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ABSTRACT The last experiment the team conducted was all about the two basic types of connecting electrical components: series and parallel circuits. The behavior of the three components of a simple circuit namely the voltage, current, and resistance were carefully analyzed and studied under the two types of electric circuits. An electric circuit is any arrangement of materials that permits electrons to flow. This study is very important in many areas in the industry as all modern machines make use of electricity. In this paper, we verified the relationship that exists between the three fundamental components of an electric circuit. By understanding the principle suggested by the Ohm’s Law, the team gathered numerical evidences by using suitable instruments to measure the quantities directly and compare it with the equation suggested by the Ohm’s law. The team established a model circuit to represent the two types of circuits. This paper limits itself only to the idea of the Ohm’s Law about the relationship between the quantities. Its degree of accuracy is high because the quantities gained are near to the true value. INTRODUCTION We live in a modern world where almost everything is run by electricity. Electricity is governed by the three fundamental components: resistance, current, and voltage. They are always part of simple circuits. A series circuit is one in which the current has only one path to takefrom one side of the source through the load, and back to the other side of the source. On the other hand, a parallel circuit is characterized by all the loads working at the same voltage and the source and independent of one another. The relationship that exists between current, resistance, and voltage is governed by the Ohm’s Law. Ohm's law states that the current through a conductor between two points is directly proportional to the potential difference across the two points holding the temperature constant. Introducing the constant of proportionality, the resistance, one arrives at the usual mathematical equation that describes this relationship:

where I is the current through the conductor in units of amperes, V is the potential difference measured across the conductor in units of volts, and R is the resistance of the conductor in units of ohms. More specifically, Ohm's law states that the R in this relation is constant, independent of the current. The law was named after the German physicist Georg Ohm, who described

measurements of applied voltage and current through simple electrical circuits containing various lengths of wire. According to Ohm’s law, in series circuits, the current is constant among the loads whereas the total voltage is the summation of all the voltage in each load. The overall resistance is also the sum total of the individual resistance between the loads. According to Ohm’s law, in parallel circuits, the voltage is constant among the loads whereas the total current is the summation of all the current in each load. The reciprocal of the overall resistance is the sum total of the reciprocals of the individual resistance between the loads. The objectives of this experiment are the following: 1. To determine the total current flowing through a series and parallel circuit. 2. To determine the voltage across each resistors and the current flowing through a series and parallel circuit. 3. To investigate the relationship between voltages across each resistor and the total voltage. 4. To investigate the relationship between current flowing through each resistor and total current. MATERIALS AND METHODS Materials: 3 pc Resistance Boxes 5 pcs 1.2 Batteries

12 pcs Connecting wires 1 pc VOM 1 pc Ammeter

Fig-306-1 Materials Used Methods: A.Resistors in Series 1. Connect the 5 batteries as shown below. Fig-306-2 Primary Set-up 2. Using three resistors, build the circuit by connecting the wires. Fig-306-1 Connecting the wire to the resistor 3. Connect the VOM across the resistors one at a time to measure the voltages: Fig-306-3 Getting the voltage Note: In measuring voltage turn the selector knob so that it points to the desired range of voltage. 4. Connect the VOM to the circuit at the following points: A, B, C, D. Note: In measuring the current turn the knob selector knob so that it points to the desired range of current. Fig-306-4 Measuring the current by ammeter 5. Determine the equivalent resistance. 6. Compute the value of the total current flowing through the circuit and the current flowing through each resistor and voltages across each resistor using equivalent resistance and the measured voltage ( across the batteries. (Use Ohm’s Law and rules for series circuit. B.Resistors in Parallel 1. Connect the 5 batteries as shown below. Fig-306-5 Primary set-up for parallel 2. Using three resistors, build the circuit by connecting the wires as shown. 3. Connect the VOM across the resistors one at a time to measure the voltages: Fig-306-6 Getting the voltage for parallel Note: In measuring voltage turn the selector knob so that it points to the desired range of voltage.

