rectifier's output waveform is very large and consequently difficult to filter. Furthermore, AC power source only works to supply power to the load once every half-cycle, meaning that much of its capacity is unused. Half-wave rectification is, however, a very simple way to reduce power to a resistive load. Some two-position lamp dimmer switches apply full AC power to the lamp filament for "full" brightness and then half-wave rectify it for a lesser light output:

In the "Dim" switch position, the incandescent lamp receives approximately one-half the power it would normally receive operating on full-wave AC. Because the half-wave rectified power pulses far more rapidly than the filament has time to heat up and cool down, the lamp does not blink. Instead, its filament merely operates at a lesser temperature than normal, providing less light output. This principle of "pulsing" power rapidly to a slow-responding load device in order to control the electrical power sent to it is very common in the world of industrial electronics. Since the controlling device (the diode, in this case) is either fully conducting or fully nonconducting at any given time, it dissipates little heat energy while controlling load power, making this method of power control very energy-efficient. This circuit is perhaps the crudest possible method of pulsing power to a load, but it suffices as a proof-of-concept application. If we need to rectify AC power so as to obtain the full use of both half-cycles of the sine wave, a different rectifier circuit configuration must be used. Such a circuit is called a full-wave rectifier. One type of full-wave rectifier, called the center-tap design, uses a transformer with a center-tapped secondary winding and two diodes, like this:

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This circuit's operation is easily understood one half-cycle at a time. Consider the first half-cycle, when the source voltage polarity is positive (+) on top and negative (-) on bottom. At this time, only the top diode is conducting; the bottom diode is blocking current, and the load "sees" the first half of the sine wave, positive on top and negative on bottom. Only the top half of the transformer's secondary winding carries current during this half-cycle:

During the next half-cycle, the AC polarity reverses. Now, the other diode and the other half of the transformer's secondary winding carry current while the portions of the circuit formerly carrying current during the last half-cycle sit idle. The load still "sees" half of a sine wave, of the same polarity as before: positive on top and negative on bottom:

One disadvantage of this full-wave rectifier design is the necessity of a transformer with a centertapped secondary winding. If the circuit in question is one of high power, the size and expense of a suitable transformer is significant. Consequently, the center-tap rectifier design is seen only in lowpower applications. Another, more popular full-wave rectifier design exists, and it is built around a four-diode bridge configuration. For obvious reasons, this design is called a full-wave bridge:

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Current directions in the full-wave bridge rectifier circuit are as follows for each half-cycle of the AC waveform:

Remembering the proper layout of diodes in a full-wave bridge rectifier circuit can often be frustrating to the new student of electronics. I've found that an alternative representation of this circuit is easier both to remember and to comprehend. It's the exact same circuit, except all diodes are drawn in a horizontal attitude, all "pointing" the same direction:

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Laboratory Experiment 4 Diode Biasing Check the diode resistances in forward biased and record the results in the table.

Remember that in using a SUNWA tester, the polarity is reverse.

Fill up the table for the measured resistance values of the nodes. Diode

Forward Biased Resistance

Reverse Biased Resistance

1 2 3 4

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Section 4.6 Capacitors Capacitance is the ability of a dielectric to store electric charges. The unit is farad, named after Michael Faraday. A capacitor consists of an insulator between two conductors. They are manufactured for a specific value of capacitance. A capacitor is basically a device that stores electric charge. Any two conducting surfaces (plates) separated by an insulating medium form a capacitor. A capacitor stores energy in an electrostatic field and accepts a charge of electricity or returns electrons to the circuit in an attempt to maintain a constant voltage. Capacitance is that property of a circuit that opposes a change in current. Representation of the simple capacitor

A strong electrostatic field exists in the dielectric between the plates of a charged capacitor. Electrons existing in this field would have a tendency to move toward the positive plate. The electrons associated with each atom dielectric material are distorted out of their regular orbits and assume new locations in the direction of the positive plate. They remain in this position under the influence of the static field. When the capacitor is discharged, the electrons return to their original orbits, by doing so, return energy to the circuit. All capacitors have a Working Voltage Direct Current (WVDC) rating which is the specified voltage at which the capacitor can withstand without the destruction of the dielectric. This specification must always be considered by the technician when using or replacing capacitors.

The unit of measurements of capacitance The base unit of measurement of capacitance is farad, symbol is F. A Farad (1F) is the capacitance which will cause one ampere of charging current to flow when the applied voltage is changing at a rate of 1 volt per second. Expressed mathematically: i C= v/t

where: C = is the capacitance unit is in Farad (F) i = is the charging current unit is in Amperes (A) v = is the change in voltage unit is in Volts (V) t = is the change in time unit is in seconds (s)

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Example: What is the capacitance of a capacitor having a charging current of 100 mA flows when the voltage changes 10 V at a frequency of 100 hertz? Solution: 1. Convert 100mA to A which is equal to 0.1A. 2. The period of time T = 1/f. That makes T = 1/100 = 0.01 seconds. 3. C = .1 / (10/0.01) = 0.0001 F = 100 microfarads symbol is µF.

Schematic symbols of a capacitor

Polarized capacitors are used in circuits having a combination of a DC and AC voltage. The DC voltage maintains the polarity. A common application is the electrolytic filter capacitors used to eliminate the AC ripple voltage in a DC power supply. The non – polarized are available for applications in AC circuits without any DC polarizing voltage. One use is for motors. The capacitor's function is to store electricity, or electrical energy. The capacitor also functions as a filter, passing alternating current (AC), and blocking direct current (DC).This symbol is used to indicate a capacitor in a circuit diagram. The capacitor is constructed with two electrode plates facing each other, but separated by an insulator. When DC voltage is applied to the capacitor, an electric charge is stored on each electrode. While the capacitor is charging up, current flows. The current will stop flowing when the capacitor has fully charged.

When a circuit tester, such as an analog meter set to measure resistance, is connected to a 10 microfarad (µF) electrolytic capacitor, a current will flow, but only for a moment. You can confirm that the meter's needle moves off of zero, but returns to zero right away. When you connect the meter's probes to the capacitor in reverse, you will note that current once again flows for a moment. Once again, when the capacitor has fully charged, the current stops flowing. So the capacitor can be used as a filter that blocks DC current. (A "DC cut" filter.) However, in the case of alternating current, the current will be allowed to pass. Alternating current is similar to repeatedly switching the test meter's probes back and forth on the capacitor. Current flows every time the probes are switched.

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The value of a capacitor (the capacitance), is designated in units called the Farad ( F ). The capacitance of a capacitor is generally very small, so units such as the microfarad ( 10-6F ), nanofarad ( 10-9F ), and picofarad (10-12F ) are used. Recently, a new capacitor with very high capacitance has been developed. The Electric Double Layer capacitor has capacitance designated in Farad units. These are known as "Super Capacitors." Sometimes, a three-digit code is used to indicate the value of a capacitor. There are two ways in which the capacitance can be written. One uses letters and numbers, the other uses only numbers. In either case, there are only three characters used. [10n] and [103] denote the same value of capacitance. The method used differs depending on the capacitor supplier. In the case that the value is displayed with the three-digit code, the 1st and 2nd digits from the left show the 1st figure and the 2nd figure, and the 3rd digit is a multiplier which determines how many zeros are to be added to the capacitance. Picofarad ( pF ) units are written this way. For example, when the code is [103], it indicates 10 x 103, or 10,000pF = 10 nanofarad( nF ) = 0.01 microfarad( µF ). If the code happened to be [224], it would be 22 x 104 = or 220,000pF = 220nF = 0.22µF. Values under 100pF are displayed with 2 digits only. For example, 47 would be 47pF. The capacitor has an insulator( the dielectric ) between 2 sheets of electrodes. Different kinds of capacitors use different materials for the dielectric. Score: Instructor’s signature: Date: Remarks:

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Laboratory Experiment 5 Capacitor Action

Check your capacitors using an ohmmeter and observe the capacitor action. Capacitor action is when you connect the capacitor to the ohmmeter and the needle of the meter deflects (almost 0 Ω), then return back to its original position (infinite resistance).

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Breakdown voltage When using a capacitor, you must pay attention to the maximum voltage which can be used. This is the "breakdown voltage." The breakdown voltage depends on the kind of capacitor being used. You must be especially careful with electrolytic capacitors because the breakdown voltage is comparatively low. The breakdown voltage of electrolytic capacitors is displayed as Working Voltage. The breakdown voltage is the voltage that when exceeded will cause the dielectric (insulator) inside the capacitor to break down and conduct. When this happens, the failure can be catastrophic.

Section 4.7 Different types of capacitors capacitors) rs) Electrolytic Capacitors (Electrochemical type capacito Aluminum is used for the electrodes by using a thin oxidization membrane. Large values of capacitance can be obtained in comparison with the size of the capacitor, because the dielectric used is very thin. The most important characteristic of electrolytic capacitors is that they have polarity. They have a positive and a negative electrode.[Polarised] This means that it is very important which way round they are connected. If the capacitor is subjected to voltage exceeding its working voltage, or if it is connected with incorrect polarity, it may burst. It is extremely dangerous, because it can quite literally explode. Make absolutely no mistakes. Generally, in the circuit diagram, the positive side is indicated by a "+" (plus) symbol. Electrolytic capacitors range in value from about 1µF to thousands of µF. Mainly this type of capacitor is used as a ripple filter in a power supply circuit, or as a filter to bypass low frequency signals, etc. Because this type of capacitor is comparatively similar to the nature of a coil in construction, it isn't possible to use for high-frequency circuits. (It is said that the frequency characteristic is bad.)

The photograph on the left is an example of the different values of electrolytic capacitors in which the capacitance and voltage differ. From the left to right: 1µF (50V) [diameter 5 mm, high 12 mm] 47µF (16V) [diameter 6 mm, high 5 mm] 100µF (25V) [diameter 5 mm, high 11 mm] 220µF (25V) [diameter 8 mm, high 12 mm] 1000µF (50V) [diameter 18 mm, high 40 mm]

The size of the capacitor sometimes depends on the manufacturer. So the sizes shown here on this page are just examples.

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In the photograph to the right, the mark indicating the negative lead of the component can be seen. You need to pay attention to the polarity indication so as not to make a mistake when you assemble the circuit.

