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VOCATIONAL TRAINING CENTRE BASIC TRAINING PROGRAM Electrical

MODULE E-01

ELECT.FUNDAMENTALS-1

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CHAPTER 1 MAGNETISM AND ELECTROMAGNETISM 1.1 MAGNETISM Long ago, in the Middle Ages, it was found that a mineral called 'lodestone', which is in fact an iron ore attracted small iron objects. So 'magnetism', which is a natural phenomenon, was discovered. It got its name from a district in Asia Minor called 'Magnesia' where lodestone was found. It was found too that an iron bar or needle, if rubbed with lodestone, could also be made to attract small pieces of iron - that is, the magnetism could be imparted from the lodestone to the iron. Such a needle, if placed on a wooden raft and left to float in a bowl of water, always tended to lie in a rough North to South direction. So we had the first primitive compass. At this stage it never occurred to anybody that there was any connection whatever  between magnetism and electricity, and it was left to Faraday to bring these two together in 'electromagnetism '.

1.2 ELECTROMAGNETISM , In 1820 Oersted discovered that an electric current flowing in a wire caused a magnetic field around it. This can easily be detected by placing a small compass near the wire and observing the movement 07 the needle when current is switched on. This is shown in Figure 1.1

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The effect can be intensified by bending the wire into a loop. The magnetic fields from each bit of the wire are brought together inside the loop, where the magnetic field is concentrated and intensified.

If now the wire is bent into several loops, or a 'helix', as shown in Figure. 1.2, the magnetic fields of each ‘turn' are superimposed, and the field down the middle is still further intensified. The result is a ‘coil' which, when current flows in it, produces an artificial magnet, called an 'electromagnet'. Unlike a natural magnet, whose magnetism is always present, an electromagnet can be switched on or off at will. If iron is introduced inside the coil, the magnetic strength is still further increased, and 'permanent' magnets can be made this way. Very powerful electromagnets can be built, which are widely used: they' can actuate solenoids or valves directly; they can drive any device needing a fore-and-aft motion; and they are used with cranes in scrap-yards for  picking up large weights of scrap-iron. On a smaller scale they are used to operate relays and switching devices. Although it may not at first seem so, solenoids and other electromagnets operate just as well with alternating as with direct current.

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CHAPTER-- 2 SIMPLE D.C. CIRCUIT - OHM'S LAW

2.1 VOLTS AND AMPS in an equivalent water circuit, the pump delivers a pressure (measured in psi, kgf/cm 2 or bars). and the water flow is measured in gal/min, or m3fs or other unit. 50 for an electric circuit. Pressure is measured in VOLTS (after Volta, the early Italian experimenter) and current in AMPERES (after an early French pioneer). Instruments are made which indicate pressures in volts and currents in amperes all switchboards have voltmeters and ammeters. On platforms and large installations pressures tend to be very high, involving thousands or tens of thousands of volts. In those cases the 'kilovolt' (equals one thousand volts) is usually taken as the unit of pressure. Thus on most Shell platforms the main generation pressure is 6.6kv, or 6.6 thousand volts, For  domestic appliances and small services 440 or 250 volts is usual on platforms and 415 or 240 volts ashore.

2.2 CURRENT FLOW - OHi\1'S LAW Once the units of pressure and current flow were established, a German experimenter named Georg Simon Ohm discovered a very important relationship between them. It has already been seen that some materials (mainly metals) allow electrons to move freely but not as freely as each other), whereas others do not do so and tend to resist such movement :- again some more so than others.

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Ohm discovered that, for a given sample of material, the current flowing / (in amperes) was directly proportional to the pressure applied V (in volts). In other  words, for that given sample. The ratio of voltage to current was constant:

v = const.

T This was true for anyone sample, but the constant itself differed from sample to sample. The ratio is called the 'resistance' of that sample, symbol R. it can be considered as opposition to the flow of electrons - like friction. Ohm's Law can then be stated:

V =R I

Or V = IR Where R is the resistance of the sample and differs from sample to sample. If V is measured in volts and 1 in amperes, R is measured in 'ohms'.

2.3 HEATING An important result stems from this. Since the resistance R of a conductor is akin to friction in the mechanical equivalent. it might be expected that loss of energy by heating might result from a current flow. This indeed is so. Whenever current is forced by pressure of voltage to flow through a conductor which has resistance and all conductors do, even metals), heat is generated in that, conductor. The rate of heat generation is proportional to the resistance (in ohms) and to the square of the current in amperes scuared). That is to say, the heat generated is L 2 R, and. since it represents continuing loss 07 energy, it is expressed in the energy-rate unit 'watts' (W). It is important to remember that current flowing in any conductor, be it cable, generator, motor or transformer, gives rise to heat. Which must be conducted away if the temperature is not to rise to a level witch can damage the insulation and possibly lead to flashover or breakdown and severe damage, or even danger to life. To reduce heJt generation either the current (I) or the resistance (R) must be reduced (for example, b,' increasing the cross-section or the conductor).

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CHAPTER. 3 RESISTANCES IN SERI ES AND PARALLEL 3.1 SERIES CIRCUITS The term 'in series' means that two or more circuits are supplied one after the other  in any single circuit, as shown diagrammatically in Figure 3.1.

Since there is only one single path from the power source through the circuits and back again, the same current flows through all. The voltage, or 'pressure', is reduced by resistance according to Ohm's Law: each circuit element causes a 'voltage drop' across it, very similar to the 'loss of head' due to fluid flow in a hydraulic system. Also the sum of the individual volt-drops is equal to the applied voltage. By Ohm's Law the volt-drop V 1 across the load R 1 is

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That is to say, the total resistance of a series circuit is equal to the sum of all the individual resistances. It is evident that the failure of any single component in a series circuit interrupts the supply to all; also that each element of load must work at a reduced voltage. For  these reasons the series arrangement of loads is seldom used in power circuits.

