What factors affect the resistance of a wire
John Saunders (10R) April '02
Assessment practical
Investigation: what factors affect the resistance of a wire?
Introduction:
In the experiment I will see if the resistance is affected by diameter of a wire.
In this case, it wouldn't matter how long the wire were to be, as long as a wire has a larger diameter, then it would have a larger volume in which the electrons flowing in it could use up. This extra space will create more space per electron to flow in, and so it is likely that fewer collisions will occur. Smaller number of collisions means that the resistance will be smaller, so the resistance should be affected because it will now be less.
The diagram above shows two wires of the same length, but with a different diameter. Whereas a longer wire has a larger area in which more collisions can occur (because the electrons have further to travel), a wider wire has more area in which less collisions can occur. This is because the wires are the same length, which means the electrons have the same distance to travel, but at the same time wider wires have more room per electron when flowing. This means there is less chance of two electrons colliding.
This can be demonstrated by people walking down a corridor, if there are a thousand people walking down a five meter wide corridor, it would be a lot harder and a lot slower than if the corridor were 50 metres wide, because there would be more room for people to get down it and less friction (heat energy) will be produced. Heat energy also causes resistance.
Method:
In the experiment, we will use:
* An ammeter and voltmeter
* A lab pack (for mains supply)
* Different diameter wires (that are 0.16, 0.25, 0.31, 0.45, 0.71 and 1.25mm wide), all being one metre long.
* Link wires (to complete the circuit)
* A one-metre ruler
In this circuit, which we will use for the experiment, the cell represents the lab pack battery, the circled V and A represent the voltage reader and current reader respectively, and the dotted line represents the one metre wire we shall use with the different diameters.
In the experiment, I will use one metre of wire, which will be measured using a board set up by the science dept. so that the wires are perfectly straight and parallel to each other, and so that it cuts out all the nonsense of measuring wires which are not fixed in place anywhere. The main advantage of this isn't only that it will save a lot of time, but if the wires are coiled in the experiment, the resistance could have been affected more than we wanted (like with the filament in light bulbs).
I will also need to do several tests with the experiment, to make sure that any inaccurate results don't affect my final results too much. As I will explain in more detail in my fair test section, if I was to only do one test, then any anomalous results will look a lot more inaccurate than if I was to do two tests, in which I could look for flaws in my method that could have been making my tests inaccurate. This could make my second test a lot better, and therefore make my average result a lot more accurate.
I will set the lab pack voltage to 2V. I will measure the voltage of the circuit in volts and I will measure the amp level of the circuit in amps. I will then use these measurements of the voltage and current to find the resistance of the wire, in ohms (?)
I will use the formula R = V ? I, meaning resistance (?) = voltage (volts) ? current (amps) to work out the resistance of the wire.
Fair test:
I am going to make this experiment a fair test by doing several things. ...
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I will set the lab pack voltage to 2V. I will measure the voltage of the circuit in volts and I will measure the amp level of the circuit in amps. I will then use these measurements of the voltage and current to find the resistance of the wire, in ohms (?)
I will use the formula R = V ? I, meaning resistance (?) = voltage (volts) ? current (amps) to work out the resistance of the wire.
Fair test:
I am going to make this experiment a fair test by doing several things. As far as the preparation of the circuit is concerned, I will use a ruler to measure each length of wire to be the same (one metre). Also, I will set the lab pack so that each voltage running through the circuit will be the same (2 volts).
I will do the experiment once, but then I will do the experiment again to make sure no wild results will affect the final results too much. I will do this by taking the average of both my results using the mean (add the results up and divide them by two). This will make my error margins less because if my second test was correct, but my first test went completely wrong for some reason, then that error wouldn't matter as much. This would be because the average result would mean the deficit of the first test would only be half of what it would be if I only used my first test as the result, because the second test here would be right.
The only problem with the method for the experiment is that heat energy will be produced when the experiment will be happening, by the friction between the colliding electrons. This would create more resistance, because the slightly higher temperatures of the one metre wire will mean that the bonds will weaken between each atom of it, making it more difficult for electrons to get through them to the next atom in the wire. Sadly, there isn't anything I can do about this problem, but hopefully this extra resistance produced won't affect my results too much.
Prediction:
I think that the wider the diameter of the wire, the smaller the resistance will be, because as I explained in my introduction, there will be more room in the wire per electron in the current of the circuit. This will mean fewer collisions will occur and therefore the electrons won't be slowed down, which is how resistance is caused.
I think there will be proportionality between diameter and resistance. This is because there should be no reason as to why there should be more collisions within a set area with the same number of electrons flowing through it (as explained under fair test). It will depend as to whether my table of results will show proportionality because there may be no set pattern between the different diameters. I will overcome this to see whether the results are proportional by making a scale on my diameter axis on the graph, for example, I could make every 10x10 square a millimetre diameter.
The only way that this prediction could go wrong is if the heat energy caused affects this proportionality (again explained under my introduction). Even if this does affect it though, it should still make a perfect curve on my graph, because there should be a link between the diameters of the wires and the amount of heat energy created, because after all, heat energy is another form of resistance.
Results:
TEST 1
TEST 2
Average of tests
Wire
Diameter
(mm)
Volts
(V)
Amps
(A)
Volts
(V)
Amps
(A)
Volts
(V)
Amps
(A)
R = V ? I
(Resistance ?)