Tantalum Capacitors Tantalum Capacitors are electrolytic capacitors that is use a material called tantalum for the electrodes. Large values of capacitance similar to aluminum electrolytic capacitors can be obtained. Also, tantalum capacitors are superior to aluminum electrolytic capacitors in temperature and frequency characteristics. When tantalum powder is baked in order to solidify it, a crack forms inside. An electric charge can be stored on this crack. These capacitors have polarity as well. Usually, the "+" symbol is used to show the positive component lead. Do not make a mistake with the polarity on these types. Tantalum capacitors are a little bit more expensive than aluminum electrolytic capacitors. Capacitance can change with temperature as well as frequency, and these types are very stable. Therefore, tantalum capacitors are used for circuits which demand high stability in the capacitance values. Also, it is said to be common sense to use tantalum capacitors for analog signal systems, because the current-spike noise that occurs with aluminum electrolytic capacitors does not appear. Aluminum electrolytic capacitors are fine if you don't use them for circuits which need the high stability characteristics of tantalum capacitors. The photograph on the left illustrates the tantalum capacitor. The capacitance values are as follows, from the left: 0.33 µF (35V) 0.47 µF (35V) 10 µF (35V) The "+" symbol is used to show the positive lead of the component. It is written on the body.

Ceramic Capacitors Ceramic capacitors are constructed with materials such as titanium acid barium used as the dielectric. Internally, these capacitors are not constructed as a coil, so they can be used in high frequency applications. Typically, they are used in circuits which bypass high frequency signals to ground. These capacitors have the shape of a disk. Their capacitance is comparatively small. The capacitor on the left is a 100pF capacitor with a diameter of about 3 mm. The capacitor on the right side is printed with 103, so 10 x 103pF becomes 0.01 µF. The diameter of the disk is about 6 mm. Ceramic capacitors have no polarity.

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Ceramic capacitors should not be used for analog circuits, because they can distort the signal.

Multilayer Ceramic Capacitors The multilayer ceramic capacitor has a many-layered dielectric. These capacitors are small in size, and have good temperature and frequency characteristics. Square wave signals used in digital circuits can have a comparatively high frequency component included. This capacitor is used to bypass the high frequency to ground. In the photograph, the capacitance of the component on the left is displayed as 104. So, the capacitance is 10 x 104 pF = 0.1 µF. The thickness is 2 mm, the height is 3 mm, the width is 4 mm. The capacitor to the right has a capacitance of 103 (10 x 103 pF = 0.01 µF). The height is 4 mm, the diameter of the round part is 2 mm. These capacitors are not polarized. That is, they have no polarity.

Polystyrene Film Capacitors In these devices, polystyrene film is used as the dielectric. This type of capacitor is not for use in high frequency circuits, because they are constructed like a coil inside. They are used well in filter circuits or timing circuits which run at several hundred KHz or less. The component shown on the left has a red color due to the copper leaf used for the electrode. The silver color is due to the use of aluminum foil as the electrode. The device on the left has a height of 10 mm, is 5 mm thick, and is rated 100pF. The device in the middle has a height of 10 mm, 5.7 mm thickness, and is rated 1000pF. The device on the right has a height of 24 mm, is 10 mm thick, and is rated 10000pF. These devices have no polarity.

Electric Double Layer Capacitors (Super Capacitors) This is a "Super Capacitor," which is quite a wonder. The capacitance is 0.47 F (470,000 µF). I have not used this capacitor in an actual circuit. Care must be taken when using a capacitor with such a large capacitance in power supply circuits, etc. The rectifier in the circuit can be destroyed by a huge rush of current when the capacitor is empty. For a brief moment, the capacitor is more like a short circuit. A protection circuit needs to be set up.

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The size is small in spite of capacitance. Physically, the diameter is 21 mm, the height is 11 mm. Care is necessary, because these devices do have polarity.

Polyester Film Capacitors This capacitor uses thin polyester film as the dielectric. They are not high tolerance, but they are cheap and handy. Their tolerance is about ±5% to ±10%. From the left in the photograph Capacitance: 0.001 µF (printed with 001K) [the width 5 mm, the height 10 mm, the thickness 2 mm] Capacitance: 0.1 µF (printed with 104K) [the width 10 mm, the height 11 mm, the thickness 5mm] Capacitance: 0.22 µF (printed with .22K) [the width 13 mm, the height 18 mm, the thickness 7mm] Care must be taken, because different manufacturers use different methods to denote the capacitance values.

Here are some other polyester film capacitors.

Starting from the left Capacitance: 0.0047 µF (printed with 472K) [the width 4mm, the height 6mm, the thickness 2mm] Capacitance: 0.0068 µF (printed with 682K) [the width 4mm, the height 6mm, the thickness 2mm] Capacitance: 0.47 µF (printed with 474K) [the width 11mm, the height 14mm, the thickness 7mm] These capacitors have no polarity. Polypropylene Capacitors This capacitor is used when a higher tolerance is necessary than polyester capacitors offer. Polypropylene film is used for the dielectric. It is said that there is almost no change of capacitance in these devices if they are used with frequencies of 100KHz or less. The pictured capacitors have a tolerance of ±1%. From the left in the photograph Capacitance: 0.01 µF (printed with 103F) [the width 7mm, the height 7mm, the thickness 3mm] Capacitance: 0.022 µF (printed with 223F) [the width 7mm, the height 10mm, the thickness 4mm] Capacitance: 0.1 µF (printed with 104F) [the width 9mm, the height 11mm, the thickness 5mm] When I measured the capacitance of a 0.01 µF capacitor with the meter which I have, the error was +0.2%.

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These capacitors have no polarity.

Mica Capacitors These capacitors use Mica for the dielectric. Mica capacitors have good stability because their temperature coefficient is small. Because their frequency characteristic is excellent, they are used for resonance circuits, and high frequency filters. Also, they have good insulation, and so can be utilized in high voltage circuits. It was often used for vacuum tube style radio transmitters, etc. Mica capacitors do not have high values of capacitance, and they can be relatively expensive. Pictured at the right are "Dipped mica capacitors." These can handle up to 500 volts. The capacitance from the left Capacitance: 47pF (printed with 470J) [the width 7mm, the height 5mm, the thickness 4mm] Capacitance: 220pF (printed with 221J) [the width 10mm, the height 6mm, the thickness 4mm] Capacitance: 1000pF (printed with 102J) [the width 14mm, the height 9mm, the thickness 4mm] These capacitors have no polarity.

Metallized Polyester Film Capacitors These capacitors are a kind of a polyester film capacitor. Because their electrodes are thin, they can be miniaturized. From the left in the photograph Capacitance: 0.001µF (printed with 1n. n means nano:10-9) Breakdown voltage: 250V [the width 8mm, the height 6mm, the thickness 2mm] Capacitance: 0.22µF (printed with u22) Breakdown voltage: 100V [the width 8mm, the height 6mm, the thickness 3mm] Capacitance: 2.2µF (printed with 2u2) Breakdown voltage: 100V [the width 15mm, the height 10mm, the thickness 8mm] Care is necessary, because the component lead easily breaks off from these capacitors. Once lead has come off, there is no way to fix it. It must be discarded. These capacitors have no polarity.

Variable Capacitors Variable capacitors are used for adjustment etc. of frequency mainly. On the left in the photograph is a "trimmer," which uses ceramic as the dielectric. Next to it on the right is one that uses polyester film for the dielectric. The pictured components are meant to be mounted on a printed circuit board.

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When adjusting the value of a variable capacitor, it is advisable to be careful. One of the component's leads is connected to the adjustment screw of the capacitor. This means that the value of the capacitor can be affected by the capacitance of the screwdriver in your hand. It is better to use a special screwdriver to adjust these components. Pictured in the upper left photograph are variable capacitors with the following specifications: Capacitance: 20pF (3pF - 27pF measured) [Thickness 6 mm, height 4.8 mm] Their are different colors, as well. Blue: 7pF (2 - 9), white: 10pF (3 - 15), green: 30pF (5 - 35), brown: 60pF (8 - 72). In the same photograph, the device on the right has the following specifications: Capacitance: 30pF (5pF - 40pF measured) [The width (long) 6.8 mm, width (short) 4.9 mm, and the height 5 mm] The components in the photograph on the right are used for radio tuners, etc. They are called "Varicons" but this may be only in Japan. The variable capacitor on the left in the photograph, uses air as the dielectric. It combines three independent capacitors. For each one, the capacitance changed 2pF - 18pF. When the adjustment axis is turned, the capacitance of all 3 capacitors change simultaneously. Physically, the device has a depth of 29 mm, and 17 mm width and height. (Not including the adjustment rod.) There are various kinds of variable capacitor, chosen in accordance with the purpose for which they are needed. The pictured components are very small. To the right in the photograph is a variable capacitor using polyester film as the dielectric. Two independent capacitors are combined. The capacitance of one side changes 12pF - 150pF, while the other side changes from 11pF - 70pF. Physically, it has a depth of 11mm, and 20mm width and height. (Not including the adjustment rod.) The pictured device also has a small trimmer built in to each capacitor to allow for precise adjustment up to 15pF.

Characteristics of Capacitors Plate Area – the capacitance is increased with an increase in plate area. The variable capacitor is a working example of this principle. Spacing between plates – as the plates move closer together, the capacitance is increased. An increase in the spacing between plates will decrease the capacitance. Kind of dielectric – when plates are separated by air, a certain value of capacitance is realized. If a piece of material such as glass of paper is placed between the plates, the capacitance will increase. Due to the molecular formation of different materials, they will have different abilities to store electrical energy when used as a dielectric in a capacitor.

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The following could be used as a dielectric: Air Waxed paper Mica Rubber Pure Water

Glass Wood

Capacitor Connections Series – the property is like that of resistors connected in parallel. Series capacitors reduce the total capacitance. Examples: Find CT if all capacitors are 100µF. 1. In polarized capacitors, be careful with the polarity when connecting them in series. Notice the connection in the polarities. The positive terminal is always connected in the negative terminal of the other capacitor. 2. There is no problem in the polarity of the non – polarized capacitors.