3.2 PARALLEL CIRCUITS The term 'in parallel' means that the circuits are so arranged that there is a separate path through each, as shown in Figure 3.2

The voltage applied to every circuit element is the same throughout. The total current divides  between the circuits according to the resistance of each of each element, so that the current flowing through each individual circuit is less than the total, and the sum of the of the currents flowing through the individual elements is equal to the total available current.

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By Ohm's Law the current L 1 flowing through the load R 1 is:

That is to say, the inverse of the equivalent resistance of a set of parallel circuits is equal to the sum of the inverses of each individual resistance. It is evident that for the' power engineer the parallel circuit has two important practical advantages. First, the failure of any element of load has no effect on the rest; they continue to receive a supply at the correct voltage and to draw the current which each individually requires. Second, all apparatus is supplied at the same voltage. Consequently, the parallel circuit is used almost exclusively for  power supply in industrial plant. It should be observed in passing that the characteristic of the series circuit, in which resistances in series have the effect of reducing the voltage at different points of the circuit, finds wide practical application in electronic apparatus such as radio, control, and 'solid-state' measuring equipment,

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IF R is R is the single resistance equivalent to a number of individual resistances R 1, R2, R3… then

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CHAPTER 4 ELECTROMAGNETIC INDUCTION

4,1 FARADAY'S LAW One day in 1837 Michael Faraday was working in his laboratory when by accident he dropped a magnet into a coil of wire which happened to be connected to a galvanometer. He noticed, to his surprise, that the galvanometer needle gave a kick when this happened. He was even more surprised to see, when he took the magnet out, that the needle kicked the other way. . This started a train of thought, which finally led to a monumental discovery, which was to become the whole basis of modern electrical engineering: it was the theory' of ‘Electromagnetic Induction'. .

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These are heavy words, but in short they mean that, if a conductor is moved in a magnetic field, then an 'electromotive force' (emf) - that is, a voltage - is induced in that conductor. This is shown in Figure 4.1. It follows that, if the ends of the conductor are connected to a load, then an electric current, driven by that voltage, will flow from the conductor, through the load and back again. Whereas Oersted had shown that an electric current moving in a wire gives rise to an artificial magnetic field, Faraday showed the opposite - that if a wire moves in a magnetic field an artificial charge, or voltage, will be created in that wire. Electricity and magnetism were now firmly tied together by these two great discoveries. Here then is the basis of electrical power generation. We start with a magnetic field, either a natural magnet or an artificial electromagnet of Oersted's type, and cause a conductor or a number of conductors to move past it. from which the current can be extracted as they are moving. Figure 4.1 shows 'Fleming's Right-hand Rule for Generators'. If the right hand is held with the thumb, forefinger and centre finger extended mutually at right angles as shown in the figure, then, with the magnetic field in the direction (North to South) pointed by the forefinger and the motion of the, conductor in the direction indicated by the thumb, the centre finger will point in the direction in which the emf  (i.e. voltage) is induced in that conductor (and in which current will flow when connected to a load). The magnitude of the voltage induced in the moving conductor depends on the strength of the magnetic field and the speed of movement, and on nothing else. Use is made of these laws and rules when considering the Principles of  Generation.

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CHAPTER 5 FORCES ON A CONDUCTOR 5.1 CURRENT.CARRYING CONDUCTOR IN A f'v1AGNETIC FIELD Figure 5.1 is similar to Figure 4.1 in that it shows a conductor in a magnetic field, but in this case there is a current from an external source being passed through that conductor.

The reaction between the current and the magnetic field through which it is passing causes a mechanical sideways force on the conductor. If the conductor is free to move, it will move sideways in the direction of the force. This is the basis of  operation of all electric motors. VTC

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There is for motors a 'Fleming's Left-hand Rule' corresponding to his Right-hand Rule for generators. If the left hand is held with the thumb, forefinger and centre finger extended mutually at right angles, then, with the magnetic field in the direction (North to South) pointed by the forefinger and the direction of current in the direction indicated by the centre finger I the thumb will point in the direction of  the mechanical force on the conductor (or of its motion if it is free to move). The magnitude of the force on the conductor depends on the strength of the magnetic field and the strength of the current, and on nothing else. Use is made of these laws and rules when considering the Principle of Operation of Motors,

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C HAPTE R. 6 INDUCTANCE 6.1 WHAT IS INDUCTANCE? Wherever a magnetic field is produced by an electric current passing through a circuit, that circuit displays the phenomenon of 'inductance'. Before looking at the effects of inductance on a D.C. circuit, it will be useful to see what is its nature by looking at a mechanical analogy.

Suppose there is a large grindstone with a turning handle (Figure 6.1). It is old, and its bearings are stiff and rusty, giving a lot of friction. If we try to turn the handle, even slowly, we must overcome this friction, causing heat and loss of energy at the bearings and making ourselves hot with the effort expended. But there is another type of opposition to our attempts to turn the wheel - its inertia. It is heavy, and in order to accelerate it we must not only overcome friction but also provide it with an accelerating force in order that it shall gather speed. The greater  the weight or inertia, the greater the force needed to accelerate. Also, the greater  the acceleration desired, the greater the force we must apply. (This is Newton's Second Law of Motion.) An electric circuit exhibits the same effects. It has resistance, and, in order for a current to flow, a pressure in the form of a voltage is needed to overcome it. But an electrical circuit has inertia too. It opposes, like the grindstone, any attempt to speed up the current or to cause it to grow. And the faster it has to grow, the greater the voltage needed to be applied, quite apart from that needed to VTC

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overcome resistance. This inertia in an electrical circuit is called 'inductance' and is due to the fact that any electric current causes magnetisation, and that effect is greatly increased by the presence of iron (which magnetises easily). Some circuits especially those without coils and without iron, have resistance but very little inductance. They are referred to as 'resistive circuits'. Others, which have coils, and especially those with iron such as generators, motors and transformers, have both resistance and considerable inductance. They are referred to as 'inductive circuits'. In the fairly rare cases where the resistance is so small that it can be neglected compared with the inductance (say the grindstone with ball bearings) the circuit is called 'purely inductive'. How inductance arises in a circuit due to its magnetisation and causes it to display electrical inertia, or 'sluggishness', is explained in the following paragraphs.