4. Connect the VOM to the circuit at the following points: A, B, C, D. Note: In measuring the current turn the knob selector knob so that it points to the desired range of current. Fig-306-7 Getting the current by ammeter 5. Determine the equivalent resistance. 6. Compute the value of the total current flowing through the circuit and the current flowing through each resistor and voltages across each resistor using equivalent resistance and the measured voltage ( across the batteries. (Use Ohm’s Law and rules for parallel circuit.

RESULTS & GRAPHICAL ANALYSIS A. Resistors in Series Resistance 1 (R1), Ω

100

Resistance 2 (R2), Ω

93

Resistance 3 (R3), Ω

57

Total Resistance (RT), Ω

250

Total Voltage (VDA), V

6.214

TABLE 1: SERIES CIRCUIT Voltage Across Resistance 1 (VAB), V Voltage Across Resistance 2 (VBC), V Voltage Across Resistance 3 (VCD), V Current Flowing through Resistance 1, (iB), A Current Flowing through Resistance 2, (iC), A Current Flowing through Resistance 3, (iD), A Total Current, (iA) Percentage Difference

Experimental

Computed

2.48

2.486

2.32

2.312

1.414

1.417

0.024

0.025

0.024

0.025

0.024

0.025

0.024

0.025

3.504

If we try to ponder on the results gathered from the experiment, we can see that the voltage from the first resistor is different from the second and of the thirst resistor. We can observe that the voltage is decreasing as we move from one resistor to the next. This implies that the total

voltage coming out from the source which is the battery is distributed unequally to its loads or resistors. On the other hand, we can see that the current flowing though each load is the same throughout. The team also found out that the total current is the same as the total current of the

system.

Using

the

equation

the

load, we can see that the current flowing in each load is different meaning the total current of the system is distributed through the loads. If we try to compare the experimental values from that of the computed values from the equation, we can see an almost negligible difference between the values.

computed values were computed and we can see that they are very near from the values gathered from the experiment.

For SERIES constant)

B. Resistors in Parallel 84

Resistance 2 (R2), Ω

27

Resistance 3 (R3), Ω

153

Total Resistance (RT), Ω

100 50 0

5.47

1.414

TABLE 2: PARALLEL CIRCUIT

Total Current, (iA) Percentage Difference

2.32

2.48

Voltage

Experimental

Computed

5.46

5.47

5.46

5.47

5.47

5.47

0.06

0.065

The graph above shows the relationship between voltage and resistance if we held the current constant. The voltage and the resistance are directly proportional. If the resistance is higher, the higher will be the voltage needed. For PARALLEL CONNECTION (voltage is constant)

0.19

0.203

Current vs Resistance

0.034

0.036

0.29

0.303

4.537

On the other side of the line, the results gathered from the parallel circuit makes an opposite as the behavior of the parameters in the series circuit. In here, we can see that the voltages in each of the loads or resistors are the same meaning it is constant. If we try to analyze the results gathered from the current flowing through each

200

Resistance

Voltage Across Resistance 1 (VAB), V Voltage Across Resistance 2 (VBC), V Voltage Across Resistance 3 (VCD), V Current Flowing through Resistance 1, (iB), A Current Flowing through Resistance 2, (iC), A Current Flowing through Resistance 3, (iD), A

is

150

18.02524544

Total Voltage (VEA), V

(current

Voltage vs Resistance Resistance

Resistance 1 (R1), Ω

CONNECTION

150 100 50 0 0.06

0.19

0.034

Current The graph above shows the relationship between current and resistance if we held the voltage constant. . The current and the resistance are

inversely proportional. If the resistance is higher, the lower will be the current needed and vice versa. Thus, we can conclude that the behavior of the parameters current and voltage in series and parallel circuits are exactly opposite with one another. DISCUSSION & SOURCES OF ERRORS The results of the experiment tell us that resistance, current and voltage has a relationship depending on what type of circuit is it either parallel or series circuit.