Parallel – the property is like that of resistors connected in series. Parallel capacitors add to increase the total capacitance. Examples: Find CT if all capacitors are 100µF.

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Laboratory Experiment 6 Filtered Rectifier Circuits Connect your capacitors and other electronic devices as shown below. Then fill up the table for the DC voltage measurements across the nodes.

Node

Expected Value

A - GND

17 V DC

D-GND

12 V AC

D-F

24 V AC

F - GND

12 V AC

A-C

220 V AC

V AC

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Section 4.8 Transistors Introduction The invention of the bipolar transistor in 1948 ushered in a revolution in electronics. Technical feats previously requiring relatively large, mechanically fragile, power-hungry vacuum tubes were suddenly achievable with tiny, mechanically rugged, power-thrifty specks of crystalline silicon. This revolution made possible the design and manufacture of lightweight, inexpensive electronic devices that we now take for granted. Understanding how transistors function is of paramount importance to anyone interested in understanding modern electronics. My intent here is to focus as exclusively as possible on the practical function and application of bipolar transistors, rather than to explore the quantum world of semiconductor theory. Discussions of holes and electrons are better left to another chapter in my opinion. Here I want to explore how to use these components, not analyze their intimate internal details. I don't mean to downplay the importance of understanding semiconductor physics, but sometimes an intense focus on solid-state physics detracts from understanding these devices' functions on a component level. In taking this approach, however, I assume that the reader possesses a certain minimum knowledge of semiconductors: the difference between "P" and "N" doped semiconductors, the functional characteristics of a PN (diode) junction, and the meanings of the terms "reverse biased" and "forward biased." If these concepts are unclear to you, it is best to refer to earlier chapters in this book before proceeding with this one. A bipolar transistor consists of a three-layer "sandwich" of doped (extrinsic) semiconductor materials, either P-N-P or N-P-N. Each layer forming the transistor has a specific name, and each layer is provided with a wire contact for connection to a circuit. Shown here are schematic symbols and physical diagrams of these two transistor types:

The only functional difference between a PNP transistor and an NPN transistor is the proper biasing (polarity) of the junctions when operating. For any given state of operation, the current directions and voltage polarities for each type of transistor are exactly opposite each other. Bipolar transistors work as current-controlled current regulators. In other words, they restrict the amount of current that can go through them according to a smaller, controlling current. The main current that is controlled goes from collector to emitter, or from emitter to collector, depending on the

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type of transistor it is (PNP or NPN, respectively). The small current that controls the main current goes from base to emitter, or from emitter to base, once again depending on the type of transistor it is (PNP or NPN, respectively). According to the confusing standards of semiconductor symbology, the arrow always points against the direction of electron flow:

Bipolar transistors are called bipolar because the main flow of electrons through them takes place in two types of semiconductor material: P and N, as the main current goes from emitter to collector (or visa-versa). In other words, two types of charge carriers -- electrons and holes -- comprise this main current through the transistor. As you can see, the controlling current and the controlled current always mesh together through the emitter wire, and their electrons always flow against the direction of the transistor's arrow. This is the first and foremost rule in the use of transistors: all currents must be going in the proper directions for the device to work as a current regulator. The small, controlling current is usually referred to simply as the base current because it is the only current that goes through the base wire of the transistor. Conversely, the large, controlled current is referred to as the collector current because it is the only current that goes through the collector wire. The emitter current is the sum of the base and collector currents, in compliance with Kirchhoff's Current Law. If there is no current through the base of the transistor, it shuts off like an open switch and prevents current through the collector. If there is a base current, then the transistor turns on like a closed switch and allows a proportional amount of current through the collector. Collector current is primarily limited by the base current, regardless of the amount of voltage available to push it. The next section will explore in more detail the use of bipolar transistors as switching elements.

REVIEW:  Bipolar transistors are so named because the controlled current must go through two types of semiconductor material: P and N. The current consists of both electron and hole flow, in different parts of the transistor.  Bipolar transistors consist of either a P-N-P or an N-P-N semiconductor "sandwich" structure.  The three leads of a bipolar transistor are called the Emitter, Base, and Collector.  Transistors function as current regulators by allowing a small current to control a larger current. The amount of current allowed between collector and emitter is primarily determined by the amount of current moving between base and emitter.

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 In order for a transistor to properly function as a current regulator, the controlling (base) current and the controlled (collector) currents must be going in the proper directions: meshing additively at the emitter and going against the emitter arrow symbol.

Section 4.9 Meter check of a transistor Bipolar transistors are constructed of a three-layer semiconductor "sandwich," either PNP or NPN. As such, they register as two diodes connected back-to-back when tested with a multimeter's "resistance" or "diode check" functions:

Here I'm assuming the use of a multimeter with only a single continuity range (resistance) function to check the PN junctions. Some multimeters are equipped with two separate continuity check functions: resistance and "diode check," each with its own purpose. If your meter has a designated "diode check" function, use that rather than the "resistance" range, and the meter will display the actual forward voltage of the PN junction and not just whether or not it conducts current.

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Meter readings will be exactly opposite, of course, for an NPN transistor, with both PN junctions facing the other way. If a multimeter with a "diode check" function is used in this test, it will be found that the emitter-base junction possesses a slightly greater forward voltage drop than the collectorbase junction. This forward voltage difference is due to the disparity in doping concentration between the emitter and collector regions of the transistor: the emitter is a much more heavily doped piece of semiconductor material than the collector, causing its junction with the base to produce a higher forward voltage drop. Knowing this, it becomes possible to determine which wire is which on an unmarked transistor. This is important because transistor packaging, unfortunately, is not standardized. All bipolar transistors have three wires, of course, but the positions of the three wires on the actual physical package are not arranged in any universal, standardized order. Suppose a technician finds a bipolar transistor and proceeds to measure continuity with a multimeter set in the "diode check" mode. Measuring between pairs of wires and recording the values displayed by the meter, the technician obtains the following data:

Meter touching wire 1 (+) and 2 (-): "OL" Meter touching wire 1 (-) and 2 (+): "OL" Meter touching wire 1 (+) and 3 (-): 0.655 volts Meter touching wire 1 (-) and 3 (+): "OL" Meter touching wire 2 (+) and 3 (-): 0.621 volts Meter touching wire 2 (-) and 3 (+): "OL"

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The only combinations of test points giving conducting meter readings are wires 1 and 3 (red test lead on 1 and black test lead on 3), and wires 2 and 3 (red test lead on 2 and black test lead on 3). These two readings must indicate forward biasing of the emitter-to-base junction (0.655 volts) and the collector-to-base junction (0.621 volts). Now we look for the one wire common to both sets of conductive readings. It must be the base connection of the transistor, because the base is the only layer of the three-layer device common to both sets of PN junctions (emitter-base and collector-base). In this example, that wire is number 3, being common to both the 1-3 and the 2-3 test point combinations. In both those sets of meter readings, the black (-) meter test lead was touching wire 3, which tells us that the base of this transistor is made of N-type semiconductor material (black = negative). Thus, the transistor is an PNP type with base on wire 3, emitter on wire 1 and collector on wire 2:

Please note that the base wire in this example is not the middle lead of the transistor, as one might expect from the three-layer "sandwich" model of a bipolar transistor. This is quite often the case, and tends to confuse new students of electronics. The only way to be sure which lead is which is by a meter check, or by referencing the manufacturer's "data sheet" documentation on that particular part number of transistor. Knowing that a bipolar transistor behaves as two back-to-back diodes when tested with a conductivity meter is helpful for identifying an unknown transistor purely by meter readings. It is also helpful for a quick functional check of the transistor. If the technician were to measure continuity in any more than two or any less than two of the six test lead combinations, he or she would immediately know that the transistor was defective (or else that it wasn't a bipolar transistor but rather something else -- a distinct possibility if no part numbers can be referenced for sure identification!). However, the "two diode" model of the transistor fails to explain how or why it acts as an amplifying device. To better illustrate this paradox, let's examine one of the transistor switch circuits using the physical diagram rather than the schematic symbol to represent the transistor. This way the two PN junctions will be easier to see:

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A grey-colored diagonal arrow shows the direction of electron flow through the emitter-base junction. This part makes sense, since the electrons are flowing from the N-type emitter to the P-type base: the junction is obviously forward-biased. However, the base-collector junction is another matter entirely. Notice how the grey-colored thick arrow is pointing in the direction of electron flow (upwards) from base to collector. With the base made of P-type material and the collector of N-type material, this direction of electron flow is clearly backwards to the direction normally associated with a PN junction! A normal PN junction wouldn't permit this "backward" direction of flow, at least not without offering significant opposition. However, when the transistor is saturated, there is very little opposition to electrons all the way from emitter to collector, as evidenced by the lamp's illumination! Clearly then, something is going on here that defies the simple "two-diode" explanatory model of the bipolar transistor. When I was first learning about transistor operation, I tried to construct my own transistor from two back-to-back diodes, like this:

My circuit didn't work, and I was mystified. However useful the "two diode" description of a transistor might be for testing purposes, it doesn't explain how a transistor can behave as a controlled switch. What happens in a transistor is this: the reverse bias of the base-collector junction prevents collector current when the transistor is in cutoff mode (that is, when there is no base current). However, when the base-emitter junction is forward biased by the controlling signal, the normally-blocking action of the base-collector junction is overridden and current is permitted through the collector, despite the fact that electrons are going the "wrong way" through that PN junction. This action is dependent on the quantum physics of semiconductor junctions, and can only take place when the two junctions are properly spaced and the doping concentrations of the three layers are properly proportioned. Two diodes wired in series fail to meet these criteria, and so the top diode can never "turn on" when it is reversed biased, no matter how much current goes through the bottom diode in the base wire loop. That doping concentrations play a crucial part in the special abilities of the transistor is further evidenced by the fact that collector and emitter are not interchangeable. If the transistor is merely viewed as two back-to-back PN junctions, or merely as a plain N-P-N or P-N-P sandwich of materials, it may seem as though either end of the transistor could serve as collector or emitter. This, however, is not true. If connected "backwards" in a circuit, a base-collector current will fail to control current between collector and emitter. Despite the fact that both the emitter and collector layers of a bipolar transistor are of the same doping type (either N or P), they are definitely not identical! So, current through the emitter-base junction allows current through the reverse-biased base-collector junction. The action of base current can be thought of as "opening a gate" for current through the

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collector. More specifically, any given amount of emitter-to-base current permits a limited amount of base-to-collector current. For every electron that passes through the emitter-base junction and on through the base wire, there is allowed a certain, restricted number of electrons to pass through the base-collector junction and no more.