6.2 ' THE INDUCTOR (OR 'CHOKE') Faraday's Law of Electromagnetic Induction, as explained in Chapter 4 states that, if a conductor moves in a magnetic field, an emf (or voltage) is induced in it. Such movement need only be relative; it is equally true if the magnetic field moves past a stationary conductor. Movement implies change - that is to say, Faraday's Law applies also to any conductor around which the field is changing, that is, growing or decreasing.

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Suppose there were a coil of wire through which a current is flowing, as in Figure 6.2. Then, by Oersted's principle, there is a magnetic field concentrated along its axis. If now the current started to change - say to increase - the magnetic field through all the turns of the coil would also be increasing. This is then a changing field which, by Faraday's Law, induces in each turn an emf (or voltage), and its direction would be such as to oppose the change - that is, to try to prevent the current in this case increasing. What happens is shown diagrammatically in Figure 6.2. A voltage V is applied through a variable resistance R to the coil. For any given setting of R the current L through the coil (assumed to have no resistance of its own) is given by Ohm's Law:

V I = R If now R is decreased to R' with a view to increasing the current in the coil, the increasing current gives rise to an induced voltage E in the coil in a direction opposed to V. This induced voltage E is called the 'back-emf' of the coil. Consequently the net voltage appearing across R' is no longer V but is now (V - E), and, by Ohm's Law:

V-E I = Ŕ Although R has been reduced to R', 1 is not proportionately higher because E reduces the effective voltage. In other words, Ohm's Law does not seem to apply in this case. The back-emf E depends on the rate of change of current (~) through the coil and on the physical construction, including the number of turns, of the coil. It is written:

di E = dt As stated di / dt is the rate of change of current (positive if increasing), and L is a property of the coil. The minus sign indicates that its direction opposes the increasing current, so that E is then negative. L is called the 'inductance' of the coil; for any given coil it is a fixed quantity, but it differs From coil to coil. The presence of iron in the core increases L considerably. Inductance is measured in the unit 'henry' (H).

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A coil carrying electric current, especially one with an iron core, becomes thereby magnetised, and an electromagnet is a store of energy. The energy stored in a coil of inductance L (in henrys) and carrying a current L (in amperes) is: 1/2

L /2 (joules)

(Compare the kinetic energy of a mass m moving with velocity v; it is ½ mv 2.) If  ever the current in the coil is stopped, this energy has to be given up, in one form or another.

6.3 SWITCHING AN INDUCTIVE CIRCUIT WITH RESISTANCE A special case arises when a voltage is suddenly switched on to a circuit containing resistance R and an inductance L (assumed to have no resistance of its own). Before the switching no current at all was flowing. When the switch is closed the current starts to flow and tries to build up, but this change is opposed by a back-emf proportional to the rate of build-up and which reduces the effective voltage to (V - E). As the current increases, its rate of rise slows down; so therefore does the backemf E, and the net voltage (V - E) approaches nearer and nearer to V. Eventually the current levels off, and, since there is now no change, there is no back-emf, and the full voltage V appears across the resistance R, giving the steady current by Ohm's Law

V I = R

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This type of current rise, shown in Figure 6.3, is known as 'exponential' and. is found in all branches of physics where the rate of change depends on the amount already present. In this case, where a voltage is suddenly applied to a circuit containing inductance and resistance, the current rises, not suddenly, but at a reduced rate, or 'sluggishly', the rate falling off 'exponentially' until it finally settles down at a value given by Ohm's Law, namely I = V/R. In the discussion so far the coil has been assumed to be inductive but to have no resistance of its own (L but no R). In practice of course, all coils must have some resistance, but it is convenient to regard that resistance as separate from the purely inductive coil. One aspect of this treatment should be realised. Since the back-emf depends on the rate of change of current di/dt, any attempt to stop the current suddenly by opening the switch causes the rate di/dt to rise steeply towards infinity, and therefore a very large back-emf would be induced to oppose the change - it would be many times greater than the applied voltage V. This greatly increased voltage would appear across the open switch contacts (which could be regarded as a resistance of very high ohmic value) and would cause severe sparking or arcing at the switch contacts and possibly voltages dangerous to personnel.

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Therefore a d.c. inductive circuit of any size must never be simply broken by a switch. Special precautions must be taken, one of which is shown in Figure 6.4

The inductive coil, which in practice has some resistance of its own (R 1 ),  ), is shunted by another resistance (R 2   ). 2   In normal use the switch is closed and current flows in parallel through both the coil and the shunt resistance, the I 2  R 2  2  energy in the latter  being wasted as heat. When the switch is opened, the current already flowing in the coil, instead of being stopped, finds a backward path through R 2  2  and continues to circulate round the coil and the shunt resistance. Eventually the stored energy in the coil will be dissipated 2  2  in heat loss in both R 2   ), 2  and R  1 (= I  R  2  2  + I  R  2  2   and the current will fall exponentially to zero. The rate of change, even at the beginning, is therefore quite slow, so the back-emf is also low, and the voltage appearing across the switch contacts is quite small and causes little sparking - it is in fact only equal to the volt-drop IR 2  2  across the shunt resistance at the start. The slow decay of current in the coil may however  delay the release of whatever mechanism the coil is driving, such as the opening of  a solenoid-operated valve. A shunt resistance used in this way is often called a 'discharge resistance' because it discharges and dissipates the energy stored in the coil and reduces contact sparking. The greater its ohmic value the quicker the discharge of energy (i 2  R 2   ), 2   but the greater the 'spark voltage' (IR 2   ) appearing across the switch contacts. It is 2  always necessary to make a compromise, taking into account also the time delay for the coil's discharge.

