Physics 102
Ohm's Law
Juan Guerrero, Phuc La
February 14, 2006
Abstract:
The purpose of this lab is to determine variations in current intensity and potential
differences which occur when conductors of different resistance are connected in parallel, in
series, or in series-parallel. This will be shown by graphing the voltage and the
current versus the resistors, and calculating theoretical values of voltage and
current to compare with experimental values.
Equipment: In this lab the devices below were used.
 Digital voltmeter
 Digital ammeter
 Resistors (decade boxes)
 Variable D.C. power supply
 wires
Procedure:


R1, R2 and R3 were chosen 30Ω, 40Ω and 50Ω.
The power supply is set to 6V.
In series circuit
1. The circuit was constructed like in Picture 01:
Picture 01
1-10
2. The dial of VOM is set to DCV. The black probe is connected to A1 and
the red probe is connected to B1 to measure and record the voltage of
resistor 1. Then repeat the process with the resistors 2 and 3.
3. Then have one wire that is connecting the resistor to the battery, or power
supply, removed to connect the VOM, which is set to DCA, to measure
and record the current of the circuit. The current is the same throughout
the entire circuit.
In parallel circuit
1. The circuit was constructed like Picture 02:
Picture 02
2. Set the dial of the VOM to DCV. Connect the black probe to A1 and
connect the red probe to B1 to measure and record the voltage of resistor
1. Then continue to do this with the resistors 2 and 3.
3. Now set the dial of the VOM to DCA. To measure and record the current
of each resistor one wire of each branch should be replaced by the VOM.
In series-parallel
1. The circuit was constructed like in Picture 03:
2-10
Picture 03
2. Set the dial of the VOM to DCV. Connect the black probe to A1 and the
red probe to B1 in order to measure and record the voltage of resistor 1.
Then continue with the resistor 2 and 3.
3. Set the dial of VOM to DCA. One wire of each branch is replaced by the
VOM to measure and record the current of each resistor.
Data:
R: The equivalent resistance of resistors
R1
R2
R3
R
Resistor
Ω
30
40
50
Series Circuit
Current
Voltage
A
V
0.05
1.538
0.05
2.130
0.05
2.395
0.05
5.985
Parallel Circuit
Current
Voltage
A
V
0.190
5.71
0.140
5.71
0.115
5.71
0.430
5.71
Table 01
Series-Parallel Circuit
Current
Voltage
A
V
0.115
3.60
0.063
2.60
0.052
2.60
0.112
6.00
Analysis
Calculations:
Part 1: Preparation for graphing
Ohm’s Law is V=IR.
In the series circuit, the current is the same when it runs through each
component. Therefore, the current is assumed to be constant throughout the
circuit. Ohm’s Law is a function V(R). R, the resistance, is an independent
variable. Besides, I, the current, is a slope of function V(R). Table 02 shows
relationship between voltage and resistance. Graph 01 illustrates data from Table
02.
3-10
R1
R2
R3
Resistor
Ω
30
40
50
Voltage
V
1.538
2.130
2.395
Table 02
In the parallel circuit, the voltage is not changed. So, the voltage is assumed
to be constant. The Ohm’s Law is rearranged so that it is being solved for the
V
current, I  . V is a slope of function I(1/R). 1/R is an independent variable.
R
Table 03 shows relationship between current and 1/resistor. Graph 02 gets data
from Table 03.
R1
R2
R3
Resistor
Ω
30
40
50
1/Resistor
1/Ω
0.033
0.025
0.020
Current
A
0.190
0.140
0.115
Table 03
Part 2: Find the theoretical voltage and current
In the series circuit
In the circuit the current is the same through each resistor. The power is 6 volts
and resistors are 30Ω, 40Ω, and 50Ω. The equivalent resistance of resistors in
series is
R = R1 + R2 + R3 = 30 Ω + 40 Ω + 50 Ω = 120 Ω.