REVIEW:  Tested with a multimeter in the "resistance" or "diode check" modes, a transistor behaves like two back-to-back PN (diode) junctions.  The emitter-base PN junction has a slightly greater forward voltage drop than the collector-base PN junction, due to more concentrated doping of the emitter semiconductor layer.  The reverse-biased base-collector junction normally blocks any current from going through the transistor between emitter and collector. However, that junction begins to conduct if current is drawn through the base wire. Base current can be thought of as "opening a gate" for a certain, limited amount of current through the collector.

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5

CHAPTER

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+

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5-1 Voltage Divider Circuits 5-2 Kirchoff’s Voltage Law 5-3 Current Divider Circuits 5-4 Kirchoff’s Current Law

Section 5.1 Voltage divider circuits

5-5 Thevenin’n Theorem

Let's analyze a simple series circuit, determining the voltage drops across individual resistors:

5-6 Norton’s Theorem 5-7 Thevenin and Norton Equivalences 5-8 Superposition Theorem

+

From the given values of individual resistances, we can determine a total circuit resistance, knowing that resistances add in series:

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From here, we can use Ohm's Law (I=E/R) to determine the total current, which we know will be the same as each resistor current, currents being equal in all parts of a series circuit:

Now, knowing that the circuit current is 2 mA, we can use Ohm's Law (E=IR) to calculate voltage across each resistor:

It should be apparent that the voltage drop across each resistor is proportional to its resistance, given that the current is the same through all resistors. Notice how the voltage across R2 is double that of the voltage across R1, just as the resistance of R2 is double that of R1. If we were to change the total voltage, we would find this proportionality of voltage drops remains constant:

The voltage across R2 is still exactly twice that of R1's drop, despite the fact that the source voltage has changed. The proportionality of voltage drops (ratio of one to another) is strictly a function of resistance values. With a little more observation, it becomes apparent that the voltage drop across each resistor is also a fixed proportion of the supply voltage. The voltage across R1, for example, was 10 volts when the battery supply was 45 volts. When the battery voltage was increased to 180 volts (4 times as much), the voltage drop across R1 also increased by a factor of 4 (from 10 to 40 volts). The ratio between R1's voltage drop and total voltage, however, did not change:

Likewise, none of the other voltage drop ratios changed with the increased supply voltage either:

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For this reason a series circuit is often called a voltage divider for its ability to proportion -- or divide -the total voltage into fractional portions of constant ratio. With a little bit of algebra, we can derive a formula for determining series resistor voltage drop given nothing more than total voltage, individual resistance, and total resistance:

The ratio of individual resistance to total resistance is the same as the ratio of individual voltage drop to total supply voltage in a voltage divider circuit. This is known as the voltage divider formula, and it is a short-cut method for determining voltage drop in a series circuit without going through the current calculation(s) of Ohm's Law. Using this formula, we can re-analyze the example circuit's voltage drops in fewer steps:

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Voltage dividers find wide application in electric meter circuits, where specific combinations of series resistors are used to "divide" a voltage into precise proportions as part of a voltage measurement device.

One device frequently used as a voltage-dividing component is the potentiometer, which is a resistor with a movable element positioned by a manual knob or lever. The movable element, typically called a wiper, makes contact with a resistive strip of material (commonly called the slidewire if made of resistive metal wire) at any point selected by the manual control:

The wiper contact is the left-facing arrow symbol drawn in the middle of the vertical resistor element. As it is moved up, it contacts the resistive strip closer to terminal 1 and further away from terminal 2, lowering resistance to terminal 1 and raising resistance to terminal 2. As it is moved down, the opposite effect results. The resistance as measured between terminals 1 and 2 is constant for any wiper position.

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Linear Potentiometer Construction Shown here are internal illustrations of two potentiometer types, rotary and linear:

Some linear potentiometers are actuated by straight-line motion of a lever or slide button. Others, like the one depicted in the previous illustration, are actuated by a turn-screw for fine adjustment ability. The latter units are sometimes referred to as trimpots, because they work well for applications requiring a variable resistance to be "trimmed" to some precise value. It should be noted that not all linear potentiometers have the same terminal assignments as shown in this illustration. With some, the wiper terminal is in the middle, between the two end terminals.

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The following photograph shows a real, rotary potentiometer with exposed wiper and slidewire for easy viewing. The shaft which moves the wiper has been turned almost fully clockwise so that the wiper is nearly touching the left terminal end of the slidewire:

Here is the same potentiometer with the wiper shaft moved almost to the full-counterclockwise position, so that the wiper is near the other extreme end of travel:

If a constant voltage is applied between the outer terminals (across the length of the slidewire), the wiper position will tap off a fraction of the applied voltage, measurable between the wiper contact and either of the other two terminals. The fractional value depends entirely on the physical position of the wiper:

Using a potentiometer as a variable voltage divider

Just like the fixed voltage divider, the potentiometer's voltage division ratio is strictly a function of resistance and not of the magnitude of applied voltage. In other words, if the potentiometer knob or lever is moved to the 50 percent (exact center) position, the voltage dropped between wiper and either outside terminal would be exactly 1/2 of the applied voltage, no matter what that voltage happens to be, or what the end-to-end resistance of the potentiometer is. In other words, a potentiometer functions as a variable voltage divider where the voltage division ratio is set by wiper position.

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This application of the potentiometer is a very useful means of obtaining a variable voltage from a fixed-voltage source such as a battery. If a circuit you're building requires a certain amount of voltage that is less than the value of an available battery's voltage, you may connect the outer terminals of a potentiometer across that battery and "dial up" whatever voltage you need between the potentiometer wiper and one of the outer terminals for use in your circuit:

When used in this manner, the name potentiometer makes perfect sense: they meter (control) the potential (voltage) applied across them by creating a variable voltage-divider ratio. This use of the three-terminal potentiometer as a variable voltage divider is very popular in circuit design. Shown here are several small potentiometers of the kind commonly used in consumer electronic equipment and by hobbyists and students in constructing circuits:

The smaller units on the very left and very right are designed to plug into a solderless breadboard or be soldered into a printed circuit board. The middle units are designed to be mounted on a flat panel with wires soldered to each of the three terminals. Here are three more potentiometers, more specialized than the set just shown:

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The large "Helipot" unit is a laboratory potentiometer designed for quick and easy connection to a circuit. The unit in the lower-left corner of the photograph is the same type of potentiometer, just without a case or 10-turn counting dial. Both of these potentiometers are precision units, using multiturn helical-track resistance strips and wiper mechanisms for making small adjustments. The unit on the lower-right is a panel-mount potentiometer, designed for rough service in industrial applications.

REVIEW: Series circuits proportion, or divide, the total supply voltage among individual voltage drops, the proportions being strictly dependent upon resistances: ERn = ETotal (Rn / RTotal) A potentiometer is a variable-resistance component with three connection points, frequently used as an adjustable voltage divider.

Section 5.2 Kirchhoff's Voltage Law (KVL) Let's take another look at our example series circuit, this time numbering the points in the circuit for voltage reference:

If we were to connect a voltmeter between points 2 and 1, red test lead to point 2 and black test lead to point 1, the meter would register +45 volts. Typically the "+" sign is not shown, but rather implied, for positive readings in digital meter displays. However, for this lesson the polarity of the voltage reading is very important and so I will show positive numbers explicitly:

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When a voltage is specified with a double subscript (the characters "2-1" in the notation "E2-1"), it means the voltage at the first point (2) as measured in reference to the second point (1). A voltage specified as "Ecg" would mean the voltage as indicated by a digital meter with the red test lead on point "c" and the black test lead on point "g": the voltage at "c" in reference to "g".

If we were to take that same voltmeter and measure the voltage drop across each resistor, stepping around the circuit in a clockwise direction with the red test lead of our meter on the point ahead and the black test lead on the point behind, we would obtain the following readings:

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We should already be familiar with the general principle for series circuits stating that individual voltage drops add up to the total applied voltage, but measuring voltage drops in this manner and paying attention to the polarity (mathematical sign) of the readings reveals another facet of this principle: that the voltages measured as such all add up to zero:

This principle is known as Kirchhoff's Voltage Law (discovered in 1847 by Gustav R. Kirchhoff, a German physicist), and it can be stated as such: "The algebraic sum of all voltages in a loop must equal zero" By algebraic, I mean accounting for signs (polarities) as well as magnitudes. By loop, I mean any path traced from one point in a circuit around to other points in that circuit, and finally back to the initial point. In the above example the loop was formed by following points in this order: 1-2-3-4-1. It doesn't matter which point we start at or which direction we proceed in tracing the loop; the voltage sum will still equal zero. To demonstrate, we can tally up the voltages in loop 3-2-1-4-3 of the same circuit:

This may make more sense if we re-draw our example series circuit so that all components are represented in a straight line:

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It's still the same series circuit, just with the components arranged in a different form. Notice the polarities of the resistor voltage drops with respect to the battery: the battery's voltage is negative on the left and positive on the right, whereas all the resistor voltage drops are oriented the other way: positive on the left and negative on the right. This is because the resistors are resisting the flow of electrons being pushed by the battery. In other words, the "push" exerted by the resistors against the flow of electrons must be in a direction opposite the source of electromotive force. Here we see what a digital voltmeter would indicate across each component in this circuit, black lead on the left and red lead on the right, as laid out in horizontal fashion:

If we were to take that same voltmeter and read voltage across combinations of components, starting with only R1 on the left and progressing across the whole string of components, we will see how the voltages add algebraically (to zero):