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CHAPTER 7 CAPACITANCE

7.1 THE CAPACITOR A capacitor, or 'condenser' as it used to be called, is a device for storing electrostatic energy. In the early days, when the only sources of electricity were the electrostatic machines such as the Van der Graaf and Wimshurst, electrical energy so created was stored in 'Leyden Jars' for future use (Figure.7.1). For many years the property of capacitance was measured in the unit 'jar'.

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The modern condenser or capacitor is the direct descendent of the Leyden jar, and the modern unit of measurement is the 'farad' (F). The farad is however an extremely large unit, much too large for practical use, so the unit one-millionth of a farad, or one microfarad (µ F), is in general use. One jar is equal to about onethousandth of a microfarad (0.001 µ For 10 -9 F). Care is needed to distinguish between the following: Capacitor:

the actual device for storing the energy.

Capacitance:

the ability to store the energy, measured in µ F

The word 'capacity' should not be used in this connection.

The ability to store energy is best explained by looking at the construction of a capacitor. It consists of several parallel metal plates, in flat or cylindrical form, separated from a similar set of metal plates by a thin insulating substance such as glass, mica or paraffin-waxed paper. These insulating layers are called the 'dielectric'. When a potential difference (or voltage) is applied across each set of  plates, a strong electric field is set up between them through the thin dielectric. The closer the plates are together, the stronger the electric field. This field causes electric strain in the material of the dielectric, causing it to behave like a spring, which has been squeezed in a vice. When an external circuit is provided between the two sets of plates - say by a wire connecting them - this electric spring is released and gives up its energy. Although the property of capacitance is the principal reason for providing a capacitor, capacitance is found in many other places, often where it is not wanted. When it exists in this way it is called 'self-capacitance'. It is particularly noticeable in cables and overhead power lines, but it is also to be found in machine windings and transformers - in fact anywhere where conductors are arranged close to one another with a thin layer of insulation between. Self-capacitance exists not only between adjacent conductors but also between conductors and earth or cable -sheath.

7.2 CHARGE AND DISCHARGE OF CAPACITOR The mechanism of charge can best be understood by considering the mechanical analogy of Figure 7.2. .

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A large, rigid tank is completely full of water, which is regarded as incompressible. Down the middle is a flexible elastic membrane. One side of the tank is connected through a valve to a water supply under pressure, and the other to suction. Initially the valve is closed. Both sides of the membrane are at equal pressure and the membrane is undistorted. If  now the valve is opened and water admitted under  pressure, it will flow into the right side of the t4nk and out from the left side. The water movement through the tank itself, being over a wide cross-section, will be small compared with the movement of water in the pipes. As the water in the tank is displaced from right to left, so the membrane becomes distorted to the left and stretches, imposing increasing pressure on the right-hand side. Eventually, when the distortion is such as to produce a pressure equal to that of the incoming water, the water flow will cease. A definite volume of water will have entered the tank on the right-hand side, and an equal amount will have departed from the left. The stretched membrane will be in a state of elastic strain.

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The valve can now be closed, leaving the membrane in the position shown. The right side of the tank is under pressure and the static energy is stored in the stretched elastic membrane. Although the water can move in either direction through the external piping, in considerable quantity in the case of a large tank, there is no transfer of water within the tank across the membrane.

An electric capacitor (Figure 7.3) behaves in much the same way A d.c. Voltage is applied across the two plates of a capacitor by closing battery switch' A', so that one plate is at a higher potential than the other. The dielectric, which can be regarded as .an 'electrically compressible' substance, is subject to a strong electric field which puts it into a state of electric strain, just as the stretched membrane was in a state of mechanical strain. If the battery switch' A' is now opened, the capacitor will be left in that state of  strain - it is said to be 'charged' - and it will remain so until discharged or until it discharges itself by internal leakage. Some large oil-filled capacitors have been known to hold their full charge for many months. The current entering one side and leading the other side of the capacitor is the 'charging current', exactly akin to the water entering one side and leaving the other  side of the tank. If switch 'B' is now closed, the two plates are short-circuited together, and the charge on the positive plate is conveyed back to the negative, driven by the dielectric 'spring' unwinding. The stored energy has been released, and the dielectric has relaxed.

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The amount of energy that could be stored in the water tank analogy depended on the volume of water and the elastic properties of the membrane. In the case of a capacitor the amount of energy that can be stored depends on the total plate area, on their distance apart and on the electrical properties of the dielectric used. Taking these into account, the ability of any given capacitor to store electric energy is called its 'capacitance', symbol C. If the given capacitor has a capacitance of C farads, and a voltage V is applied across it, the amount of electrostatic energy stored is 1/2CV2

joules

(This should be compared with the magnetic energy 1/2L I 2  stored in an inductance (see Chapter 6), or with the kinetic energy 1/2mv 2 stored in a moving mass.) The water analogy showed that passing the water in and out through pipes and under pressure caused the tank to store energy, and on reversal to allow the stretched membrane to relax. Similarly passing a current into a capacitor 'charges' it and causes it to store electric energy; reversing that current discharges it and recovers the energy (Figure 7.4-).

The analogy can be taken a little further. If the water pump were reversed so that water enters the tank from the left and leaves it from the right, the membrane would simply stretch to the right until its pressure balanced the incoming pressure from the left. Similarly, if the charging current is reversed (Figure 7.4), the left plate of the capacitor would become positive and the right negative. The electric field across the dielectric would still be present but reversed in direction and would still be in a state of electric strain.

