To make this a fair test all wire must be of the same material and thickness and must all be at the same temperature. All components in the circuit except for the variable must say the same.
Drawing the graph for each length of wire will ensure measurements are as reliable and accurate as possible by averaging out the results.
Apparatus needed for this experiment:
Power supply,
Variable resistor,
Wires (crocodile clips),
Voltmeter,
Ammeter,
Metre ruler,
Wire.
Experimental set-up
Safety problems
When a lot of current flows through a wire it tends to get bit warm, sometimes even glowing red hot, touching wire when in this state could cause severe burns and if it touched work surfaces at this temperature it could be a fire hazard. To deal with this we elevate the wire using crocodile clips and stand and clamp. This stops it touching all surfaces.
Predictions
My predictions are that by increasing the length of the wire we will also increase the resistance. This is because of the class work we did on resistors. This showed that two equal resistors, connected in series, is equal to one resistor with the resistance of both resistors added together. e.g.
This would also apply to wire. Effectively if you double the length of the wire, you double the resistance. e.g.
I also predict that the thicker the wire, the less resistance e.g.
Resisters in parallel (thickness of wire)
- = 1 + 1
R R1 R2
Doubled Area
- = 1 + 1 = 2
R r r
R = r
2
Double the thickness = Halved resistance
Triple the thickness = 1/3 resistance
Quadruple the thickness = ¼ resistance
Preliminary Testing
I did a preliminary investigation of 50cm of wire to re-enforce my predictions. The graph I produced also tested the formulae used to calculate the average resistance for the length of wire.
The graph (next page)re-enforced my predictions and confirmed that the correct method for calculating the resistance was being used.
At 50cm of wire I did an average current table to prove that the results did not vary enough to warrant doing it for every measurement.
The results all proved to be so close together that it proves it’s not worth doing it for every measurement.
Results
This table shows the results we took, with the length in centimetres running along the side, and the voltage along the top. The corresponding values in the table is the current, measured in Amps.
I will now plot these results onto nine separate graphs and a final graph showing Length plotted against resistance.
These results were taken in conjunction with Adam Cubbage. Each of us took part the taking of results.
Final Results
Analysing and drawing conclusions
All these results and graphs show things about the relationship between Resistance and length of wire. The final graph shows an almost perfect straight line of results through the origin. This proves that resistance is directly proportional to the length of wire. If you look carefully on the graph you can see a slight change in pattern after the result for 50cm. This is due to the fact that results were taken over two lessons, the first 4 one day and the final 5 the next. The slight split could be due to a different set of equipment, slightly different components (different power supply etc.) or even something as little as room temperature. If the results were taken over a single period of time I have no doubt there would be an absolutely straight line.
The results also prove that doubling the length of wire, effectively doubles the resistance. For example if you look at the results for 20cm of wire (0.8Ω) and then the results for 40cm of wire (1.6Ω) you will see that the resistance for 40cm of wire is exactly double that of 20cm.
All this evidence supports the prediction I made at the start, that the length of a piece of wire does indeed affect its resistance, and that there is a direct and proportional link between the two.
Evaluation
I think my results were fairly reliable and this was mostly thanks to the system of getting an average resistance from each length of wire, using a graph to average out the results.
As I said before, there is a slight change in pattern after the result for 50cm. This is due to the fact that results were taken over two lessons, the first 4 one day and the final 5 the next. The slight split could be due to a different set of equipment, slightly different components (different power supply etc.) or even something as little as room temperature. The equipment used over the two lessons may have differed slightly, e.g. the meters used to measure current and p.d. If the results were all taken in one go I have no doubt there would be an absolutely straight line. If you draw a line from the point of origin up to the fourth point you can see it is perfect, likewise if you draw a line from the fifth point on the graph to the ninth.
I think this was a very suitable procedure and was certainly the most accurate way of performing this experiment. The only way I would improve it would be by taking all the results over a single period of time. This would avoid the split in the middle of the results. You could do another couple of different lengths but it wouldn’t make much difference to the results. Just using the range that I have you can see all that you need to see to draw conclusions. I would like to try an identical experiment with a wire made of different material, just to see how different the results would be and then compare the two experiments.
The real test for how accurate my results were is to calculate the Resistivity of my results and to compare it with the Resistivity that the wire should be.
Resistivity is a property of a metal (whereas resistance is a property of a component). Resistivity does not depend on the dimensions of a component, only on the material from which it is made. We have done previous experiments to show that the resistance (R) of a conductor is directly proportional to its length (l) and is inversely proportional to its area (A). The diameter for the wire used was around 0.8mm.
To put this into a formula, where p is the Resistivity:
R = pl
A
So:
P (Resistivity) = AR
l
If we take the results for 80cm of wire we can work out the Resistivity of Constantan (the alloy wire we are using).
When l = 0.8m R = 2.7Ω
P = 0.000000173 x 2.7 = 6.07x10 –8 Ω/m
0.8
In an A-level textbook I looked up the Resistivity of Constantan and discovered it should be 4.9 x 10 –8 Ω/m
These two figures are fairly close and this indicates how accurate my experiments were.