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The fact that series voltages add up should be no mystery, but we notice that the polarity of these voltages makes a lot of difference in how the figures add. While reading voltage across R1, R1--R2, and R1--R2--R3 (I'm using a "double-dash" symbol "--" to represent the series connection between resistors R1, R2, and R3), we see how the voltages measure successively larger (albeit negative) magnitudes, because the polarities of the individual voltage drops are in the same orientation (positive left, negative right). The sum of the voltage drops across R1, R2, and R3 equals 45 volts, which is the same as the battery's output, except that the battery's polarity is opposite that of the resistor voltage drops (negative left, positive right), so we end up with 0 volts measured across the whole string of components. That we should end up with exactly 0 volts across the whole string should be no mystery, either. Looking at the circuit, we can see that the far left of the string (left side of R1: point number 2) is directly connected to the far right of the string (right side of battery: point number 2), as necessary to complete the circuit. Since these two points are directly connected, they are electrically common to each other. And, as such, the voltage between those two electrically common points must be zero. Kirchhoff's Voltage Law (sometimes denoted as KVL for short) will work for any circuit configuration at all, not just simple series. Note how it works for this parallel circuit:

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Being a parallel circuit, the voltage across every resistor is the same as the supply voltage: 6 volts. Tallying up voltages around loop 2-3-4-5-6-7-2, we get:

Note how I label the final (sum) voltage as E2-2. Since we began our loop-stepping sequence at point 2 and ended at point 2, the algebraic sum of those voltages will be the same as the voltage measured between the same point (E2-2), which of course must be zero. The fact that this circuit is parallel instead of series has nothing to do with the validity of Kirchhoff's Voltage Law. For that matter, the circuit could be a "black box" -- its component configuration completely hidden from our view, with only a set of exposed terminals for us to measure voltage between -- and KVL would still hold true:

Try any order of steps from any terminal in the above diagram, stepping around back to the original terminal, and you'll find that the algebraic sum of the voltages always equals zero. Furthermore, the "loop" we trace for KVL doesn't even have to be a real current path in the closedcircuit sense of the word. All we have to do to comply with KVL is to begin and end at the same point in the circuit, tallying voltage drops and polarities as we go between the next and the last point. Consider this absurd example, tracing "loop" 2-3-6-3-2 in the same parallel resistor circuit:

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KVL can be used to determine an unknown voltage in a complex circuit, where all other voltages around a particular "loop" are known. Take the following complex circuit (actually two series circuits joined by a single wire at the bottom) as an example:

To make the problem simpler, I've omitted resistance values and simply given voltage drops across each resistor. The two series circuits share a common wire between them (wire 7-8-9-10), making voltage measurements between the two circuits possible. If we wanted to determine the voltage between points 4 and 3, we could set up a KVL equation with the voltage between those points as the unknown:

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Stepping around the loop 3-4-9-8-3, we write the voltage drop figures as a digital voltmeter would register them, measuring with the red test lead on the point ahead and black test lead on the point behind as we progress around the loop. Therefore, the voltage from point 9 to point 4 is a positive (+) 12 volts because the "red lead" is on point 9 and the "black lead" is on point 4. The voltage from point 3 to point 8 is a positive (+) 20 volts because the "red lead" is on point 3 and the "black lead" is on point 8. The voltage from point 8 to point 9 is zero, of course, because those two points are electrically common. Our final answer for the voltage from point 4 to point 3 is a negative (-) 32 volts, telling us that point 3 is actually positive with respect to point 4, precisely what a digital voltmeter would indicate with the red lead on point 4 and the black lead on point 3:

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In other words, the initial placement of our "meter leads" in this KVL problem was "backwards." Had we generated our KVL equation starting with E3-4 instead of E4-3, stepping around the same loop with the opposite meter lead orientation, the final answer would have been E3-4 = +32 volts:

It is important to realize that neither approach is "wrong." In both cases, we arrive at the correct assessment of voltage between the two points, 3 and 4: point 3 is positive with respect to point 4, and the voltage between them is 32 volts.

REVIEW: Kirchhoff's Voltage Law (KVL): "The algebraic sum of all voltages in a loop must equal zero"

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Section 5.3 Current divider circuits Let's analyze a simple parallel circuit, determining the branch currents through individual resistors:

Knowing that voltages across all components in a parallel circuit are the same, we can fill in our voltage/current/resistance table with 6 volts across the top row:

Using Ohm's Law (I=E/R) we can calculate each branch current:

Knowing that branch currents add up in parallel circuits to equal the total current, we can arrive at total current by summing 6 mA, 2 mA, and 3 mA:

The final step, of course, is to figure total resistance. This can be done with Ohm's Law (R=E/I) in the "total" column, or with the parallel resistance formula from individual resistances. Either way, we'll get the same answer:

Once again, it should be apparent that the current through each resistor is related to its resistance, given that the voltage across all resistors is the same. Rather than being directly proportional, the

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relationship here is one of inverse proportion. For example, the current through R1 is half as much as the current through R3, which has twice the resistance of R1. If we were to change the supply voltage of this circuit, we find that (surprise!) these proportional ratios do not change:

The current through R1 is still exactly twice that of R2, despite the fact that the source voltage has changed. The proportionality between different branch currents is strictly a function of resistance. Also reminiscent of voltage dividers is the fact that branch currents are fixed proportions of the total current. Despite the fourfold increase in supply voltage, the ratio between any branch current and the total current remains unchanged:

For this reason a parallel circuit is often called a current divider for its ability to proportion -- or divide - the total current into fractional parts. With a little bit of algebra, we can derive a formula for determining parallel resistor current given nothing more than total current, individual resistance, and total resistance:

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The ratio of total resistance to individual resistance is the same ratio as individual (branch) current to total current. This is known as the current divider formula, and it is a short-cut method for determining branch currents in a parallel circuit when the total current is known. Using the original parallel circuit as an example, we can re-calculate the branch currents using this formula, if we start by knowing the total current and total resistance:

If you take the time to compare the two divider formulae, you'll see that they are remarkably similar. Notice, however, that the ratio in the voltage divider formula is Rn (individual resistance) divided by RTotal, and how the ratio in the current divider formula is RTotal divided by Rn:

It is quite easy to confuse these two equations, getting the resistance ratios backwards. One way to help remember the proper form is to keep in mind that both ratios in the voltage and current divider equations must equal less than one. After all these are divider equations, not multiplier equations! If the fraction is upside-down, it will provide a ratio greater than one, which is incorrect. Knowing that total resistance in a series (voltage divider) circuit is always greater than any of the individual resistances, we know that the fraction for that formula must be Rn over RTotal. Conversely, knowing

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that total resistance in a parallel (current divider) circuit is always less then any of the individual resistances, we know that the fraction for that formula must be RTotal over Rn. Current divider circuits also find application in electric meter circuits, where a fraction of a measured current is desired to be routed through a sensitive detection device. Using the current divider formula, the proper shunt resistor can be sized to proportion just the right amount of current for the device in any given instance:

REVIEW: Parallel circuits proportion, or "divide," the total circuit current among individual branch currents, the proportions being strictly dependent upon resistances: In = ITotal (RTotal / Rn)

Section 5.4 Kirchhoff's Current Law (KCL) Let's take a closer look at that last parallel example circuit:

Solving for all values of voltage and current in this circuit:

At this point, we know the value of each branch current and of the total current in the circuit. We know that the total current in a parallel circuit must equal the sum of the branch currents, but there's more going on in this circuit than just that. Taking a look at the currents at each wire junction point (node) in the circuit, we should be able to see something else:

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At each node on the negative "rail" (wire 8-7-6-5) we have current splitting off the main flow to each successive branch resistor. At each node on the positive "rail" (wire 1-2-3-4) we have current merging together to form the main flow from each successive branch resistor. This fact should be fairly obvious if you think of the water pipe circuit analogy with every branch node acting as a "tee" fitting, the water flow splitting or merging with the main piping as it travels from the output of the water pump toward the return reservoir or sump. If we were to take a closer look at one particular "tee" node, such as node 3, we see that the current entering the node is equal in magnitude to the current exiting the node:

From the right and from the bottom, we have two currents entering the wire connection labeled as node 3. To the left, we have a single current exiting the node equal in magnitude to the sum of the two currents entering. To refer to the plumbing analogy: so long as there are no leaks in the piping, what flow enters the fitting must also exit the fitting. This holds true for any node ("fitting"), no matter how many flows are entering or exiting. Mathematically, we can express this general relationship as such:

Mr. Kirchhoff decided to express it in a slightly different form (though mathematically equivalent), calling it Kirchhoff's Current Law (KCL):

Summarized in a phrase, Kirchhoff's Current Law reads as such: "The algebraic sum of all currents entering and exiting a node must equal zero" That is, if we assign a mathematical sign (polarity) to each current, denoting whether they enter (+) or exit (-) a node, we can add them together to arrive at a total of zero, guaranteed. Taking our example node (number 3), we can determine the magnitude of the current exiting from the left by setting up a KCL equation with that current as the unknown value:

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The negative (-) sign on the value of 5 milliamps tells us that the current is exiting the node, as opposed to the 2 milliamp and 3 milliamp currents, which must were both positive (and therefore entering the node). Whether negative or positive denotes current entering or exiting is entirely arbitrary, so long as they are opposite signs for opposite directions and we stay consistent in our notation, KCL will work. Together, Kirchhoff's Voltage and Current Laws are a formidable pair of tools useful in analyzing electric circuits. Their usefulness will become all the more apparent in a later chapter ("Network Analysis"), but suffice it to say that these Laws deserve to be memorized by the electronics student every bit as much as Ohm's Law.

REVIEW: Kirchhoff's Current Law (KCL): "The algebraic sum of all currents entering and exiting a node must equal zero"

Section 5.5 Thevenin's Theorem Any combination of batteries and resistances with two terminals can be replaced by a single voltage source e and a single series resistor r. The value of e is the open circuit voltage at the terminals, and the value of r is e divided by the current with the terminals short circuited.