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So it is possible, in general, to charge a capacitor in either direction, and it will store the same amount of energy (depending on the voltage) in either case: this energy is 1/2CV 2 . An exception to this statement applies to electrolytic capacitors, which, for  chemical reasons, may not be reverse-charged. These capacitors consist of a single spiral aluminum foil coated with a very thin film of aluminum oxide, which acts as the dielectric. The electrolyte itself (ammonium borate) acts as the second 'plate' and makes contact with the metal case. The very thin dielectric film allows the 'plates' to come very close to each other and so to increase the capacitance greatly. In fact the electrolytic capacitor has a far greater capacitance, size for size, than the conventional type and is now widely used, especially in electronic circuits. However, any attempt to reverse the polarity will destroy the oxide film, and their  application is therefore limited. The polarity of such capacitors is clearly marked on them to prevent their reverse connection. One suitable use for them is for  smoothing a rectified a.c. circuit, where the d.c. Polarity is always maintained. Figure. 7.5 shows a capacitor, capacitance C, charging from a d .c. source V through a resistance R.

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When the switch is closed (Figure. 7.5(a)) the capacitor is at first without charge, which means that there is no potential difference, or voltage, across its plates. At the instant of closing therefore, the full applied voltage V appears across the resistance only, and, by Ohm's Law, the current I through it is V/R; this flows round the loop and into the capacitor and is therefore the initial charging current of the capacitor. After a short time (Figure, 7.5,fb)) the current has produced some charge in the capacitor - suppose it has acquired a voltage E. This must be in a direction to oppose the applied voltage V and to reduce its effectiveness; it is very similar to the back-emf in an inductance when the current is rising (see Chapter 8). The effective voltage trying to charge the capacitor is now reduced to (V - E), with E growing all the time. This is the voltage appearing across the resistor, so the charging current I is falling steadily. This is once again the classic case of the rate of charge depending on the amount present, which, as in the inductive case, gives an exponential voltage/time curve, as shown in Figure 7.5(c). The voltage-charge (E) on the capacitor rises exponentially until it eventually equals the applied voltage, at which point E = V, the charging current stops and the charge voltage remains steady at the value V.

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If a capacitor is charged, and is then switched to discharge through a resistance, the voltage would decay exponentially towards zero, and the discharge current would follow the same pattern (Figure--7.6).

7.3 CAPACITORS IN PARALLEL AND SERIES The behaviour of capacitors when placed in parallel or series is best explained by considering how the energy is disposed between them. Parallel If a voltage V is applied to, say, three parallel capacitors each of capacitance C, then the full voltage is applied to each, and the energy stored by each. is !/2CV 2 (Figure 7.71). The total energy stored by the three is therefore three times this, namely 3/2CV 2 .

If C' is the capacitance of the equivalent capacitor which stores the same total energy, then this energy will be 1/2C'V 2

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To generalise, the capacitance of a single capacitor equivalent to n in parallel is n times that of each individual capacitor, assuming that they are of equal value.

Series If a voltage V is V is applied to, say, three series capacitors each of capacitance C, then one-third of the applied voltage will appear across each (Figure 7.81). Therefore the energy stored by each is

The total energy of the three is therefore three times, or 1/6CV 2.

If C' is the capacitance of the equivalent capacitor which stores the same total energy, then this energy will be 1/2C'V 2 To generalise, the reciprocal capacitance of a single capacitor equivalent to n in

series is n times the reciprocal capacitance of each individual capacitor, assuming that they are of equal value. It should be noted that the equivalent capacitance of  series capacitors is smaller than that of the individual elements. VTC

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Summary The total capacitance of capacitors in parallel add directly:

But that of capacitors in series add inversely:

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CHAPTER 8 D.C. POWER 8.1 POWER UNITS Power is defined as the rate of using (or providing) energy and, in the electrical world, is measured in the unit 'watt' (W). In the mechanical world of hydraulics, power is the product of pressure and volume flow. In modern SI units pressure is measured in Newton’s per square metre (N/m2) and volume flow in cubic metres per second. The product of these two

The electrical equivalent- of pressure is the volt, and the electrical equivalent of  hydraulic flow is the ampere, so that the power in watts is the product of voltage and current - that is

Where V is V is measured in volts and I in I in amperes; W is W is then in watts.

These are two alternative forms for power when only I and R, or when only V and R, are known. In earlier years the power output of electric motors was measured in 'horsepower' to align them with mechanical engine practice. Many motor nameplates are still marked in 'hp', but more and more are now being marked in kilowatts (kW). The kilowatt used in this case is the equivalent of the mechanical power output of  the motor. Horsepower and kilowatts are directly related: 1 hp = 0.746kW (= 3AkW approximately)

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The horsepower in this case is British horsepower. (Some Continental countries use a slightly different unit, known as the 'metric horsepower', which is equivalent to 0. 735kW, a difference of about 1 1/2%.) Special care is needed when referring to the power of motors. Motors are rated by their mechanical output (hp or kW), but, because no motor is 100% efficient, its electrical power input, also measured in kW, is always greater than its mechanical power output. Because both may be measured in kilowatts. Confusion can easily arise. When it is desired to distinguish between mechanical output and electrical input, suffixes 'm' and 'e' are often used: thus output is kW m- and input kWe. Their  ratio is the efficiency of the motor, thus:

Power - that is, the rate of producing, absorbing or transmitting energy - is in the SI system always measured in watts or, more usually, kilowatts. It occurs in fields other than electricity and mechanics. For example energy can be produced thermally in boilers or reactors, or chemically in batteries or by burning fuel. The power being developed is still measured in kilowatts and would be distinguished by suffixes 'kW th ' or 'kWch '.

