# ohms law(1)

```Set Up &amp; Components
Experiment
Results and Discussions
PYHSICS 1002 Laboratory
Experiment III: OHM’S LAW
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Experiment
Results and Discussions
Objective: Defining factors affectting the electrical resistance of a
material
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Components:
&sect; 1m long resistive wires: Constantan 1.0mm, 0.7mm (2 wires),
0.5mm; Brass 0.5mm diameter
&sect; Power Source
&sect; Banana Connection Cables
&sect; Multimeter
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Experiment
&sect;Turn on the power source and tune it to voltage values given
in page 35 of your physics laboratory booklet
&sect;Read the current values from the multimeter.
&sect;Note the current value and proceed to next voltage level
&sect;Once you apply all the voltage values, change the resistive
wire. Follow thick to thin order. Once you finish the constantan
wire, proceed with brass wire.
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Results and Discussions
Table 1: Current – Voltage values for 1m long Constantan wire with 1.0mm diameter.
Constantan - 1.0 mm 1m
V
I1
I2
I3
Iavg
0,1
0,11
0,13
0,1
0,11
0,2
0,17
0,19
0,24
0,20
0,3
0,25
0,32
0,34
0,30
0,4
0,38
0,42
0,38
0,39
0,5
0,49
0,45
0,5
0,48
0,6
0,53
0,55
0,54
0,54
0,7
0,66
0,64
0,66
0,65
0,8
0,7
0,76
0,81
0,76
0,9
0,81
0,81
0,9
0,84
1
0,91
0,9
0,96
0,92
1,1
0,99
1
1
1,00
1,2
1,08
1,07
1,15
1,10
In table 1 you can see results for 1m long Constantan wire with 1.0mm diameter. Column
“V” stands for applied voltage and I1, I2 and I3 are current values of repeated measurments.
Iavg is simply average of these measurments.
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Results and Discussions
Figure 1: Current – Voltage graph for Constantan wire with 1.0mm diameter.
Figure 1 shows the variation of current with changing voltage. Since current changes
linearly we can write an equation between current and voltage as:
V=IR
Slope of the graph is defined as resistance “R” of a wire. In our first case, resistance of our
wire is 1.12Ohms (1.12W)
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Experiment
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Results and Discussions
Table 2: Current – Voltage values for 1m long Constantan wire with 0.7mm and 0.5mm
diameter.
Constantan - 0.7mm 1m
Constantan - 0.5mm 1m
V
I1
I2
I3
Iavg
V
I1
I2
I3
Iavg
0,2
0,08
0,11
0,09
0,09
0,4
0,09
0,09
0,08
0,09
0,4
0,2
0,19
0,2
0,20
0,8
0,15
0,18
0,17
0,17
0,6
0,27
0,29
0,29
0,28
1,2
0,22
0,26
0,26
0,25
0,8
0,34
0,37
0,37
0,36
1,6
0,3
0,33
0,35
0,33
1
0,46
0,43
0,49
0,46
2
0,38
0,42
0,44
0,41
1,2
0,54
0,53
0,56
0,54
2,4
0,46
0,49
0,53
0,49
1,4
0,61
0,64
0,65
0,63
2,8
0,55
0,56
0,62
0,58
1,6
0,72
0,74
0,72
0,73
3,2
0,62
0,65
0,7
0,66
1,8
0,8
0,81
0,84
0,82
3,6
0,7
0,74
0,79
0,74
2
0,87
0,91
0,91
0,90
2,2
0,98
0,97
1,01
0,99
In Table 2 you can see results for 1m long Constantan wire with different ticknesses.
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Results and Discussions
Figure 2: Combined Current – Voltage graphs for Constantan wires with diffent diameters:
Dark blue 1.0 mm diameter, Dark red 0.7mm diameter, Green 0.5 mm diameter
Figure 2 combined graph for 1m long Constantan wire with 1.0mm, 0.7mm and 0.5mm
ticknesses. It’s visually clear that slope is increasing with decreasing wire diameter
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Results and Discussions
Figure 3: Combined Current – Voltage graphs for Constantan wires with diffent diameters:
Dark blue 1.0 mm diameter, Dark red 0.7mm diameter, Green 0.5 mm diameter with trend
lines and slopes
Figure 3 combined graph with slope values for 1m long Constantan wire with different
ticknesses. From slopes, we can see that slope and thus resistance of wires increasing with
decreasing wire diameter.
