The Resistance of aWire
Introduction
Electrons move more easily through some conductors than others when a
potential difference is applied. The opposition of a conductor has a
low resistance and a poor conductor has a high resistance. The
resistance of a wire of a certain material:
l Increases as it's length increases,
l Increases as it's cross-section area increases,
l Depend on the material
A long wire has more resistance than a short thick one of the same
material.
Aim
To investigate the effect of length and thickness have on the
resistance of a wire.
Planning
These are the key factors for this experiment:
l Length
l Area of cross-section
l Temperature
l Voltage
l Material
In the first experiment the length of the wire is going to be varied,
and in the second experiment the area of cross-section of the wire is
going to be varied, all the other variables will have to be kept
constant in both experiments.
Preliminary Work
I have referred to our textbook (GCSE Physics 3^rd edition, Tom
Duncan) to find out what results I should be expecting. On the Chapter
51, I found a similar experiment under the title Practical
Work-Measuring Resistance:
The resistance R of a conductor can be found by measuring the current
I through it when a pd. V is applied across it and then using R=V/I.
Hypothesis
According to the Ohm's law:
The current through a metallic conductor is directly proportional to
the voltage across its ends if the temperature and other conditions
are constant.
[image001.gif]
V
Therefore, if the length of the wire doubles, then the resistance
doubles. If the cross-section of the wire is doubles, then the
resistance halves.
Apparatus
l resistor wire
l power pack(variable cell)
l ammeter
l voltage meter
l connecting wires
Procedure to Ensure Accuracy
l Measure the length of the wire carefully with a meter rule.
l Make sure the wire is not touching anything in case it ...
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the voltage across its ends if the temperature and other conditions
are constant.
[image001.gif]
V
Therefore, if the length of the wire doubles, then the resistance
doubles. If the cross-section of the wire is doubles, then the
resistance halves.
Apparatus
l resistor wire
l power pack(variable cell)
l ammeter
l voltage meter
l connecting wires
Procedure to Ensure Accuracy
l Measure the length of the wire carefully with a meter rule.
l Make sure the wire is not touching anything in case it affects
the result.
l Use crocodile clips to attach the wire to circuit, for extra
grip.
l Make sure the voltage doesn't go too high incase the wire got
over heated.
l Check all the connecting wires are securely attached to the
voltmeter, the ammeter, and the resistor wire
l Do at least 5 different length and thickness in order to spot a
more accurate trend.
Method
l Set up the circuit.(see diagram)
l Make sure the power pack is in
D.C mode.
l Switch on the power pack starting
at the lowest voltage.
l Record the number on the voltage
Meter and the ammeter onto a neat
Table.
l Switch off the power pack.
l Switch it on again with a different
voltage.
l After going up to a certain voltage,
switch off the power pack. Step
back, and wait for a while for the
wire to cool down.
Results Table
Here is a table of all the evidence I have obtained. Also, the
calculation for Resistance and Average Resistance in each length has
been calculated. There are a few odd results, which I have
highlighted. I did not exclude them in the calculation, because all
the error shall be evaluated.