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CHAPTER 9 USEFUL FORMULAE

D.C. CIRCUITS AND OHM'S LAW

INDUCTANCE

CAPACITANCE

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RESISTANCES IN SERIES AND PARALLEL

D.C. POWER

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INTRODUCTION The aim of this unit is to explain the operation of a capacitor and an inductor when supplied with A.C. both individually and in combination with resistors.

A.C. AND THE INDUCTOR

The previous unit showed the effect of applying D.C. to an inductor. The back EMF across the inductor falls from maximum to zero and the current rises from zero to maximum. A.C. is a form of continuously switching D.C. The diagram and the graph (see Figure 6-1) show the effect of supplying A.C. to an inductor. The voltage waveform leads the current waveform by 90°. When the voltage is maximum the current is zero. When the current is maximum the voltage is zero and so on. The faster the A.C. changes (the higher the frequency) the greater the back EMF which is produced. The back EM F reduces the current. The alternating current resistance provided by the coil is called INDUCTIVE REACTANCE (XL) and is given by the formula XL = 2 π f L Ohms. XL = Inductive reactance (Ohms) L = Coil inductance in Henrys (H) f = Frequency in Hz π = Mathematical constant (3.142).

This formula must be remembered.

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A.C. AND THE CAPACITOR

The previous unit showed the effect of applying D.C. to a capacitor. The charging current starts at a maximum and falls to zero and the voltage across the capacitor  starts at zero and rises to a maximum. The effect is the exact opposite to an inductor. The diagram (see Figure 6-2) shows the effect of supplying A.C. to a capacitor. This time the graph shows the current leading the voltage by 90°. When the current is maximum the voltage is zero and so on. The faster the A.C. changes (the frequency) the less time the capacitor has to charge so the current through the device increases. The A.C. resistance (reactance) of a capacitor (Xc) goes down as the frequency goes up and is given by the formula.

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The Inductor-Resistor Combination

Figure 6-3 shows the series and parallel circuits of an RL combination. Calculating the unknown values of V s and Is is difficult because the current and voltage waveforms through the inductor are 90 0 apart.

A simple line diagram is used to illustrate the problem. From the diagram we get the following formulas. These must be remembered. The total A.C. resistance, IMPEDANCE (Z) for a series circuit is given by the formula:

The parallel circuit using the standard parallel formula is

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The Capacitor-Resistor Combination

Figure 6-4 shows the series and parallel circuits of an RC combination. The formulas for the total A.C. resistance (IMPEDANCE) of the above circuits follow the same principle as for the resistance and inductor circuits to give:

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RL and C in Combination

Figure 6-5 shows the series and parallel circuits for an RLC combination. In this case the reactance of the reactive parts oppose each other to give the formulas.

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Resonance When the value of X L equals the value of X C then XL – XC = 0. So the formula for  impedance changes to:

Therefore Z = R for both circuits This effect is called RESONANCE. At one frequency the circuit i: only resistive. At resonance;

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The frequency (f) is called the RESONANCE FREQUENCY of the circuit. It produces a circuit that is purely resistive. This circuit is useful because it is used to select one frequency from all others. A range of these circuits is used to select a television channel or radio station. Each channel transmits at a different frequency to stop interference. Let's take as an example the radio guide in the Gulf News. The parallel circuit used to get Dubai FM 92 will have a resonance frequency of 92 MHz, Capital Radio 100.5 MHz, Abu Dhabi 810kHz etc.

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SUMMARY OF IMPORTANT FORMULAS

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The simplest form of a capacitor. It consists of two conducting plates separated by an insulator (dielectric). When a voltage (V) is applied across the plates the insulator will take in a charge and produce an electric field between the plates. The charge (Q) taken in is given by this equation Q = CV C is called the CAPACITANCE of the device. The unit of measurement is the FARAD (F). Q The total charge stored has a unit called the COULOMB (C). V Is the voltage applied across the plates. Total charge is also given by the equation

Q = AMPS. SUPPLIED x SECONDS The electrostatic energy in a capacitor is given by the equation

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KIRCHHOFF'S LAWS Kirchhoff's laws are extensions of Ohm's law. You must remember them. They will be used in the next unit on series and parallel circuits: First Law

"The sum of electric currents flowing into a point (X) in an electrical circuit equals the sum of the electric currents flowing out of that point". Thus from Figure

I 1 + I2 = I3 + I4 Second Law "The sum of the voltages around a circuit must equal the supply EMF"

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SUMMARY OF IMPORTANT FORMULAS OHM'S LAW V = IR I=V/R R=V/I POWER = I V = I 2 R = V2/ R

Watts

ENERGY = AMPS x VOLTS x SECONDS

Joules

1 kWh = 3.6 MJ

KIRCHHOFF'S LAWS First Law: At a point in a circuit: Currents in = Currents out Second Law: Supply EMF = Sum 'of voltages around the circuit.

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BASIC ELECTRICITY AMMETER IN SERIES

CURRENT is the flow of electrons (negative charges). The symbol for current is I. Current flows from a negative potential to a positive potential but convention states that it flows from a positive potential to a negative potential. In this course we will use conventional flow. The unit of current is the ampere and the symbol for ampere is A. Current flows through a component. You measure the value of current through a component, by placing an ammeter in line (series) with the component.

VOLTMETER IN PARALLEL

VOLTAGE is the force that drives the current around a circuit. The symbol for  voltage is V. The unit of voltage is the volt and the symbol-for volt is V. If current flows through a component it creates a volt drop across that component You measure the voltage across a component by placing a voltmeter across (in parallel with) the component.

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RESISTANCE is the opposition to current flow around a circuit. The symbol for resistance is R. the unit of resistance is the ohm and the symbol for ohm is n. to measure resistance you turn the supply off and remove the component from the circuit. Then, and only then, can you connect an ohmmeter across the component.