In a series circuit it is found that the current here is constant and the voltage and resistance are directly proportional to each other. While in a parallel circuit it is found that voltage is constant and the resistance and current are inversely proportional to each other. The concept of series and parallel circuits shows us the basic electrical engineering concepts showing the difference of the series circuit from the parallel circuit and the relationship between the parameters involved in the Ohm’s Law. A series circuit is a circuit having a constant flow of current throughout the path but having a variable individual voltage that will depend on the number of the resistors present. We can say that the resistance is directly proportional to the voltage while maintaining the flow of current constant. We can also conclude that the resistance is a load when the amount of load increases the flow of current the voltage must also increase to keep the flow of electricity. It was found evident that the series circuit is not good for home used since the total current is equal to the individual. On the other side of the line, the parallel circuit is a circuit where the total voltage used is equal to the individual voltage used and the flow of current is varying depending on the values of the resistors. The total resistance is the reciprocal of the sum of the reciprocal of the individual resistance. In this particular circuit we can say that the resistance is indirectly proportional to the flow of current, as the resistance increases the individual current

decreases. Comparing the two types of basic circuits we can say that parallel circuit is more convenient and appropriate to use because it uses different current that is why when one of the current is zero ampere other current will not be affected resulting to a continuous flow of electricity. Sources of errors: The temperature of the working environment may not be constant. The flow of electricity inside the wire already consumed electricity. The reading from the ammeter and VOM might be incorrect. To study the basics of electricity are very important to almost all field in the industry especially now that we are at a modern age. The idea of electric circuits make it possible for engineers and designers to build macro and micro engineering systems such as the installation of electric wiring in a building up to the smallest design of a microchip used in computers. ACKNOWLEDGMENT & REFERENCE To the following who had helped me finish this paper, I would like to thank: To God, for giving us the wisdom and to understand more of his fine creations especially the sound that makes life more beautiful. To my friend Bryan, for letting me use his internet connection for the online resources. To my groupmates, for their help and teamwork that made our experiment successful. To my blockmates Alex, Christian, Leif, Marc, and Airyl, for helping me find a source from the internet. To Prof. Ricardo F. De Leon Jr., for assisting and mentoring us during the laboratory hours. To the two laboratory assistants, Mang Gerry and Mang Jose, for being so friendly in lending us the tools and guiding us regarding its proper usage. To my previous Physics highschool teacher, Mrs. Gonzales, for teaching me a lot about electricity. Thank you very much. To God be the Glory! [1]Young, Hugh D., et al. University Physics With Modern Physics. Jurong, Singapore

6297733: Pearson Education South Asis Pte Ltd,,2008. [2]http://en.wikipedia.org/wiki/Ohm's_law [3]http://en.wikipedia.org/wiki/Series_and_parall el_circuits [4]http://www.allaboutcircuits.com/vol_1/chpt_5 /1.html [5]http://en.wikipedia.org/wiki/Ohm's_law

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where I is the current through the conductor in units of amperes, V is the potential difference measured across the conductor in units of volts, and R is the resistance of the conductor in units of ohms. More specifically, Ohm's law states that the R in this relation is constant, independent of the current. The law was named after the German physicist Georg Ohm, who described

measurements of applied voltage and current through simple electrical circuits containing various lengths of wire. According to Ohm’s law, in series circuits, the current is constant among the loads whereas the total voltage is the summation of all the voltage in each load. The overall resistance is also the sum total of the individual resistance between the loads. According to Ohm’s law, in parallel circuits, the voltage is constant among the loads whereas the total current is the summation of all the current in each load. The reciprocal of the overall resistance is the sum total of the reciprocals of the individual resistance between the loads. The objectives of this experiment are the following: 1. To determine the total current flowing through a series and parallel circuit. 2. To determine the voltage across each resistors and the current flowing through a series and parallel circuit. 3. To investigate the relationship between voltages across each resistor and the total voltage. 4. To investigate the relationship between current flowing through each resistor and total current. MATERIALS AND METHODS Materials: 3 pc Resistance Boxes 5 pcs 1.2 Batteries

