An investigation intoThe resistance of a wire
An investigation into
The resistance of a wire
Physics Coursework
Ben Smith, 10S
Aim: To discover if a relationship exists between the length and resistance of a wire.
Prediction: I believe that I will discover that the resistance of a wire increases proportionally with the length. I think that this is due to the way resistance occurs in a typical wire.
Resistance is the result of negatively charged electrons (the actual current) colliding with the positively charged ions that make up the wire. The collisions cause the energy in the electron to be lost, and when they occur on a larger scale there is a noticeable difference between the start and end voltage of a circuit.
As the length of the wire increases, so must the number of particles. As the number of particles increases, so will the number of collisions, and therefore the amount of resistance encountered.
George Ohm discovered that the voltage of a circuit is directly proportional to the current flowing through the circuit, meaning that if you triple one, you triple the other. He then came up with a rule for working out the resistance of a circuit (rearranged from his original equation):
Resistance = Current / Voltage
This is the formula I will use to calculate the resistance of the wire.
A wire, showing collisions occurring
If you double the length of the wire, I believe you will double the resistance.
Background:
The flow of charge in a wire is called the current. It is expressed in terms of the number of "coulombs" per second going past a given point on a wire. One coulomb/sec equals 1 ampere (symbol A), a unit of electric current named after a French physicist.
I have explained how resistance occurs above, and volts are an expression of the amount of energy being carried by the electrons flowing through a circuit. The electrons are negatively charged, and move round the circuit (from the negative side to the positive side of the battery) as a result of attraction to the protons.
Plan:
I will carry out the experiment by first affixing the 100cm length of the chosen wire to a ruler, using sellotape.
I will then set the power supply to approximately the right voltage, and then use the variable resistor to set the exact current (measured on the voltmeter). I have to use this method because the PSU itself is not accurate enough for our purposes.
Once this preparation is complete, I will attach the first crocodile clip to one end of the ruler, and the second clip at the first distance, completing the circuit drawn below. The power supply will then be turned on long enough for the measurement to be taken, to prevent the wire heating up.
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I will then set the power supply to approximately the right voltage, and then use the variable resistor to set the exact current (measured on the voltmeter). I have to use this method because the PSU itself is not accurate enough for our purposes.
Once this preparation is complete, I will attach the first crocodile clip to one end of the ruler, and the second clip at the first distance, completing the circuit drawn below. The power supply will then be turned on long enough for the measurement to be taken, to prevent the wire heating up.
Circuit diagram:
Variables and Constants:
o The length of the wire, obviously, will change to give a series of readings.
o I will also vary the voltage used, to see if the same relationship exists at differing voltages.
o The equipment used (see below for list) will all be kept the same, to ensure a fair experiment.
o The temperature of the wire I will attempt to keep the same by turning off equipment when not in use. The wire will heat up (as a result of resistance), and so I will give it a chance to cool.
Apparatus used:
o Meter rule
o 1M length of chosen wire, attached with sellotape to above rule.
o Crocodile clips
o Voltmeter and Ammeter
o Standard power supply
o Variable resistor
o Connecting cables
Safety Considerations:
o The wire will heat up during the experiment, so care must be taken to ensure it does not burn. The current will only be left on for the minimum amount of time, to prevent dangerous heating.
o Some wires available are very thin but strong, and can cut easily into flesh.
o Trailing cables are a hazard, and I must make sure no cables drape onto the floor or similar.
o The power unit is heavy, and should be positioned carefully. Care must be taken when carrying or moving it.
o Crocodile clips can pinch hard, so must not be clipped to fingers.
Analysis of pilot experiment:
I carried out a pilot experiment to determine which wire I should use. I tested several different wire thicknesses, and after considering a number of factors decided the best was Nickel-Chromium of 34 gauge. This was chosen because it was able to handle a range of voltages safely (other wires immediately became dangerously hot), and gave accurate, repetitive results (I tested it several times, and each time the results were the same).
As a result of potentially dangerous incidents with lesser wires, I added the safety point concerning time: the longer any wire is left with current running through it, the hotter it gets.
Measurements
I am going to test the chosen wire at voltages between 2 and 9 volts, the safe maximum for my chosen gauge. This should give a range of results to compare.
The lengths I believe will provide the most easily comparable results are 20,40 and 80 cm, 25, 50 and 100 cm, and 30 and 60cm. You will notice that the series are multiples of one another: this allows me to test my hypothesis (of direct proportionality) several times.
I have decided not to carry out replicates because there are not enough variables to warrant them. If I follow my plan correctly, human error is unlikely and should be obvious, giving a chance to repeat the reading.