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BASIC ELECTRICITY OHM'S LAW This states that the voltage across any resistor is proportional to the current flowing through that resistor. If you know two of the values the third can easily be found by using the formula-

V= I x R Remember that the voltage must be in volts, the current in amperes and the resistance in ohms. This formula is very important and you will use it often during this course.

POWER is the product of current and. voltage. Different components have different power ratings. The symbol for power is P. The unit of power is the watt and the symbol is W. To calculate power you need to know two of the other values. Remember when doing calculations to use the basic units (amps, volts and ohms).

Question A 10-kilohm resistor is connected across a 20-volt supply, how much current flows in the circuit? Answer

By Ohm's law I=V/R

V = 20 volt R = 10 000 ohms I = 20/10000 A

I = 0..002 A

I=2mA

Answer The current is 2 milliamperes

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ALTERNATING AND DIRECT CURRENT Direct Current is the current we get from a battery or cell. Direct current flows only in one direction. The abbreviation for direct current is dc and so to write six volts direct current you write 6 Vdc.

Alternating Current or ac changes its direction of flow continuously. It changes direction many times in one second. The rate at which it changes its direction is called the frequency. The abbreviation for frequency is f. The unit of frequency is the hertz, abbreviated to Hz. One hertz is the same as one change in direction every second.

Alternating current is usually in the shape of a sine wave (sinusoidal) but can be any shape, as long as it goes above and below zero. The waves shown have the same frequency as they go positive and negative at the same rate.

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It is possible to get pulsating dc. This current will go up and down but as it does not go through zero it is not ac.

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RESISTOR Most resistors today are colour coded. They have different colour bands on them that will tell us the value of resistance, Most have three bands for the value and a fourth band for  their tolerance. The tolerance tells you how near to the nominal value (the value as stated by the bands) the resistor should be. Resistors come in different power ratings, 1/8 W, 1/4 Wand 1/2 W being the most common.

When you connect resistors in series the total resistance increases. The total resistance of a series circuit is equal to the sum of the individual resistances.

If you connect them in parallel then the resistance will decrease. This is because there are more paths for the current in a parallel path and so the resistance to current flow decreases as you put more parallel branches. To find the resistance of  a parallel circuit the reciprocal rule is used.

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Before measuring resistance, turn the power off. Take the resistor out of circuit in case anything is in parallel with it. If there is anything in parallel you will get a low reading. Always start with your meter on the highest range and work down.

COLOUR BANDING

The diagram shows a colour coded resistor. The colour code is there to show you the resistance of the resistor. Reading from left to right, the first and seconds bands indicate a number, (eg. if the first colour band is 4 and the second colour  band is 7 then the number is 47). The third band is the multiplier in power form, (eg. 103). The fourth band indicates the tolerance of the resistor (eg. ± 5%). The numbers to match the colors are internationally fixed and are given below.

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WHEATSTONE BRIDGE The Wheatstone bridge is widely used in instrumentation to measure resistance accurately. It is also used to show changes in the resistance of sensors used to measure pressure, level, temperature, etc. The following notes explain the basic principle of the Wheatstone bridge. Practical applications will be shown later in the training.

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The Bridge Circuit

The Wheatstone Bridge

The Wheatstone bridge circuit consists of two very accurate (standard) resistors (R1, & R2) called the ratio arms. There is an accurate variable resistor (Decade Box R3). A very sensitive ammeter which will detect very small currents (called a Galvanometer (G)) is connected across points D and B. A supply voltage is connected across points A and C. There are also two terminals to connect an unknown resistor R x across the points A and B. The value of the unknown resistor is given by the equation.

The value of the unknown resistor is found by adjusting the value of the variable resistor until the galvanometer reads zero. This is called the balanced position so that at balance when I 3 = 0

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This is the balance equation for a Wheatstone bridge and must be remembered.

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SUMMARY OF IMPORTANT FORMULAS Resistors in Series Rt = R1 + R2 + R3 etc. Resistors in Parallel 1/ Rt = 1 / R1 + 1/ R 2 + 1/ R3 etc. Wheatstone Bridge Rx = Ratio Arms x Decade Box Value.

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INTRODUCTION The aim of this unit is to explain the operation of a capacitor and an inductor when supplied with A.C. both individually and in combination with resistors.

A.C. AND THE INDUCTOR

The previous unit showed the effect of applying D.C. to an inductor. The back EMF across the inductor falls from maximum to zero and the current rises from zero to maximum. A.C. is a form of continuously switching D.C. The diagram and the graph (see Figure 6-1) show the effect of supplying A.C. to an inductor. The voltage waveform leads the current waveform by 90°. When the voltage is maximum the current is zero. When the current is maximum the voltage is zero and so on. The faster the A.C. changes (the higher the frequency) the greater the back EMF which is produced. The back EMF reduces the current. The alternating current resistance provided by the coil is called INDUCTIVE REACT At-JCE (XL) and is given by the formula

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A.C. AND THE CAPACITOR

The previous unit showed the effect of applying D.C. to a capacitor. The charging current starts at a maximum and falls to zero and the voltage across the capacitor  starts at zero and rises to a maximum. The effect is the exact opposite to an inductor. The diagram (see Figure 6-2) shows the effect of supplying A.C. to a capacitor. This time the graph shows the current leading the voltage by 90°. When the current is maximum the voltage is zero and so on. The faster the A.C. changes (the frequency) the less time the capacitor has to charge so the current through the device increases. The A.C. resistance (reactance) of a capacitor (Xc) goes down as the frequency goes up and is given by the formula.

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The Inductor-Resistor Combination

Figure 6-3 shows the series and parallel circuits of an RL combination. Calculating the unknown values of V s and Is is difficult because the current and voltage waveforms through the inductor are 90 0 apart.

