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MATHEMATICS AND PHYSICAL SCIENCE DEPARTMENT
Laboratory Experiment #6 Resistors in Series and Parallel
Submitted by: Vince Lim Submitted to: Prof. Lilian Jadormio Gumban IPHYLAB2 – M181 February 26, 2019
Objectives To determine the total resistance R of a series connected resistors To find out the relationship between the total current It and the individual currents I1, I2, and I3 in a series connected resistors To find out the relationship between the total voltage Vt and the individual voltages V1, V2, and V3 in a series connected resistors To determine the total resistance R of a parallel connected resistors To find out the relationship between the total current It and the individual currents I1, I2, and I3 in a parallel connected resistors To find out the relationship between the total voltage Vt and the individual voltages V1, V2, and V3 in a parallel connected resistors
Observations, Interpretations, and Analysis of Data Table 7.1 THREE RESISTORS IN SERIES Calculated Values
Measured Values
Resistors Resistance R Voltage V Current I Voltage V Current I R1
100 Ohms
4.04 V 0.0404 A
4V
0.0404 A
R2
47 Ohms
1.39 V 0.0404 A
1V
0.0404 A
R3
100 Ohms
4.04 V 0.0404 A
4V
0.0404 A
Total
10V
Table 7.2 TWO RESISTORS IN SERIES Calculated Values
Measured Values
Resistors Resistance R Voltage V Current I Voltage V Current I R1
100 Ohms
6.3 V
0.0680 A
8V
0.0608 A
R2
47 Ohms
3.19 V 0.0680 A
2V
0.0608 A
Total
10 V
Table 7.3 EQUAL RESISTORS IN PARALLEL Calculated Values
Measured Values
Resistors Resistance R Voltage V Current I Voltage V Current I R1
100 Ohms
10 V
0.1 A
10 V
0.1 A
R2
47 Ohms
10 V
0.2 A
10 V
0.2 A
Total
10 V
Table 7.4 DIFFERENT RESISTORS IN PARALLEL Calculated Values
Measured Values
Resistors Resistance R Voltage V Current I Voltage V Current I R1
100 Ohms
10 V
0.1 A
10 V
0.1 A
R2
47 Ohms
10 V
0.3 A
10 V
0.3 A
Total
10 V
Table 7.5 RESISTORS IN SERIES AND PARALLEL Calculated Values
Measured Values
Resistors Resistance R Voltage V Current I Voltage V Current I R1
100 Ohms
2.5 V
0.025 A
2.5 V
0.03 A
R2
47 Ohms
2.35 V
0.05 A
2.5 V
0.06 A
R3
100 Ohms
2.5 V
0.025 A
2.5 V
0.03 A
Total
10V
Evaluation Question and Problems. 1. How is the total resistance affected when the number of identical resistors is increased in a series connected resistors? In parallel-connected resistors? If the resistors are connected in series, the total resistance would increase by the same amount of resistance the added resistor would provide. In the case of the resistors being connected in parallel, the following would hold true. 1/R ; Total resistance = R 1/R + 1/R ; Total resistance = R/2 1/R + 1/R + 1/R ; Total resistance = R/3 The total resistance would be multiplied by a factor of 1/n where n is the total number of resistors present in the connection. 2. When the number of identical resistors is increased, what happens to the total circuit current in a series connected circuit? In a parallel connected circuit? In a series connection, it was established that the total resistance increases with each resistor added. As a consequence of that, from V = IR and assuming that the voltage remains constant, we can say that the current would decrease. On the other hand, in a parallel connection, the total resistance decreases with an added identical resistor and from that, the total current would increase. 3. Refer to the circuit below. Determine the total resistance and current of the circuit. What are the voltage and current on A, B, and C?
From the formula presented in question 1, the total resistance is 6 Ohms. The total current is equal to 5 A. The total voltage is equal to IR = (5 A)(6 Ohms) = 30 V. The voltage is 30 V for A, B, and C given that it is in parallel. The current for A and B is 30 V/15 Ohms = 2 A and for C, the current is 30 V/30 Ohms = 1 A. 4. What is the voltage on A, B, D? What is the current on A, B, C, D? What is the resistance on C? Determine the total current and the total resistance of the circuit.
The voltage for D is 80 V. The voltage for A and B is equal to 230 – 80 = 150 V. The current on A, B, C, and D is equal to V/R = 150 V/15 Ohms = 10 A. For the resistance on C, 10 A = (80V)/(1/(1/40 + 1/x)), R = 10 Ohms. The total current is 10 A and the total resistance is 23 Ohms.
Conclusion In a series connection, the current is constant and the total resistance is the sum of all resistances available. In a parallel connection, the total current is the summation of all currents and the total resistance is equal to the reciprocal of the summation of one over the value of a given resistor.