A
.25
.24
2.80
.26
2.83
.25
2.815
0.44404
B
0.71
2.16
.71
2.15
.72
2.155
.715
0.76554
C
0.45
2.90
0.90
2.88
0.92
2.89
0.91
3.17582
D
0.31
3.29
0.52
3.24
0.52
3.265
0.52
6.27884
E
0.25
3.60
0.28
3.60
0.28
3.60
0.28
2.85714
F
0.16
3.82
0.12
3.84
0.12
3.83
0.12
31.91666
As you can see, the diameters of the wires are not in a set pattern, so even though no obvious pattern can be seen within the 'R = V ? I' column (the resistance), there may be one if we were to plot these results on a graph.
Analysis:
I have obtained similar results to both tests for each, wire, so I would like to say first of all that I think unless I made the same mistake in the experiment twice, then these results will be pretty accurate overall. This would be especially as I have then obtained the mean average (results added together ? number of results) so the results would be guaranteed to be as close as they could be to the actual results professional scientists would get.
My graph of the results on page 5 show my results overall. Because the diameters of each wire didn't have a set pattern to them, I used a scale on my 'x' axis so that each result didn't look different to each other in relevance to the extra/less difference in diameter they had between them. This would also allow us to be able to tell us any resistance of a wire on the between 0.185mm and 1.25mm diameter, where my line of best has been drawn.
As for the actual experiment, it didn't fit my prediction at all. I expected proportional results because unless the voltage was altered from 2V to start with, then there would be no extra obstructions to the flowing electrons. This may be true but I think have an explanation for this. As the resistance increases, more and more electrons crash into each other slowing then down. This also causes friction, which in turn causes heat energy. Look in the final paragraph of 'fair test' for a more detailed explanation of this.
This would explain the reason that the graph is a perfect curve as far as my line of best fit is concerned, because the extra heat generated will mean it should slow down more proportionally to create this perfect curve. Also, I could still back up my results, as I can say that the points all still follow the same basic pattern so that all the results look as if they're correct. I still think though, that if it wasn't for this heat energy, then my prediction would have been correct, as the resistance and diameter of the wire should have been proportional.
So, in conclusion, I can say that as the diameter of a wire gets less, the resistance increases more, because there is less room for electrons to flow through it (refer to introduction) and that heat caused by friction has a positive impact on increasing the resistance too, thus creating a perfect curve on a graph (refer to last paragraph on fair test)
I could back up my conclusion to say its correct by looking at where a specific or random diameter length of a wire is on the 'y' axis, and then going across this point horizontally until the it meets the line of best fit. Then, you can to vertically down from this point until you get to the 'x' axis (resistance in ohms), and then read what it says. If in another experiment set up in exactly the same way as this one, only using different diameters, was to show the same results as on the graph, I could then say my conclusion is correct.
The two lines that join the resistance and diameter axis up and the line of best fit indicate to us that we can find the resistance that is relevant to any diameter wire as long as we use this method. If in another experiment exactly the same as this one the diameter of the wire tells us the correct resistance, then I could therefore say that my conclusion is correct
Evaluation:
Overall, I think my experiment went pretty well, and therefore was pretty accurate. This was because apart from 2-3 hundredths of an amp or volts, the results were the same for both tests.
Firstly, as time was running out, we gradually had less care in measuring the wires, because we didn't have quite so much time in doing the second test. Supposing every time we measured, 1cm was under or over measured, the result within the trend of the line of best fit could have been slightly affected. This is particularly with the thicker wires where the difference in the resistance was less than an ohm.
We could have got over this by using several methods. Firstly, I think we could have used a permanent marker or even paint on the wires (so that the marks wouldn't wipe of the wires) to make 1m marks on all the wires. This would have been a very good way of saving time, but yet making a very effective way to measure 1m marks precisely.
Infact, you would only have to make 2 marks instead of what you would think to be making - 6. This is because you could simply measure wires A and F (which were at either end of all the wires) and because the wires are all parallel to each other (see method), we could simply put the ruler against these two marks to draw a straight mark down the middle, and over each wire where exactly 1m of wire was.
Although I found this mistake, the results were pretty accurate. There were only two very slightly anomalous results, which I think can be accounted for in the very slight inaccurate measuring in the second test.
If this didn't cause these anomalous results, then I think that it wasn't the experiment that went wrong, but the unavoidable lack of accuracy on the very large scale of the graph. To plot results in the exact right spot on such a large scale would be virtually impossible by hand because in the end, where I plot my result is human judgement and I could have so easily plotted one ever so slightly wrong. I could back this up by the fact that the anomalous result for a diameter of 0.45mm didn't look like an anomalous result to me until I drew my line of best fit on.
Even if I decided to draw a graph over several pages so that I could try and get rid of this human error, by making a much smaller scale for the 'x' axis, then I think the line of best fit would have been a lot harder to draw correctly, creating more room for human error in this way, too. This is a 'catch 22' situation, because if I was to draw either a small graph or a larger graph, I probably could never get the results or the line of best fit plotted perfectly.
Overall, I think that these results could back up my conclusion sufficiently. This is because apart from the two very slight anomalous results, that the results all did follow a trend (the perfect curve), and I do think that the experiment was carried out pretty well on the whole.