Thevenin's Theorem states that it is possible to simplify any linear circuit, no matter how complex, to an equivalent circuit with just a single voltage source and series resistance connected to a load. The qualification of "linear" is identical to that found in the Superposition Theorem, where all the underlying equations must be linear (no exponents or roots). If we're dealing with passive components (such as resistors, and later, inductors and capacitors), this is true. However, there are some components (especially certain gas-discharge and semiconductor components) which are

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nonlinear: that is, their opposition to current changes with voltage and/or current. As such, we would call circuits containing these types of components, nonlinear circuits. Thevenin's Theorem is especially useful in analyzing power systems and other circuits where one particular resistor in the circuit (called the "load" resistor) is subject to change, and re-calculation of the circuit is necessary with each trial value of load resistance, to determine voltage across it and current through it. Let's take another look at our example circuit:

Let's suppose that we decide to designate R2 as the "load" resistor in this circuit. We already have four methods of analysis at our disposal (Branch Current, Mesh Current, Millman's Theorem, and Superposition Theorem) to use in determining voltage across R2 and current through R2, but each of these methods are time-consuming. Imagine repeating any of these methods over and over again to find what would happen if the load resistance changed (changing load resistance is very common in power systems, as multiple loads get switched on and off as needed. the total resistance of their parallel connections changing depending on how many are connected at a time). This could potentially involve a lot of work! Thevenin's Theorem makes this easy by temporarily removing the load resistance from the original circuit and reducing what's left to an equivalent circuit composed of a single voltage source and series resistance. The load resistance can then be re-connected to this "Thevenin equivalent circuit" and calculations carried out as if the whole network were nothing but a simple series circuit:

. . . after Thevenin conversion . . .

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The "Thevenin Equivalent Circuit" is the electrical equivalent of B1, R1, R3, and B2 as seen from the two points where our load resistor (R2) connects. The Thevenin equivalent circuit, if correctly derived, will behave exactly the same as the original circuit formed by B1, R1, R3, and B2. In other words, the load resistor (R2) voltage and current should be exactly the same for the same value of load resistance in the two circuits. The load resistor R2 cannot "tell the difference" between the original network of B1, R1, R3, and B2, and the Thevenin equivalent circuit of EThevenin, and RThevenin, provided that the values for EThevenin and RThevenin have been calculated correctly. The advantage in performing the "Thevenin conversion" to the simpler circuit, of course, is that it makes load voltage and load current so much easier to solve than in the original network. Calculating the equivalent Thevenin source voltage and series resistance is actually quite easy. First, the chosen load resistor is removed from the original circuit, replaced with a break (open circuit):

Next, the voltage between the two points where the load resistor used to be attached is determined. Use whatever analysis methods are at your disposal to do this. In this case, the original circuit with the load resistor removed is nothing more than a simple series circuit with opposing batteries, and so we can determine the voltage across the open load terminals by applying the rules of series circuits, Ohm's Law, and Kirchhoff's Voltage Law:

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The voltage between the two load connection points can be figured from the one of the battery's voltage and one of the resistor's voltage drops, and comes out to 11.2 volts. This is our "Thevenin voltage" (EThevenin) in the equivalent circuit:

To find the Thevenin series resistance for our equivalent circuit, we need to take the original circuit (with the load resistor still removed), remove the power sources (in the same style as we did with the Superposition Theorem: voltage sources replaced with wires and current sources replaced with breaks), and figure the resistance from one load terminal to the other:

With the removal of the two batteries, the total resistance measured at this location is equal to R1 and R3 in parallel: 0.8 Ω. This is our "Thevenin resistance" (RThevenin) for the equivalent circuit:

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With the load resistor (2 Ω) attached between the connection points, we can determine voltage across it and current through it as though the whole network were nothing more than a simple series circuit:

Notice that the voltage and current figures for R2 (8 volts, 4 amps) are identical to those found using other methods of analysis. Also notice that the voltage and current figures for the Thevenin series resistance and the Thevenin source (total) do not apply to any component in the original, complex circuit. Thevenin's Theorem is only useful for determining what happens to a single resistor in a network: the load. The advantage, of course, is that you can quickly determine what would happen to that single resistor if it were of a value other than 2 Ω without having to go through a lot of analysis again. Just plug in that other value for the load resistor into the Thevenin equivalent circuit and a little bit of series circuit calculation will give you the result.

REVIEW:  Thevenin's Theorem is a way to reduce a network to an equivalent circuit composed of a single voltage source, series resistance, and series load.  Steps to follow for Thevenin's Theorem:  Find the Thevenin source voltage by removing the load resistor from the original circuit and calculating voltage across the open connection points where the load resistor used to be.  Find the Thevenin resistance by removing all power sources in the original circuit (voltage sources shorted and current sources open) and calculating total resistance between the open connection points.  Draw the Thevenin equivalent circuit, with the Thevenin voltage source in series with the Thevenin resistance. The load resistor re-attaches between the two open points of the equivalent circuit.  Analyze voltage and current for the load resistor following the rules for series circuits.

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Section 5.6 Norton's Theorem Norton's Theorem states that it is possible to simplify any linear circuit, no matter how complex, to an equivalent circuit with just a single current source and parallel resistance connected to a load. Just as with Thevenin's Theorem, the qualification of "linear" is identical to that found in the Superposition Theorem: all underlying equations must be linear (no exponents or roots). Contrasting our original example circuit against the Norton equivalent: it looks something like this:

. . . after Norton conversion . . .

Remember that a current source is a component whose job is to provide a constant amount of current, outputting as much or as little voltage necessary to maintain that constant current. As with Thevenin's Theorem, everything in the original circuit except the load resistance has been reduced to an equivalent circuit that is simpler to analyze. Also similar to Thevenin's Theorem are the steps used in Norton's Theorem to calculate the Norton source current (INorton) and Norton resistance (RNorton). As before, the first step is to identify the load resistance and remove it from the original circuit:

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Then, to find the Norton current (for the current source in the Norton equivalent circuit), place a direct wire (short) connection between the load points and determine the resultant current. Note that this step is exactly opposite the respective step in Thevenin's Theorem, where we replaced the load resistor with a break (open circuit):

With zero voltage dropped between the load resistor connection points, the current through R1 is strictly a function of B1's voltage and R1's resistance: 7 amps (I=E/R). Likewise, the current through R3 is now strictly a function of B2's voltage and R3's resistance: 7 amps (I=E/R). The total current through the short between the load connection points is the sum of these two currents: 7 amps + 7 amps = 14 amps. This figure of 14 amps becomes the Norton source current (INorton) in our equivalent circuit:

Remember, the arrow notation for a current source points in the direction opposite that of electron flow. Again, apologies for the confusion. For better or for worse, this is standard electronic symbol notation. Blame Mr. Franklin again! To calculate the Norton resistance (RNorton), we do the exact same thing as we did for calculating Thevenin resistance (RThevenin): take the original circuit (with the load resistor still removed), remove

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the power sources (in the same style as we did with the Superposition Theorem: voltage sources replaced with wires and current sources replaced with breaks), and figure total resistance from one load connection point to the other:

Now our Norton equivalent circuit looks like this:

If we re-connect our original load resistance of 2 Ω, we can analyze the Norton circuit as a simple parallel arrangement:

As with the Thevenin equivalent circuit, the only useful information from this analysis is the voltage and current values for R2; the rest of the information is irrelevant to the original circuit. However, the same advantages seen with Thevenin's Theorem apply to Norton's as well: if we wish to analyze load resistor voltage and current over several different values of load resistance, we can use the Norton equivalent circuit again and again, applying nothing more complex than simple parallel circuit analysis to determine what's happening with each trial load.

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REVIEW:  Norton's Theorem is a way to reduce a network to an equivalent circuit composed of a single current source, parallel resistance, and parallel load.  Steps to follow for Norton's Theorem:  Find the Norton source current by removing the load resistor from the original circuit and calculating current through a short (wire) jumping across the open connection points where the load resistor used to be.  Find the Norton resistance by removing all power sources in the original circuit (voltage sources shorted and current sources open) and calculating total resistance between the open connection points.  Draw the Norton equivalent circuit, with the Norton current source in parallel with the Norton resistance. The load resistor re-attaches between the two open points of the equivalent circuit.  Analyze voltage and current for the load resistor following the rules for parallel circuits.

Section 5.7 Thevenin-Norton Equivalencies Since Thevenin's and Norton's Theorems are two equally valid methods of reducing a complex network down to something simpler to analyze, there must be some way to convert a Thevenin equivalent circuit to a Norton equivalent circuit, and visa-versa (just what you were dying to know, right?). Well, the procedure is very simple. You may have noticed that the procedure for calculating Thevenin resistance is identical to the procedure for calculating Norton resistance: remove all power sources and determine resistance between the open load connection points. As such, Thevenin and Norton resistances for the same original network must be equal. Using the example circuits from the last two sections, we can see that the two resistances are indeed equal:

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Considering the fact that both Thevenin and Norton equivalent circuits are intended to behave the same as the original network in suppling voltage and current to the load resistor (as seen from the perspective of the load connection points), these two equivalent circuits, having been derived from the same original network should behave identically. This means that both Thevenin and Norton equivalent circuits should produce the same voltage across the load terminals with no load resistor attached. With the Thevenin equivalent, the opencircuited voltage would be equal to the Thevenin source voltage (no circuit current present to drop voltage across the series resistor), which is 11.2 volts in this case. With the Norton equivalent circuit, all 14 amps from the Norton current source would have to flow through the 0.8 Ω Norton resistance, producing the exact same voltage, 11.2 volts (E=IR). Thus, we can say that the Thevenin voltage is equal to the Norton current times the Norton resistance:

So, if we wanted to convert a Norton equivalent circuit to a Thevenin equivalent circuit, we could use the same resistance and calculate the Thevenin voltage with Ohm's Law. Conversely, both Thevenin and Norton equivalent circuits should generate the same amount of current through a short circuit across the load terminals. With the Norton equivalent, the short-circuit current would be exactly equal to the Norton source current, which is 14 amps in this case. With the Thevenin equivalent, all 11.2 volts would be applied across the 0.8 Ω Thevenin resistance, producing the exact same current through the short, 14 amps (I=E/R). Thus, we can say that the Norton current is equal to the Thevenin voltage divided by the Thevenin resistance:

This equivalence between Thevenin and Norton circuits can be a useful tool in itself, as we shall see in the next section.

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REVIEW:  Thevenin and Norton resistances are equal.  Thevenin voltage is equal to Norton current times Norton resistance.  Norton current is equal to Thevenin voltage divided by Thevenin resistance.