Experiment 1 - The resistance of wire with different length
length(cm)
voltage(V)
current(Amps)
Resistance
Average Resistace
10.0
0.14
0.08
1.75
1.90
1.04
0.60
1.73
1.13
0.61
1.85
2.80
1.43
1.96
4.35
2.13
2.04
5.93
2.88
2.06
7.44
3.75
1.98
20.0
0.21
0.05
4.20
4.29
1.60
0.36
4.44
3.27
0.76
4.30
4.79
1.12
4.28
6.49
1.52
4.27
4.86
1.14
4.26
8.22
1.90
4.33
30.0
0.23
0.03
7.67
6.59
1.68
0.26
6.46
3.49
0.55
6.35
5.13
0.82
6.26
6.75
1.06
6.37
6.82
1.05
6.50
8.47
1.30
6.52
40.0
0.25
0.03
8.33
8.65
1.75
0.19
9.21
3.64
0.42
8.67
5.24
0.61
8.59
5.27
0.62
8.50
6.90
0.80
8.63
50.0
0.23
0.03
7.67
7.89
1.68
0.25
6.72
3.46
0.53
6.53
5.10
0.78
6.54
5.41
0.51
10.61
6.80
1.04
6.54
7.03
0.66
10.65
60.0
0.20
0.03
6.67
6.73
1.61
0.21
7.67
3.43
0.52
6.60
5.09
0.77
6.61
6.79
1.03
6.59
6.89
1.05
6.56
8.48
1.31
6.47
70.0
0.26
0.01
26.00
16.46
1.83
0.12
15.25
3.85
0.26
14.81
5.61
0.38
14.76
5.55
0.37
15.00
7.23
0.49
14.76
7.37
0.50
14.74
Length
Average Resistance
10.00
1.90
20.00
4.29
30.00
6.59
40.00
8.65
50.00
7.89
60.00
6.73
70.00
16.46
Thickness
Voltage
Current
Resistance
Average Resistance
1
0.64
0.17
3.76
3.77
2.07
0.56
3.70
3.89
1.04
3.74
5.43
1.42
3.82
7.11
1.85
3.84
2
0.59
0.27
2.19
2.16
1.94
0.91
2.13
3.62
1.7
2.13
5.17
2.4
2.15
6.61
3.02
2.19
3
0.51
0.39
1.31
1.35
1.76
1.31
1.34
3.35
2.48
1.35
4.72
3.43
1.38
6.01
4.33
1.39
4
0.59
0.44
1.34
1.43
1.82
1.29
1.41
3.32
2.3
1.44
4.82
3.28
1.47
6.08
4.12
1.48
5
0.52
0.54
0.96
1.00
1.61
1.65
0.98
2.99
3.06
0.98
4.38
4.28
1.02
5.7
5.47
1.04
Thickness
Average Resistance
1
3.77
2
2.16
3
1.35
4
1.43
5
1
[image003.gif]
Conclusion
We can clearly spot a line of best fit on the graph length/Resistance,
which means the results are mostly accurate. However there are two
anomalous results for the length 50 and 60. Looking back at the
hypothesis, I predicted that the resistance would be doubled when the
length is doubled. And the result does support my statement. There
fore my prediction was correct.
When the length of the wire is doubled, the more neurones the
electrons will have to pass through, and the more energy will be lost
on the way by transferring into heat energy due to collision. (See
diagram)
We can make out a curve line from the hand drawn graph of mine. And
most results are perfectly accurate. This show that as the wire gets
thicker, the resistance gets smaller. And when the resistance has been
decreased till a certain point, the results does not show the
resistance halves as the thickness doubled. In addition, there is a
minimum amount of resistance to the wire. (Which is around 1 Ohms
shown by the graph) And I have not put that into consideration in my
hypothesis.
However, if we look at the 1^st two set of data. When the wire's
thickness is one, the resistance is around four. When the wire's
thickness is two, the resistance is around two, which is a half of the
resistance for the 1^st wire. This supports my prediction that, when
the thickness of the wire is doubled, the resistance halves.
When the thickness of the wire is doubled, the more room there is for
the electrons to pass through. Therefore less collision will be taking
place, causing less energy loss.
(See diagram)
Evaluation
There are two anomalous results in the 1^st experiment, and some not
so accurate results in the 2^nd experiment.
Generally, the results were reliable due to so many different length
and thickness I have experimented with. However, it would be better if
I have repeated the experiment a few more times for accuracy.
I recall this experiment was done in the summer term, when the
temperature was high. We asked to open the windows at one point for
some fresh air, and closed it again because it got cold. I suspect
that special event has affected my results in the 1^st experiment,
since temperature was one of the key factors which can affect the
resistance.
References
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