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Results and Discussions
Table 3: Resitance, diameter and area values of constantan wires
R (W)
d (mm)
Area (mm2)
4,87
0,5
0,2
2,25
0,7
0,4
1,12
1,0
0,8
Figure 4: Dependence of resistance to diameter (a) and crossection area (b)
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Results and Discussions
Resistance values for different diameter and crossection area values are given in Table 3. You
can numerically see that how resistance changes with diameter and crossection area. Figure 4
(a) and (b) gives variation of resistance graphically. From Figure 4a you can see dependence
of resistance is given with ax-2, here a is a proportion constant (if you wonder, it is equal to
4&times;p-1). But if you check Figure 4b, you’ll see dependence of resistance is directly given by x-1.
Using this result we can conclude that resistance is inversely propotional with
crossection area
1
R
A
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Results and Discussions
Table 4: Current – Voltage values for 0.7mm diameter Constantan wire with 1m and 2m
length
V
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
Constantan - 0.7mm 1m
I1
I2
I3
0.08 0.11 0.09
0.2
0.19
0.2
0.27 0.29 0.29
0.34 0.37 0.37
0.46 0.43 0.49
0.54 0.53 0.56
0.61 0.64 0.65
0.72 0.74 0.72
0.8
0.81 0.84
0.87 0.91 0.91
0.98 0.97 1.01
Iavg
0.09
0.20
0.28
0.36
0.46
0.54
0.63
0.73
0.82
0.90
0.99
V
0.4
0.8
1.2
1.6
2
2.4
2.8
3.2
3.6
4
4.4
Constantan - 0.7mm 2m
I1
I2
I3
0.09
0.1
0.09
0.16
0.18
0.19
0.26
0.27
0.29
0.34
0.36
0.38
0.42
0.45
0.47
0.51
0.55
0.56
0.6
0.64
0.64
0.67
0.73
0.73
0.77
0.82
0.83
0.85
0.9
0.9
0.94
0.99
0.97
Iavg
0.09
0.18
0.27
0.36
0.45
0.54
0.63
0.71
0.81
0.88
0.97
In Table 4 you can see results for Current – Voltage values for 0.7mm diameter Constantan
wire with 1m and 2m length.
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Results and Discussions
Figure 5: Combined Current – Voltage graphs for 0.7mm diameter Constantan wire with 1m
and 2m length: Dark blue 1m long, Dark red 2m long.
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Results and Discussions
Figure 6: Combined Current – Voltage graphs with trend lines and slopes for 0.7mm
diameter Constantan wire with 1m and 2m length: Dark blue 1m long, Dark red 2m long.
Figure 6 combined graph with slope values for 0.7mm diameter Constantan wire with 1m
and 2m length. From slopes, we can see that slope and thus resistance of wires increasing
with increasing wire length.
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Results and Discussions
From the slopes of graph in Figure 6, we can see that resistance is doubled as we doubled the
length.
Using this result we can conclude that resistance is propotional with length
RL
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Results and Discussions
Table 5: Current – Voltage values for 0.5mm diametered 1m long Constantan and Brass
wires.
V
0.4
0.8
1.2
1.6
2
2.4
2.8
3.2
3.6
Constantan - 0.5mm 1m
I1
I2
I3
0.09
0.09
0.08
0.15
0.18
0.17
0.22
0.26
0.26
0.3
0.33
0.35
0.38
0.42
0.44
0.46
0.49
0.53
0.55
0.56
0.62
0.62
0.65
0.7
0.7
0.74
0.79
Iavg
0.09
0.17
0.25
0.33
0.41
0.49
0.58
0.66
0.74
V
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Bras - 0.5 mm 1m
I1
I2
I3
0.33 0.44 0.36
0.7 0.46 0.51
0.82 0.75 0.84
1.16 1.01 1.08
1.32 1.21 1.34
1.49 1.44 1.55
1.83 1.75 1.78
Iavg
0.38
0.56
0.80
1.08
1.29
1.49
1.79
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From the slopes of graph in Figure 8, we can see that resistance is differed because of wire
material.
Using this result we can conclude that resistance is propotional with material’s
resistivity
R
Note: Resistivity of a material is temperature dependent. If material is metal
resistivity increases with increasing temperature, and it decreases with increasing
temperature if material is non-metal. But since we conduct the experiments in a
very narrow range, we can assume temperature as constant.
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Results and Discussions
Combining all the factors we measured we can have the equation:
L
R
A
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