12 pcs Connecting wires 1 pc VOM 1 pc Ammeter

Fig-306-1 Materials Used Methods: A.Resistors in Series 1. Connect the 5 batteries as shown below. Fig-306-2 Primary Set-up 2. Using three resistors, build the circuit by connecting the wires. Fig-306-1 Connecting the wire to the resistor 3. Connect the VOM across the resistors one at a time to measure the voltages: Fig-306-3 Getting the voltage Note: In measuring voltage turn the selector knob so that it points to the desired range of voltage. 4. Connect the VOM to the circuit at the following points: A, B, C, D. Note: In measuring the current turn the knob selector knob so that it points to the desired range of current. Fig-306-4 Measuring the current by ammeter 5. Determine the equivalent resistance. 6. Compute the value of the total current flowing through the circuit and the current flowing through each resistor and voltages across each resistor using equivalent resistance and the measured voltage ( across the batteries. (Use Ohm’s Law and rules for series circuit. B.Resistors in Parallel 1. Connect the 5 batteries as shown below. Fig-306-5 Primary set-up for parallel 2. Using three resistors, build the circuit by connecting the wires as shown. 3. Connect the VOM across the resistors one at a time to measure the voltages: Fig-306-6 Getting the voltage for parallel Note: In measuring voltage turn the selector knob so that it points to the desired range of voltage.

4. Connect the VOM to the circuit at the following points: A, B, C, D. Note: In measuring the current turn the knob selector knob so that it points to the desired range of current. Fig-306-7 Getting the current by ammeter 5. Determine the equivalent resistance. 6. Compute the value of the total current flowing through the circuit and the current flowing through each resistor and voltages across each resistor using equivalent resistance and the measured voltage ( across the batteries. (Use Ohm’s Law and rules for parallel circuit.

RESULTS & GRAPHICAL ANALYSIS A. Resistors in Series Resistance 1 (R1), Ω

100

Resistance 2 (R2), Ω

93

Resistance 3 (R3), Ω

57

Total Resistance (RT), Ω

250

Total Voltage (VDA), V

6.214

TABLE 1: SERIES CIRCUIT Voltage Across Resistance 1 (VAB), V Voltage Across Resistance 2 (VBC), V Voltage Across Resistance 3 (VCD), V Current Flowing through Resistance 1, (iB), A Current Flowing through Resistance 2, (iC), A Current Flowing through Resistance 3, (iD), A Total Current, (iA) Percentage Difference

Experimental

Computed

2.48

2.486

2.32

2.312

1.414

1.417

0.024

0.025

0.024

0.025

0.024

0.025

0.024

0.025

3.504

If we try to ponder on the results gathered from the experiment, we can see that the voltage from the first resistor is different from the second and of the thirst resistor. We can observe that the voltage is decreasing as we move from one resistor to the next. This implies that the total

voltage coming out from the source which is the battery is distributed unequally to its loads or resistors. On the other hand, we can see that the current flowing though each load is the same throughout. The team also found out that the total current is the same as the total current of the

system.

Using

the

equation

the

load, we can see that the current flowing in each load is different meaning the total current of the system is distributed through the loads. If we try to compare the experimental values from that of the computed values from the equation, we can see an almost negligible difference between the values.

computed values were computed and we can see that they are very near from the values gathered from the experiment.

For SERIES constant)

B. Resistors in Parallel 84

Resistance 2 (R2), Ω

27

Resistance 3 (R3), Ω

153

Total Resistance (RT), Ω

100 50 0

5.47

1.414

TABLE 2: PARALLEL CIRCUIT

Total Current, (iA) Percentage Difference

2.32

2.48

Voltage

Experimental

Computed

5.46

5.47

5.46

5.47

5.47

5.47

0.06

0.065

The graph above shows the relationship between voltage and resistance if we held the current constant. The voltage and the resistance are directly proportional. If the resistance is higher, the higher will be the voltage needed. For PARALLEL CONNECTION (voltage is constant)

0.19

0.203

Current vs Resistance

0.034

0.036

0.29

0.303

4.537

On the other side of the line, the results gathered from the parallel circuit makes an opposite as the behavior of the parameters in the series circuit. In here, we can see that the voltages in each of the loads or resistors are the same meaning it is constant. If we try to analyze the results gathered from the current flowing through each