With a 6 V source, using Ohm’s law V = I R, the total current in the circuit is:
6V
V
I 
 0.05 A
R 120 
The current is the same through each resistor, so
I = I1 = I2 = I3 = 0.05 A
With Ohm’s Law, the theoretical voltage of each resistor is:
V1 = I1R1 = 0.05 A * 30 Ω = 1.5 V
V2 = I2R2 = 0.05 A * 40 Ω = 2.0 V
V3 = I3R3 = 0.05 A * 50 Ω = 2.5 V
Experimental Theoretical Experimental Theoretical
Current
Current
Voltage
Voltage
Ω
A
A
V
V
30
0.05
0.05
1.538
1.50
40
0.05
0.05
2.130
2.00
Resistor
R1
R2
4-10
R3
R
50
120
0.05
0.05
0.05
0.05
2.395
5.985
2.50
6.00
Table 04
In the parallel circuit
In the parallel circuit the voltage is the same through each resistor. The power is
6 V and resistors are 30Ω, 40Ω, and 50Ω. The equivalent resistance of the
resistors in parallel is
1
1
1
1
1
1
1
47







R R1 R2 R3 30 40 50 600
600
R
 13
47
V
With 6 V of power using Ohm’s Law, I  , the total current in the circuit is:
R
V 6V
I 
 0.46 A
R 13 
The voltage is the same through each resistor, so
V = V1 = V2 = V3 = 6.0 V
With Ohm’s Law, the theoretical current of each resistor is
I1 = V1/R1 = 6.0 V / 30 Ω = 0.20 A
I2 = V2/R2 = 6.0 V / 40 Ω = 0.15 A
I3 = V3/R3 = 6.0 V / 50 Ω = 0.12 A
Resistor
Ω
R1
R2
R3
R
30
40
50
120
Experimental Theoretical Experimental Theoretical
Current
Current
Voltage
Voltage
A
A
0.19
0.14
0.115
0.43
V
0.20
0.15
0.12
0.46
V
5.71
5.71
5.71
5.71
6.00
6.00
6.00
6.00
Table 05
In the series-parallel circuit
In this circuit the power is 6 V and resistors are 30Ω, 40Ω, and 50Ω.
R2 and R3 are in parallel. The equivalent resistance of R2 and R3 resistor is
1
1
1
1
1
9





R23 R2 R3 40 50 200
200
R2  3 
 22
9
R1 and R2+3 are in series. The equivalent resistance of R1 and R2+3 resistors is
R = R1 + R2+3 = 30Ω + 22Ω = 52Ω
5-10
R1 and R2+3 are in series, so the theoretical current which goes through R1 and
R2+3 is the same.
V 6.0V
I  I 1  I 23  
 0.12 A
R 52 
With I, I1 and I2+3, the theoretical voltage of R1 and R2+3 are
V1 = I1R1 = 0.12 A * 30 Ω = 3.6 V
V2+3 = I2+3R2+3 = 0.12 A * 22 Ω = 2.6 V
R2 and R3 are in parallel, therefore V2+3 = V2 = V3. The theoretical current of R2
and R3 are
V 2.6V
I2  2 
 0.065 A
R2 40 
V 2.6V
I3  3 
 0.052 A
R3 50 
Resistor
Experimental Theoretical Experimental Theoretical
Current
Current
Voltage
Voltage
Ω
R1
R2
R3
R
A
30
40
50
120
A
0.115
0.063
0.052
0.112
V
0.11
0.06
0.05
0.11
V
3.430
2.575
2.575
6.000
3.60
2.60
2.60
6.00
Table 06
Graphs
Voltage versus Resistor in series circuit
3.000
V = 0.0428R + 0.3133
Voltage (V)
2.500
2.000
1.500
1.000
0.500
0.000
0
10
20
30
40
Resistor (Ω)
Graph 01: Voltage versus Resistor in series circuit
6-10
50
60
Current (A)
Current versus 1/Resistor in parallel circuit
0.200
0.180
0.160
0.140
0.120
0.100
0.080
0.060
0.040
0.020
0.000
0.000
I = 5.3265 (1/R) + 0.0009
0.005
0.010
0.015
0.020
0.025
0.030
0.035
1/Resistor (1/Ω)
Graph 02: Current versus 1/Resistor in parallel circuit
Error analysis:
There are some variations in the data. These variations have come from several
sources:
 Reading errors
 Device variation
 Instructions
 Calculating
Reading error is common error. In the experiment, the data is read from the
device. The device shows a variant number. Therefore the recorded data is an
estimate or average of the fluctuation quantity.
The device used in the experiment also contributed to errors. Each device has a
deviation, so it adds to the affects of the result of the experiment. In the
experiment, there is resistance in wires and devices, so the result is different
from the theory result.
Not following instructions can affect the data in the experiment. If an experiment
is done incorrectly then the, data may come out incorrect. With incorrect data, a
person’s conclusion will be incorrect.
Calculating errors are also made. When the results are rounded off early in
calculations, it affects the following steps. In the experiment, the theoretical
voltage and current are rounded off so when total voltage and current are
calculated they are not going to come out perfect.
7-10
In the experiment, there are errors in the results. The percent error shows the
difference between experimental values and theoretical values.
