Between each of my readings I will change the thickness of my wire using my 5 wire thicknesses of 22,24,26,28 and 30 SWG. This is one of the steps I have taken to ensure my results are accurate; if the results are evenly spaced out then I should be able to see a pattern easier, which in theory there should be. Another step I will take is to repeat all of my readings twice, and if after repeating this, one of my results is very different I will repeat that reading again and again till I am sure what the correct value should be. 5 points should also be enough to create a reasonably reliable graph.
I now need to consider how I am going to make this a fair test, I need to consider the other factors that affect resistance and try to stop them affecting my experiment. Below is a list of the factors which could affect the resistance and how I will try to ensure that it doesn’t:
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Firstly, temperature is a factor. If the wire is heated, the atoms will move around more because there will be an increase in energy. This would cause more collisions between the atoms and the electrons. The increase in collisions would cause the resistance to increase. I will tackle this problem by using a switch in my circuit and take the readings quickly. So that the heat energy released through resistance cannot build up, to a level which could affect my results. I will also keep the voltage at a fairly low level, to ensure that the electrons have do not lose as much energy, and therefore heat up the wire less.
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Secondly, the material used would be a factor. If the material being used contains atoms with a large number of electrons on the outer shells, then there are more electrons available. So, in theory, if the material has a large number of atoms, there should be less resistance, because of the higher number of electrons. However, if the atoms in the wire are closely packed, then this will cause an increase in resistance, due to frequent collisions. There is not much I can do as far as impurities in the metal, which can cause increased resistance, go. However, I can ensure that I use the same type of wire in each of my experiments, e.g. copper.
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Finally, the length of the wire is a factor. The longer the wire, the longer it will take electrons to get to the end of the wire. This is because there will be more collisions between electrons and atoms, the longer the wire the greater the resistance. So, in theory, the length of the wire should be directly proportional to the resistance. It is important to keep the length of the wire the same each time otherwise it could not be certain which variable is changing the resistance. I will solve this problem by laying each of my pieces of wire on a ruler, deciding the length I want my wires to be and connecting at the exact point on the ruler, diagram below.
In my experiment I will use, the following equipment:
Through using the same circuit I could have tested a number of different things that affect resistance to find the relationship between resistance and the following:
- Temperature - When the temperature of a metal increases the resistance of that metal increases. This is because when the temperature increases the atoms of the metal vibrate more vigorously, due to the increase in energy. This means that the electrons have more difficulty getting through the wire as they collide with the atoms which are in their pathway. This increases the amount of collisions, therefore there is more resistance. However it is hard to keep the temperature exactly the same as the room temperature might change from day to day. I did not investigate temperature because it is hard to control the range of temperature needed without the correct apparatus, which I don’t have.
- Length of wire - The longer the length of the wire, the greater the resistance. This is because there are more atoms from the metal so there is more chance that the electrons would collide with one of the atoms therefore there is more resistance. This is because when you have a long wire, the electrons have to squeeze together for longer to be able to pass through the wire than they do in order to be able to pass through a short wire.
- Types of material - Different materials have different resistances because the materials’ atomic structures are different, some metals have low resistances and some have high resistances. The type of material will affect the amount of free electrons that are able to flow through the wire. The number of free electrons depends on the amount of electrons in the outer shell of the atoms, so if there are more or larger atoms then there must be more electrons available. If the material has a high number of atoms there will be high number of electrons causing a lower resistance because of the increase of the number of electrons. If the particles in the material are tightly packed together, the electrons will have more collisions and therefore more resistance.
Obtaining
Below is a table of my results, including raw data and processed information:
Analysis
My results fitted my predictions well and I have included a graph of my results on the following page. I had to find a line of best fit that went through the origin, so as to find the link between cross-sectional area (CSA) and resistance. Firstly, I decided to use the CSA as apposed to the diameter, as I realized that the diameter is 2D and the CSA 3D. As electrons flow through a 3D object rather than 2D, I knew I had to use CSA. I then tried different forms of CSA but settled on 1/CSA, because it allowed a good line of best fit that went through the origin. As you can see from the graph, 1/CSA is inversely proportional to resistance, i.e. if you increase the CSA of the wire (by increasing the diameter of it) then you decrease the resistance. This is because when the cross-sectional area of the wire doubles, there will be twice as many ions and twice as many electrons bumping into them, but also twice as many electrons getting through, twice as many gaps. If there are twice as many electrons getting through, then there is twice the current, the resistance must have halved. This is the theory I stated in my plan and my results have proved this correct.
However, this does not mean that if the resistance of a wire is double that of another wire, the diameter of the first wire is half that of the first wire. This is because if you halve the diameter then you decrease the area by a factor of about 3 (A = πr2).
To calculate the CSA I used the formula A=πr2, I simply halved the diameter value for the SWG rating that I had received off the internet, to get the radius value.
My results have not been accurate enough to draw a straight line through them all points, so I have used a line of best fit. A line of best fit, if drawn well, lies in the middle of all the points, possibly not going through any but having an equal distance and number of points on each side.
In my two repeats of this experiment my results were not exactly the same, but they followed the same pattern, the greater the CSA the smaller the resistance. It is because of this that I decided I had no anomalous results; the results were also fairly close together, the greatest difference I had was between 1.33 and 1.78, which isn’t that big a difference. I compensated for these slight fluctuations in results by calculating the average.
Evaluation
I believe through this experiment that I have gathered enough evidence to say confidently that, 1/cross-sectional area is inversely proportional to resistance, which is clearly shown on my graph.
I am fairly happy with my results, although they did differ slightly; this could be down to error on my part or could be due to one or both of the following:
- For any particular result, one or more of the connections could have been faulty, causing extra resistance at the connections. A solution to this would be to, before each experiment, connect the connections together without the wire in place and measure the resistance then. If it is higher than it should be then the connections could be cleaned.
- It is possible that the batteries were providing a different voltage for some of the results. This is unlikely to be a problem as whatever the voltage is the resistance should stay the same.
- If you take into account one of the factors that Ohm’s Law applies, then another possible explanation could be that at some point the wire was not allowed to cool completely, so that the temperature was higher for that measurement. Whilst unlikely (due to the two repeats of results), this would cause a higher resistance as explained previously.
To improve my results I could have also used pointers instead of the crocodile clips which I used for connecting the wire. I would do this because pointers are a lot more accurate, they have a smaller surface area on their tips than crocodile clips. This in effect would give much more accurate measurements.