A simple line diagram is used to illustrate the problem. From the diagram we get the following formulas. These must be remembered. The total A.C. resistance, IMPEDANCE (Z) for a series circuit is given by the formula:

The parallel circuit using the standard parallel formula is

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The Capacitor-Resistor Combination

Figure 6-4 shows the series and parallel circuits of an RC combination. The formulas for the total A.C. resistance (IMPEDANCE) of the above circuits follow the same principle as for the resistance and inductor circuits to give:

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RL and C in Combination

Figure 6-5 shows the series and parallel circuits for an RLC combination. In this case the reactance of the reactive parts oppose each other to give the formulas.

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Resonance When the value of X L equals the value of X C then XL – XC = 0. So the formula for  impedance changes to:

Therefore Z = R for both circuits This effect is called RESONANCE. At one frequency the circuit i: only resistive. At resonance;

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The frequency (f) is called the RESONANCE FREQUENCY of the circuit. It produces a circuit that is purely resistive. This circuit is useful because it is used to select one frequency from all others. A range of these circuits is used to select a television channel or radio station. Each channel transmits at a different frequency to stop interference. Let's take as an example the radio guide in the Gulf News. The parallel circuit used to get Dubai FM 92 will have a resonance frequency of 92 MHz, Capital Radio 100.5 MHz, Abu Dhabi 810kHz etc.

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SUMMARY OF IMPORTANT FORMULAS

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THE ELECTRIC CURRENT AND MAGNETIC FIELDS When a current is passed through a conductor it will produce a magnetic field, as shown in the diagram.

The magnetic field around a conductor can be increased by increasing the current. However, a better method of increasing the magnetic field produced by electricity is to make a solenoid. A solenoid is made by coiling insulated wire around a cylinder. The greater the number of turns in the coil, the greater the magnetic field produced (see Figure 3-1).

When a current is passed through the coil, the magnetic field is concentrated. This field has a pattern similar to a bar magnet with N and S poles as shown.

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The Solenoid Valve The solenoid valve is an on-off device used to control the flow of liquids and gases through piping. When the supply voltage is applied to the coil, the solenoid is energised. It attracts the valve plunger and the valve opens. When the solenoid is de-energised the return spring closes the valve. A typical solenoid valve is shown

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SOLENOID APPLICATIONS The Relay A typical relay is shown

The relay consists of a solenoid and contacts. When the solenoid is energised it attracts a piece of iron (the armature) which changes over a set of contacts. The magnetic core of the solenoid is made of a material, which is magnetic only when current flows, through the coil (a temporary magnet). When the coil de-energises the return spring pulls the armature back and the contacts return to their normal positions. Relays operate using A.C or D.C supplies. The coils have many turns of  small diameter insulated wire. This gives a strong magnetic field from a small energising current.

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INTRODUCTION Explained the rules to be used when dealing with resistive circuits. The calculations can be carried out using either D.C. values or A.C RMS. Values. The results will be the same. This is not true when inductors and capacitors are included in a circuit. This unit will explain what happens when D.C is applied to an inductor and capacitor.

D.C AND THE INDUCTOR

Figure 5-1 shows D.C applied to an inductor via a switch. The graph below shows what happens when the. Switch is closed.

At the moment the switch is closed the build up of the magnetic field in the coil produces a back EMF which opposes the applied EMF. The starting current is zero. When the magnetic field is steady the back EMF is zero. The current is a maximum and is limited only by the winding resistance of the coil. The time it takes to reach maximum current flow depends flow depends on the ratio of the coil inductance to its

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winding resistance. Because of this effect relay coils and the solenoids of  electrically operated valves have increased resistance. This reduces excessive hold on currents. If the switch is open the field in the coil collapses and a high voltage is produced. When the switch is open this high voltage can destroy the switch contacts by sparking. Therefore special circuits must be used to protect the switch and the connected supply voltages. These circuits will be explained in Industrial Electronics II. Note: 1. The above principle is used to ignite the fuel of a gasoline engine. The voltage produced when the circuit of an energised coil is broken is used to make a spark across the plug fitted in the cylinder. 2. An energised coil stores energy in a magnetic form. The energy stored is given by the equation

W = 1/2 L I 2

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D.C. AND THE CAPACITOR

Figure 5-2 shows D.C applied to a capacitor. Switch A closed and switch B open charges--the capacitor. Switch A open and Switch B closed discharges tt1e capacitor. The graph below shows what happens when the switches are operated.

Circuit Operation Charging:

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When switch A is first closed the current flow into the capacitor is only limited by the loss resistance of the insulator. As the capacitor charges the current flow will fall to zero and the voltage across the capacitor will equal the supply voltage. This means that a charged capacitor is an open circuit to D.C. Discharging: When switch 8 is closed the discharge current is in the opposite direction to the charging current. It will start at maximum and then fall to zero as the capacitor  voltage falls to zero.

CAPACITOR TIMING CIRCUITS The capacitor is often used in electronics as a timing circuit. An explanation of the basic principle is given in Figure 5-3. We will look at how this circuit can be used during more advanced work in later units.

Figure 5.3 shows a basic timing circuit using the voltage across the capacitor (C). The switch is closed and when the voltage (V) rises to a set value the timing unit operates. It is normal to use what is called the time constant for the circuit. The time constant is given by the equation. TIME CONSTANT (T) (SECONDS)

=

RESISTANCE (R) (OHMS)

x

CAPACITANCE (C) (FARADS)

The voltage across the capacitor will be 63.2% of the D.C supply voltage at the time constant (T = RC).

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Example Question: A 1 MQ resistor is connected in series with a 100 μF capacitor and supplied with D.C. Find the time taken for the capacitor to reach 63.2% of its maximum value after the supply is switched on. Solution: The time to reach 63.2% of the supply voltage is the time constant of the circuit RC.

T.C = 1 X 10 6 Ω x 100 x 10 -6F Time Constant = 100 seconds.

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