Laboratory Experiment #6 Resistors in Series and Parallel
Submitted by: Vince Lim Submitted to: Prof. Lilian Jadormio Gumban IPHYLAB2 – M181 February 26, 2019
Objectives To determine the total resistance R of a series connected resistors To find out the relationship between the total current It and the individual currents I1, I2, and I3 in a series connected resistors To find out the relationship between the total voltage Vt and the individual voltages V1, V2, and V3 in a series connected resistors To determine the total resistance R of a parallel connected resistors To find out the relationship between the total current It and the individual currents I1, I2, and I3 in a parallel connected resistors To find out the relationship between the total voltage Vt and the individual voltages V1, V2, and V3 in a parallel connected resistors
Observations, Interpretations, and Analysis of Data Table 7.1 THREE RESISTORS IN SERIES Calculated Values
Measured Values
Resistors Resistance R Voltage V Current I Voltage V Current I R1
100 Ohms
4.04 V 0.0404 A
4V
0.0404 A
R2
47 Ohms
1.39 V 0.0404 A
1V
0.0404 A
R3
100 Ohms
4.04 V 0.0404 A
4V
0.0404 A
Total
10V
Table 7.2 TWO RESISTORS IN SERIES Calculated Values
Measured Values
Resistors Resistance R Voltage V Current I Voltage V Current I R1
100 Ohms
6.3 V
0.0680 A
8V
0.0608 A
R2
47 Ohms
3.19 V 0.0680 A
2V
0.0608 A
Total
10 V
Table 7.3 EQUAL RESISTORS IN PARALLEL Calculated Values
Measured Values
Resistors Resistance R Voltage V Current I Voltage V Current I R1
100 Ohms
10 V
0.1 A
10 V
0.1 A
R2
47 Ohms
10 V
0.2 A
10 V
0.2 A
Total
10 V
Table 7.4 DIFFERENT RESISTORS IN PARALLEL Calculated Values
Measured Values
Resistors Resistance R Voltage V Current I Voltage V Current I R1
100 Ohms
10 V
0.1 A
10 V
0.1 A
R2
47 Ohms
10 V
0.3 A
10 V
0.3 A
Total
10 V
Table 7.5 RESISTORS IN SERIES AND PARALLEL Calculated Values
Measured Values
Resistors Resistance R Voltage V Current I Voltage V Current I R1
100 Ohms
2.5 V
0.025 A
2.5 V
0.03 A
R2
47 Ohms
2.35 V
0.05 A
2.5 V
0.06 A
R3
100 Ohms
2.5 V
0.025 A
2.5 V
0.03 A
Total
10V
Evaluation Question and Problems. 1. How is the total resistance affected when the number of identical resistors is increased in a series connected resistors? In parallel-connected resistors? If the resistors are connected in series, the total resistance would increase by the same amount of resistance the added resistor would provide. In the case of the resistors being connected in parallel, the following would hold true. 1/R ; Total resistance = R 1/R + 1/R ; Total resistance = R/2 1/R + 1/R + 1/R ; Total resistance = R/3 The total resistance would be multiplied by a factor of 1/n where n is the total number of resistors present in the connection. 2. When the number of identical resistors is increased, what happens to the total circuit current in a series connected circuit? In a parallel connected circuit? In a series connection, it was established that the total resistance increases with each resistor added. As a consequence of that, from V = IR and assuming that the voltage remains constant, we can say that the current would decrease. On the other hand, in a parallel connection, the total resistance decreases with an added identical resistor and from that, the total current would increase. 3. Refer to the circuit below. Determine the total resistance and current of the circuit. What are the voltage and current on A, B, and C?
From the formula presented in question 1, the total resistance is 6 Ohms. The total current is equal to 5 A. The total voltage is equal to IR = (5 A)(6 Ohms) = 30 V. The voltage is 30 V for A, B, and C given that it is in parallel. The current for A and B is 30 V/15 Ohms = 2 A and for C, the current is 30 V/30 Ohms = 1 A. 4. What is the voltage on A, B, D? What is the current on A, B, C, D? What is the resistance on C? Determine the total current and the total resistance of the circuit.
The voltage for D is 80 V. The voltage for A and B is equal to 230 – 80 = 150 V. The current on A, B, C, and D is equal to V/R = 150 V/15 Ohms = 10 A. For the resistance on C, 10 A = (80V)/(1/(1/40 + 1/x)), R = 10 Ohms. The total current is 10 A and the total resistance is 23 Ohms.
Conclusion In a series connection, the current is constant and the total resistance is the sum of all resistances available. In a parallel connection, the total current is the summation of all currents and the total resistance is equal to the reciprocal of the summation of one over the value of a given resistor.
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