200

Resistance

Voltage Across Resistance 1 (VAB), V Voltage Across Resistance 2 (VBC), V Voltage Across Resistance 3 (VCD), V Current Flowing through Resistance 1, (iB), A Current Flowing through Resistance 2, (iC), A Current Flowing through Resistance 3, (iD), A

is

150

18.02524544

Total Voltage (VEA), V

(current

Voltage vs Resistance Resistance

Resistance 1 (R1), Ω

CONNECTION

150 100 50 0 0.06

0.19

0.034

Current The graph above shows the relationship between current and resistance if we held the voltage constant. . The current and the resistance are

inversely proportional. If the resistance is higher, the lower will be the current needed and vice versa. Thus, we can conclude that the behavior of the parameters current and voltage in series and parallel circuits are exactly opposite with one another. DISCUSSION & SOURCES OF ERRORS The results of the experiment tell us that resistance, current and voltage has a relationship depending on what type of circuit is it either parallel or series circuit.

In a series circuit it is found that the current here is constant and the voltage and resistance are directly proportional to each other. While in a parallel circuit it is found that voltage is constant and the resistance and current are inversely proportional to each other. The concept of series and parallel circuits shows us the basic electrical engineering concepts showing the difference of the series circuit from the parallel circuit and the relationship between the parameters involved in the Ohm’s Law. A series circuit is a circuit having a constant flow of current throughout the path but having a variable individual voltage that will depend on the number of the resistors present. We can say that the resistance is directly proportional to the voltage while maintaining the flow of current constant. We can also conclude that the resistance is a load when the amount of load increases the flow of current the voltage must also increase to keep the flow of electricity. It was found evident that the series circuit is not good for home used since the total current is equal to the individual. On the other side of the line, the parallel circuit is a circuit where the total voltage used is equal to the individual voltage used and the flow of current is varying depending on the values of the resistors. The total resistance is the reciprocal of the sum of the reciprocal of the individual resistance. In this particular circuit we can say that the resistance is indirectly proportional to the flow of current, as the resistance increases the individual current

decreases. Comparing the two types of basic circuits we can say that parallel circuit is more convenient and appropriate to use because it uses different current that is why when one of the current is zero ampere other current will not be affected resulting to a continuous flow of electricity. Sources of errors: The temperature of the working environment may not be constant. The flow of electricity inside the wire already consumed electricity. The reading from the ammeter and VOM might be incorrect. To study the basics of electricity are very important to almost all field in the industry especially now that we are at a modern age. The idea of electric circuits make it possible for engineers and designers to build macro and micro engineering systems such as the installation of electric wiring in a building up to the smallest design of a microchip used in computers. ACKNOWLEDGMENT & REFERENCE To the following who had helped me finish this paper, I would like to thank: To God, for giving us the wisdom and to understand more of his fine creations especially the sound that makes life more beautiful. To my friend Bryan, for letting me use his internet connection for the online resources. To my groupmates, for their help and teamwork that made our experiment successful. To my blockmates Alex, Christian, Leif, Marc, and Airyl, for helping me find a source from the internet. To Prof. Ricardo F. De Leon Jr., for assisting and mentoring us during the laboratory hours. To the two laboratory assistants, Mang Gerry and Mang Jose, for being so friendly in lending us the tools and guiding us regarding its proper usage. To my previous Physics highschool teacher, Mrs. Gonzales, for teaching me a lot about electricity. Thank you very much. To God be the Glory! [1]Young, Hugh D., et al. University Physics With Modern Physics. Jurong, Singapore

6297733: Pearson Education South Asis Pte Ltd,,2008. [2]http://en.wikipedia.org/wiki/Ohm's_law [3]http://en.wikipedia.org/wiki/Series_and_parall el_circuits [4]http://www.allaboutcircuits.com/vol_1/chpt_5 /1.html [5]http://en.wikipedia.org/wiki/Ohm's_law

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