Carrying out the experiment:
Method:
I followed the plan I originally decided upon, including the modifications I made as a result of the pilot experiment. I used the chosen NiChrome 34gauge wire, at the voltages and measurements discussed above.
Results:
Here is a chart showing the data I collected. It will allow me to calculate the resistance (using Ohm's law) later.
Length of wire (in centimetres)
Voltages tested (V)
20
40
80
25
50
00
30
60
2
0.4
0.2
0.1
0.32
0.16
0.08
0.26
0.13
3
0.58
0.29
0.14
0.47
0.24
0.12
0.4
0.2
4
0.79
0.38
0.19
0.62
0.31
0.16
0.52
0.26
5
0.49
0.25
0.8
0.39
0.19
0.65
0.33
6
.2
0.58
0.29
0.95
0.5
0.24
0.8
0.39
7
.36
0.67
0.34
.1
0.58
0.27
0.92
0.46
8
.58
0.77
0.39
.25
0.63
0.31
.04
0.51
9
*
0.87
0.44
*
0.72
0.36
.18
0.58
* these lengths the wire heated quickly, and for safety reasons I stopped.
Units is Amps (I)
Using the above data, I was able to calculate the resistance encountered on the wire. This was done using the formula: resistance = current/voltage
Length of wire
20
40
80
25
50
00
30
60
2
5
0
20
6.25
2.5
25
7.692
5.38
3
5.172
0.34
21.43
6.383
2.5
25
7.5
5
4
5.063
0.53
21.05
6.452
2.9
25
7.692
5.38
5
5
0.2
20
6.25
2.82
26.32
7.692
5.15
6
5
0.34
20.69
6.316
2
25
7.5
5.38
7
5.147
0.45
20.59
6.364
2.07
25.93
7.609
5.22
8
5.063
0.39
20.51
6.4
2.7
25.81
7.692
5.69
9
N/a
0.34
20.45
N/a
2.5
25
7.627
5.52
Units is Ohms, the standard measure for resistance
Summary
Length of wire (cm)
Average resistance, across voltages (?)
Standardised Table Results (for evaluation purposes)(?)
20
5.06
5.04
40
0.33
0.08
80
20.59
20.16
25
6.34
6.3
50
2.50
2.6
00
25.38
25.2
30
7.62
7.56
60
5.34
5.12
For comparative purposes, I have plotted my results on a graph, firstly current vs. voltage and then power vs. resistance. This will allow me to draw a successful conclusion.
Conclusion
From the graph I plotted, it is evident that the resistance of a wire IS directly proportional to the length, shown by the way a line of best fit passes through the origin. This result agrees with my hypothesis, proving my prediction correct. As I discovered in my background research, resistance is a result of charged electrons, while attempting to flow through the wire, colliding with the ions that make up the wire. When they collide, they lose their energy - affecting the end voltage. My initial belief was that each length of wire had the same number of fixed ions in it - and therefore the same resistance. As you increased the length of the wire, the number of fixed ions would increase as well, by a fixed amount. This directly proportional increase in number of fixed ions would lead to a directly proportional increase in resistance. From the results I have gathered, it seems my prediction of how electrons move is correct.
Comparing my results to official industry figures (from a "standardised table of results"), I can see my results were very close, further testament to the accuracy with which I carried out the experiment.
Evaluation
Looking at my table of results, I can see all the values are very close - always less than 1 ohm out. This shows a high degree of accuracy, with no stray or anomalous results. An interesting observation is that at the higher lengths (particularly evident at 100cm), the results are slightly less accurate (varying by a maximum of 1.32?) then at shorter lengths (varying by only 0.17 ? at 20cm). This may be due to the fact that I started my experiment at 100cm, before moving along to shorter lengths, and as I progressed I become more competent at taking readings. Alternatively, this may be due to the state of the wire, a factor I didn't take into account. However, these variances didn't affect my results.
My final results are also very close to those from the Standardised Table of Results, but are slightly higher, indicating a marginally higher overall resistance (present across the readings). There are numerous ways in which this overhead occurred - perhaps due to equipment or method used - but my theory of a directly-proportional increase still remains correct, because all my readings have this gain. Consequently, my readings are still accurate, and my prediction correct.
I had no anomalous (or "freak") results and all my results showed strong positive correlation, as expected. My results were very close to the official figures showing how accurately I carried out the experiment, which in turn gave me very reliable figures.
Overall, the evidence I gathered was of sufficient accuracy and reliability to allow me to prove my hypothesis and draw a successful conclusion.
If I wished to improve the experiment, I could attempt to improve the accuracy with which I measure the current, perhaps using more accurate equipment. I do not need to increase the number of measurements - the range I had was sufficient.