Section 5.8 Superposition Theorem Superposition theorem is one of those strokes of genius that takes a complex subject and simplifies it in a way that makes perfect sense. A theorem like Millman's certainly works well, but it is not quite obvious why it works so well. Superposition, on the other hand, is obvious. The strategy used in the Superposition Theorem is to eliminate all but one source of power within a network at a time, using series/parallel analysis to determine voltage drops (and/or currents) within the modified network for each power source separately. Then, once voltage drops and/or currents have been determined for each power source working separately, the values are all "superimposed" on top of each other (added algebraically) to find the actual voltage drops/currents with all sources active. Let's look at our example circuit again and apply Superposition Theorem to it:

Since we have two sources of power in this circuit, we will have to calculate two sets of values for voltage drops and/or currents, one for the circuit with only the 28 volt battery in effect. . .

. . . and one for the circuit with only the 7 volt battery in effect:

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When re-drawing the circuit for series/parallel analysis with one source, all other voltage sources are replaced by wires (shorts), and all current sources with open circuits (breaks). Since we only have voltage sources (batteries) in our example circuit, we will replace every inactive source during analysis with a wire. Analyzing the circuit with only the 28 volt battery, we obtain the following values for voltage and current:

Analyzing the circuit with only the 7 volt battery, we obtain another set of values for voltage and current:

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When superimposing these values of voltage and current, we have to be very careful to consider polarity (voltage drop) and direction (electron flow), as the values have to be added algebraically.

Applying these superimposed voltage figures to the circuit, the end result looks something like this:

Currents add up algebraically as well, and can either be superimposed as done with the resistor voltage drops, or simply calculated from the final voltage drops and respective resistances (I=E/R). Either way, the answers will be the same. Here I will show the superposition method applied to current:

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Once again applying these superimposed figures to our circuit:

Quite simple and elegant, don't you think? It must be noted, though, that the Superposition Theorem works only for circuits that are reducible to series/parallel combinations for each of the power sources at a time (thus, this theorem is useless for analyzing an unbalanced bridge circuit), and it only works where the underlying equations are linear (no mathematical powers or roots). The requisite of linearity means that Superposition Theorem is only applicable for determining voltage and current, not power!!! Power dissipations, being nonlinear functions, do not algebraically add to an accurate total when only one source is considered at a time. The need for linearity also means this Theorem cannot be applied in circuits where the resistance of a component changes with voltage or current. Hence, networks containing components like lamps (incandescent or gas-discharge) or varistors could not be analyzed. Another prerequisite for Superposition Theorem is that all components must be "bilateral," meaning that they behave the same with electrons flowing either direction through them. Resistors have no polarity-specific behavior, and so the circuits we've been studying so far all meet this criterion. The Superposition Theorem finds use in the study of alternating current (AC) circuits, and semiconductor (amplifier) circuits, where sometimes AC is often mixed (superimposed) with DC. Because AC voltage and current equations (Ohm's Law) are linear just like DC, we can use Superposition to analyze the circuit with just the DC power source, then just the AC power source, combining the results to tell what will happen with both AC and DC sources in effect. For now,

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though, Superposition will suffice as a break from having to do simultaneous equations to analyze a circuit.

REVIEW:  The Superposition Theorem states that a circuit can be analyzed with only one source of power at a time, the corresponding component voltages and currents algebraically added to find out what they'll do with all power sources in effect.  To negate all but one power source for analysis, replace any source of voltage (batteries) with a wire; replace any current source with an open (break).

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A-1 The Bread Board A-2 Soldering A-3 PCB Making A-3 Schematic Diagram of the DC Power Supply A-4 Block Diagram Of a Power Supply A-5 Block Diagram Of aTelevision Set A-6 Block Diagram of a cell phone model

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The Breadboard In general the breadboard consists of two terminal strips and two bus strips (often broken in the centre). Each bus strip has two rows of contacts. Each of the two rows of contacts are a node. That is, each contact along a row on a bus strip is connected together (inside the breadboard). Bus strips are used primarily for power supply connections, but are also used for any node requiring a large number of connections. Each terminal strip has 60 rows and 5 columns of contacts on each side of the centre gap. Each row of 5 contacts is a node. You will build your circuits on the terminal strips by inserting the leads of circuit components into the contact receptacles and making connections with 22-26 gauge wire. There are wire cutter/strippers and a spool of wire in the lab. It is a good practice to wire +5V and 0V power supply connections to separate bus strips. Fig 1. The breadboard. The orange lines indicate connected holes.

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Using Using the Breadboard (Socket Board)

The bread board has many strips of metal (copper usually) which run underneath the board. The metal strips are laid out as shown below.

These strips connect the holes on the top of the board. This makes it easy to connect components together to build circuits. To use the bread board, the legs of components are placed in the holes (the sockets). The holes are made so that they will hold the component in place. Each hole is connected to one of the metal strips running underneath the board. Each wire forms a node. A node is a point in a circuit where two components are connected. Connections between different components are formed by putting their legs in a common node. On the bread board, a node is the row of holes that are connected by the strip of metal underneath. The long top and bottom row of holes are usually used for power supply connections. The rest of the circuit is built by placing components and connecting them together with jumper wires. Then when a path is formed by wires and components from the positive supply node to the negative supply node, we can turn on the power and current flows through the path and the circuit comes alive. For chips with many legs (ICs), place them in the middle of the board so that half of the legs are on one side of the middle line and half are on the other side.

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Soldering The soldering is the basic work for electronic circuit engineering. I will introduce the tools for soldering below.The sufficient attention is necessary during work, because soldering handles a high temperature.Pay attention to the handling of the soldering iron sufficiently, because it becomes burn, fire more, carelessly.

Soldering iron Soldering iron is a necessary instrument when you solder. Solder is hardening in a normal temperature, but solder can melt easily by using the soldering iron and the parts and wiring materials can be fixed to the printed wiring board(PWB). The important piont is temperature of the soldering iron. For soldering, it needs to become the temperature of the object(PWB, parts, wire etc) to solder melting temperature. However, the temperature of soldering iron must not be too high. The electronic component gets damage with high temperature. So, you need to solder in a short time. Sometimes, the loose contact of soldering occurs. It is difficult to confirm only by looking at. When the temperature of the object is not enough, the loose contact will be occured. At the end of assembling of the electronic circuit, you need to check the soldered contact with circuit tester etc.

Electric power (Calorific (Calorific value is decided with this) There are various kind of soldering irons. I am using 3 kinds of soldering irons.

25W type I am usually using this type. This type is convenient when solder the parts on PWB.

80W type I use this type when I solder the parts to thick copper plate. In case of thick copper plate, the heat is easy to escape and the temperature rise is difficult.

15W type I use this type for the part which is easy to break by the heat. Usually, 25W type is enough.

The tip of iron

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The soldering is done at the tip of iron. So, the tip of iron is very important. There is the type that the tip of soldering iron is made of copper stick. But I don't recommend that type. Because, the copper stick rusts easily by heat and it becomes difficult to convey heat. Also the tip of copper stick melts with solder. It becomes difficult to sloder. I recommend the one that is using a special metal for tip. It is difficult to rust and melt. The tip of iron must keep clean. When it get dirty, it becomes difficult to convey heat. There are many shape of tips. The tip which fit to the DIP type IC is used to remove the ICs. All of the solder on the pins can be melt at same time then it easy to remove the IC. I do not have such kind of soldering iron. Usually the soldering iron is heated by electricity. However, there is the soldering iron heated by gas. It is convenient to carry.

Soldering iron stand The soldering iron becomes high temperature. Therefore it can't be placed on the desk directly. The stabilized soldering iron stand is necessary. When making the electronic circuit, sometime I forgot the existence of soldering iron, because I have devoted to the parts, wiring etc. It was serious when I noticed, desk was burning. You need to choose the iron stand with appropriate weight which can hold iron stably.Also you need to choose the iron stand that fit the form of iron. Usually I wipe the tip of iron with moistened sponge. Therefore I use the iron stand with the place for sponge. This is your taste.

Solder The solder is the alloy of lead and tin. As for good solder, the containment rate of tin is high. The finish of soldering is beautiful. The price is a little bit high. There are several kinds of solder, solder wire( thread form solder ) is convenient for electronic circuit making. This solder wire is doing the structure of the pipe and flux is included inside. Flux melts together with the solder and the solder becomes easy to attach to the component leads. There are some thickness of solder wire. I am usually

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using the one that diameter is 0.5 mm. The containment rate of the tin is 60%.

Solder sucker The failure of soldering occurs often. In this case, the part or the wiring must be removed. I will introduce the instruments that can be used for desoldering.

Solder pump This is the tool that can be absorbed the melted solder with the repulsion power of the spring that was built in with the principle of the piston. The usage is shown below. Pushe down the knob of the upper part of the pump against to spring until it is locked. Melt the solder of the part that wants to absorb solder with iron. Apply the nozzle of the pump to the melted solder part. Push the release knob of pump. Then the plunger of the pump is pushed up with the power of spring and solder is absorbed inside the pump. You need to do this operation quickly, otherwise the part gets damage by the heat. A little practice is needed.

Desoldering wire This is made of thin copper net wire like a screen cable in a coaxial cable. Like water inhales to cloth, the solder is absorbed to the net wire by a capillary tube phenomenon. The usage is shown below. Apply the desoldering wire to the part that wants to take solder. Apply the soldering iron from the top and Melt the solder. The melted solder is absorbed to desoldering wire with a capillary tube phenomenon. At this time you absorb solder while shifting desoldering wire. When the solder can not be removed in the once, remove repeatedly while shifting the desoldering wire. There are several kinds of width of desoldering wire. I am using the one with 2mm width.

Making PWB When assembling an electronic circuit, a board is needed on which the components can be mounted and wired together. Mainly, I use the universal prined wiring board (PWB) for assembling the circuit. But I will explain about instruments that makes the printed board.