Series Circuit
R1
R2
R3
R
Resistor
Ω
30
40
50
120
Experimental
Current
A
0.05
0.05
0.05
0.05
Theoretical
Current
A
0.05
0.05
0.05
0.05
Experimental
Voltage
V
1.538
2.130
2.395
5.985
Theoretical
Voltage
V
1.50
2.00
2.50
6.00
% error
of
current
%
0.00
0.00
0.00
0.00
% error
of
voltage
%
2.53
6.50
4.20
0.25
Theoretical
Voltage
V
6.00
6.00
6.00
6.00
% error
of
current
%
5.00
6.67
4.17
6.52
% error
of
voltage
%
4.83
4.83
4.83
4.83
Theoretical
Voltage
V
3.430
2.575
2.575
6.000
% error
of
current
%
4.55
5.00
4.00
1.82
% error
of
voltage
%
4.96
0.97
0.97
0.00
Table 07
Parallel Circuit
R1
R2
R3
R
Resistor
Ω
30
40
50
120
Experimental
Current
A
0.19
0.14
0.115
0.43
Theoretical
Current
A
0.20
0.15
0.12
0.46
Experimental
Voltage
V
5.71
5.71
5.71
5.71
Table 08
Series-Parallel Circuit
R1
R2
R3
R
Resistor
Ω
30
40
50
120
Experimental
Current
A
0.115
0.063
0.052
0.112
Theoretical
Current
A
0.11
0.06
0.05
0.11
Experimental
Voltage
V
3.60
2.60
2.60
6.00
Table 09
Questions:
1. The sum of the voltage drops in the series circuit is equal to the source
voltage.
2. The sum of the currents through the resistors in parallel circuit equals the
initial current of the circuit.
3. Looking for linear relationships and calculate the slopes of these lines. (refer
to Calculation: Part 1 and Graph)
8-10
Voltage versus Resistor in series circuit
3.000
V = 0.0428R + 0.3133
Voltage (V)
2.500
2.000
1.500
1.000
0.500
0.000
0
10
20
30
40
50
60
Resistor (Ω)
Graph 01: Voltage versus Resistor in series circuit
In graph 01, the slope of the line is 0.0428. In the Part 2 of calculation, the slope
is the current of series circuit. The experimental current is 0.05 A. There is a
small difference between 0.0428 and 0.05. So, there is a linear relationship
between resistor and voltage in series circuit. In series circuit, the slope of the
linear equation should be the current of the circuit.
Current (A)
Current versus 1/Resistor in parallel circuit
0.200
0.180
0.160
0.140
0.120
0.100
0.080
0.060
0.040
0.020
0.000
0.000
I = 5.3265 (1/R) + 0.0009
0.005
0.010
0.015
0.020
0.025
1/Resistor (1/Ω)
Graph 02: Current versus 1/Resistor in parallel circuit
9-10
0.030
0.035
In graph 02, the slope of the line is 5.3265. In Part 2 of the calculations, the slope
is the voltage of the parallel circuit. The experimental voltage is 5.71 V. There is
a small difference between 5.3265 and 5.71 therefore 5.71 is an acceptable
answer. So, there is a linear relationship between 1/resistor and current in
parallel circuit. In parallel circuit, the slope of the linear equation should be the
voltage of the circuit.
4. See Calculation: Part 2 and excel file.
Series Circuit
R1
R2
R3
R
Resistor
Ω
30
40
50
120
Experimental
Current
A
0.05
0.05
0.05
0.05
Theoretical
Current
A
0.05
0.05
0.05
0.05
Experimental
Voltage
V
1.538
2.130
2.395
5.985
Theoretical
Voltage
V
1.50
2.00
2.50
6.00
% error
of
current
%
0.00
0.00
0.00
0.00
% error
of
voltage
%
2.53
6.50
4.20
0.25
Theoretical
Voltage
V
6.00
6.00
6.00
6.00
% error
of
current
%
5.00
6.67
4.17
6.52
% error
of
voltage
%
4.83
4.83
4.83
4.83
Theoretical
Voltage
V
3.430
2.575
2.575
6.000
% error
of
current
%
4.55
5.00
4.00
1.82
% error
of
voltage
%
4.96
0.97
0.97
0.00
Table 07
Parallel Circuit
R1
R2
R3
R
Resistor
Ω
30
40
50
120
Experimental
Current
A
0.19
0.14
0.115
0.43
Theoretical
Current
A
0.20
0.15
0.12
0.46
Experimental
Voltage
V
5.71
5.71
5.71
5.71
Table 08
Series-Parallel Circuit
R1
R2
R3
R
Resistor
Ω
30
40
50
120
Experimental
Current
A
0.115
0.063
0.052
0.112
Theoretical
Current
A
0.11
0.06
0.05
0.11
Experimental
Voltage
V
3.60
2.60
2.60
6.00
Table 09
Conclusion:
In the series circuit, the current is the slope of the linear equation of voltage
and resistor. In the parallel circuit, the voltage is the slope of the linear equation
of current and 1/ resistor. Ohm’s Law shows a relationship between the voltage,
the current and the resistance.
Grade 98/100
10-10