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When you make the high frequency circuit, you need to consider the wiring length and the route of wiring etc. Therefore when you make the high frequency circuit ( radio, high speed CPU etc. ), you need to make the printed wiring board. In other countries, they are refered to as "Printed Circuit Boards," or PCBs. The printed board is doing the structure which stuck copper leaf on insulation board such as the epoxy material of glass or the epoxy material of paper or the material of bakelite. The copper leaf becomes a wiring part. There are 2 kinds of types in the printed board. They are single-sided printed board and double sided printed board. To make the printed wiring board, leaving the necessary(wiring part) place of the copper leaf, the unnecessary(insulate part) place is lost. This work is called Etching There are several method to make the printed board. Fundamentally the copper leaf is melted with the solution of the Ferric Chloride. The mask pattern is used to leave the wiring part. You can write the mask pattern directly on negative printed board with oily ink. Some ink is melted by solvent, then you had better to check beforehand. Even this method is good in the case that you make only 1 sheet. This time, I will introduce the method using positive exposure printed board as negative printed board. The sensitizer has been applied on negative printed board. The nature of the sensitizer when hit the light changes. Lighted part of sensitizer can melt to the developer and the part not lighted does not melt. The mask is made with the black color ink where the part that you want to leave the copper leaf. ( positive mask ) Dissolve the copper leaf is called Etching.

Etching liquid This is the solution of the Ferric Chloride(FeCl3·H2O).The Ferric Chloride is not the toxic substance, play thing, dangerous article that were regulated with the laws but the liquid that the copper of the printed board dissolved by the etching becomes a waste fluid regulation object.(in case of Japan) Even if it is a little it pours to sewerage and also do not bury during the soil. Processing medicine that is attached to etching liquid without fail is used or it must process it in the waste fluid processing place of the specialty. When liquid is attached to the clothes it is never able to take it. Do the attention to handling sufficiently, because the clothes have changed color. ( My experiences )

Avoid contact with eyes. If it enters to the eye it needs to wash away sufficiently with water right away.

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Battery driven mini drill

This is a mini drill that makes holes for mounting the parts on the printed board. For most of parts like resistor, cpacitor, the size of hole is about 0.6 mm.

Flux

The copper foil after removing the sensitizer becomes clean, but sheet copper is becoming bare condition then oxidization begins right away. Flux needs to be applied thinly to prevent oxidization. When flux is applied, you can make the copper leaf in clean condition forever. Also, you can carry out soldering easily.

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INTRODUCTION TO ELECTRONICS..................................................................1 Section 1.1 Electronics Safety ...................................................................................................................... 1 Section 1.2 Applications of Electronics....................................................................................................... 3 Job titles..................................................................................................................................................... 4 Exercise 1. Electronics safety comprehension exam............................................................................. 5

RESISTORS .........................................................................................................6 Section 2.1 Types of Resistors...................................................................................................................... 7 Carbon film resistors.................................................................................................................................. 7 Metal film resistors .................................................................................................................................... 8 CDS Elements............................................................................................................................................ 8 Other Resistors .......................................................................................................................................... 9 Thermistor ( Thermally sensitive resistor )................................................................................................ 9 Section 2.2 Resistor color code .................................................................................................................. 10 Exercise 2. Resistor Color Codes........................................................................................................ 12 Section 2.3 The Ohmmeter ........................................................................................................................ 13 Zero Resistance........................................................................................................................................ 13 Using the Ohmmeter................................................................................................................................ 14 Ohmmeter Ranges ................................................................................................................................... 14 Ohmmeter Safety Precautions ................................................................................................................. 15 Section 2.4 The Multimeter........................................................................................................................ 15 Multimeter Controls................................................................................................................................. 16 Multimeter Scales .................................................................................................................................... 16 Parallax Error........................................................................................................................................... 17 Multimeter Safety Precautions................................................................................................................. 18 Laboratory Experiment 1 Using the Ohmmeter .................................................................................. 19 Variable Resistors....................................................................................................................................... 20 Rheostats and Potentiometers .................................................................................................................. 20 Section 2.6 Rating of Resistors .................................................................................................................. 22 Section 2.7 Resistor Troubles .................................................................................................................... 22 Section 2.8 Resistor Connections............................................................................................................... 23 Series Combinations of Resistors ............................................................................................................ 23 Exercise 4 Resistors in Series ............................................................................................................. 26 Parallel Resistors ..................................................................................................................................... 27 Parallel Resistors - A Point to Remember ............................................................................................... 27 Exercise 5 Resistors in Parallel........................................................................................................... 28 Combinations of Resistors - Series/Parallel Circuits .............................................................................. 29 Exercise 5 Resistors in Parallel........................................................................................................... 31

OHM'S LAW .......................................................................................................36 What is Ohm’s Law? ............................................................................................................................... 36

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Section 3.1 Ohm’s Law Formula............................................................................................................... 37 OHM'S LAW SYMBOL SHORTCUT ................................................................................................... 37 Section 3.2 Application of Ohm’s Law ..................................................................................................... 38 TYPES OF CIRCUITS............................................................................................................................ 39 Section 3.3 Series Circuits.......................................................................................................................... 40 SERIES CIRCUIT CALCULATIONS.................................................................................................... 40 VOLTAGE DROP................................................................................................................................... 41 VOLTAGE DROP TOTAL..................................................................................................................... 42 VOLTAGE DROP CALCULATION...................................................................................................... 42 Section 3.4 PARALLEL CIRCUIT........................................................................................................... 43 Section 3.5 Series - Parallel Circuits ......................................................................................................... 46 Section 3.6 Voltmeters................................................................................................................................ 49 How to Use a Voltmeter .......................................................................................................................... 49 Section 3.7 Ammeters ................................................................................................................................. 53 Ammeter Connected in Series ................................................................................................................. 53 Effect on the Circuit being Measured ...................................................................................................... 54 Ammeter Sensitivity ................................................................................................................................ 55 Ammeter Ranges ..................................................................................................................................... 55 Range Selection ....................................................................................................................................... 57 Ammeter Safety Precautions ................................................................................................................... 58 Exercise 3. Problem Sets on Ohm’s Law............................................................................................ 59 Solutions to Exercise Number 3.......................................................................................................... 65

COMMON ELECTRONIC DEVICES ..................................................................73 Section 4.1 Transformer ............................................................................................................................ 73 Construction............................................................................................................................................. 73 Transformer Core..................................................................................................................................... 74 Section 4.2 Switch and Fuse....................................................................................................................... 75 Fuse.......................................................................................................................................................... 75 How to select a fuse in a circuit............................................................................................................... 76 Laboratory Experiment 3 Transformer Switch and Fuse Testing ....................................................... 79 Section 4.3 Semiconductor Diodes ............................................................................................................ 80 Introduction ............................................................................................................................................. 80 REVIEW:................................................................................................................................................. 83 Section 4.4 Meter check of a diode ............................................................................................................ 83 REVIEW:................................................................................................................................................. 86 Section 4.5 Rectifier circuits ...................................................................................................................... 87 Laboratory Experiment 4 Diode Biasing ............................................................................................ 90 Section 4.6 Capacitors ................................................................................................................................ 91 The unit of measurements of capacitance ................................................................................................ 91 Schematic symbols of a capacitor............................................................................................................ 92 Laboratory Experiment 5 Capacitor Action ........................................................................................ 93 Breakdown voltage .................................................................................................................................. 94

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Section 4.7 Different types of capacitors................................................................................................... 94 Electrolytic Capacitors (Electrochemical type capacitors) ...................................................................... 94 Tantalum Capacitors................................................................................................................................ 95 Ceramic Capacitors.................................................................................................................................. 95 Multilayer Ceramic Capacitors................................................................................................................ 96 Polystyrene Film Capacitors.................................................................................................................... 96 Electric Double Layer Capacitors (Super Capacitors) ............................................................................. 96 Polyester Film Capacitors........................................................................................................................ 97 Mica Capacitors ....................................................................................................................................... 98 Metallized Polyester Film Capacitors...................................................................................................... 98 Variable Capacitors ................................................................................................................................. 98 Characteristics of Capacitors ................................................................................................................... 99 Capacitor Connections........................................................................................................................... 100 Laboratory Experiment 6 Filtered Rectifier Circuits ........................................................................ 101 Section 4.8 Transistors ............................................................................................................................. 102 Introduction ........................................................................................................................................... 102 REVIEW:............................................................................................................................................... 103 Section 4.9 Meter check of a transistor................................................................................................... 104 REVIEW:............................................................................................................................................... 108

OTHER TECHNIQUES OF SOLVING VOLTAGE AND CURRENT VALUES .109 Section 5.1 Voltage divider circuits......................................................................................................... 109 Linear Potentiometer Construction ........................................................................................................ 113 REVIEW:............................................................................................................................................... 116 Section 5.2 Kirchhoff's Voltage Law (KVL) .......................................................................................... 116 REVIEW:............................................................................................................................................... 125 Section 5.3 Current divider circuits ........................................................................................................ 126 REVIEW:............................................................................................................................................... 129 Section 5.4 Kirchhoff's Current Law (KCL).......................................................................................... 129 REVIEW:............................................................................................................................................... 131 Section 5.5 Thevenin's Theorem.............................................................................................................. 131 REVIEW:............................................................................................................................................... 135 Section 5.6 Norton's Theorem ................................................................................................................. 136 REVIEW:............................................................................................................................................... 139 Section 5.7 Thevenin-Norton Equivalencies........................................................................................... 139 REVIEW:............................................................................................................................................... 141 Section 5.8 Superposition Theorem......................................................................................................... 141 REVIEW:............................................................................................................................................... 145

APPENDIX .......................................................................................................146 The Breadboard........................................................................................................................................ 147 Using the Breadboard (Socket Board) ................................................................................................... 148

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Soldering ................................................................................................................................................... 149 Soldering iron ........................................................................................................................................ 149 Electric power (Calorific value is decided with this)............................................................................. 149 The tip of iron ........................................................................................................................................ 149 Soldering iron stand ............................................................................................................................... 150 Solder..................................................................................................................................................... 150 Solder sucker ......................................................................................................................................... 151 Solder pump........................................................................................................................................... 151 Desoldering wire.................................................................................................................................... 151 Making PWB............................................................................................................................................. 151 Etching liquid ........................................................................................................................................ 152 Battery driven mini drill .......................................................................................................................... 153 Flux ............................................................................................................................................................ 153

Building skills for success