Investigating The Resistance of Wire.

Introduction

The aim of my investigation is to find out how the resistance of a specific wire will change within a circuit by adjusting a particular variable. There are many variables, which would have an effect upon the resistance of a wire, the most obvious being the length of the wire. By cutting different lengths of wire I think that the resistance will adjust accordingly. The other variables that would affect the resistance of the wire are its temperature, thickness and the material from which the wire is made. Having said this I have decided to investigate the significance of the length of wire because I think that not only is it one of the more simpler variables, giving simple and accurate results but also it the factor which I think will have the most significant effect on the resistance of the wire. If I were to use the temperature as my variable I think it would become very impractical and difficult to get an adequate range of different temperatures to get good results. Having said this if I were to use the temperature of the wire as my variable I think that as the temperature of the wire increased so would the resistance ie the greater the temp the greater the resistance. This is based upon the fact that as the temperature increases the atoms vibrate increasingly and to the point where they hinder the path of electrons.

If I had used the thickness as my variable (which I think would be quite complicated and would not achieve as good results as it is extremely hard to make sure that all of the pieces of wire are the same thickness throughout the length) I think that as the thickness decreased the resistance would increase ie the thinner the wire the greater the resistance. This prediction is based upon the fact that if the thickness were to decrease then there would surely be a smaller amount of paths for the electrons to travel through and the fact that less electrons would be able to travel through at one time and so the resistance of the wire would be inversely proportional to the thickness.

The material from which the wire is made would be very hard to use as a variable because once again it would be very difficult to get an adequate range of different materials to get any decent results. Having said this the material from which the wire is made would be a very significant factor in how much resistance the wire has because all different metals have different densitys. And so had I used the material as my variable I think I would have found that the higher the density the higher the resitance. This is based on the fact that the higher the density the more atoms there are to be impeded by and so the more the electrons would be slowed down by.

And so in conclusion I have chosen to use the length of the wire as my variable because it seems to be the simplest one and yet will probably achieve the best results.

Hypothesis

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And so in conclusion I have chosen to use the length of the wire as my variable because it seems to be the simplest one and yet will probably achieve the best results.

Hypothesis

I think that as the length of the wire increases so will the resistance i.e. the longer the wire is the greater its resistance. I also think that the resistance will be directly proportional to the length of the wire, by this I mean that if the length of the wire doubles the resistance will double with it. And so where ‘l’ is the length of the wire, ‘r’ its resistance, and ‘n’ any factor; n x l = n x r. therefore if I were to increase the length of the wire in the experiment by a certain factor the resistance would in turn increase by the same factor.

Explanation

Resistance is when the electrons (the electrons make up the current) bump into the atoms of a resistor and are thus slowed down.

How resistant a material is or in this case how resistant the wire is, is determined by how much the electrons bump into the atoms, thus how much they are slowed down. And so it is self explanatory that if you have two wires, one with a higher density than the other that one will obviously have the higher resistance because there are more atoms to bump into or be hindered by. Also a longer piece of wire is likely to be more resistant due to the fact that there are simply more atoms to bump into and it takes longer to get through the wire and thus are hindered by them for a longer period of time. Having said this in order to get the best resuIts possible I have only used one variable; the length and so the thickness and the material (density) of the wire has remained constant throughout the experiment. In my hypothesis I predicted that that the resistance would be directly proportional to the length. This was based on the logic that if you double the length of the wire the amount of atoms that the electrons can be impeded by is bound to double with it, along with the amount of time that they exposed to the resistance. Therefore this applies to a wire of any density or thickness; double the length and the resistance will double as well.

Plan and Method

For this experiment we have been given a specific setup to use to test our hypothesi (see above). In order for the resistance to be tested we first of all need a power supply for which I will use the mains, however the mains is far to strong for this experiment and so will need to use a unit which can be connected to the mains which allows me to control the voltage. For this experiment the voltage will be constant at 4 volts. In order to take the readings I will need an ammeter, the wire and a voltmeter the ammeter and wire will be connected in series whilst the voltmeter will be connected in parallel. In order for the circuit to work t has to be complete and so the wire is connected by a terminal at each end which will hold it in place. This allows the complete length of the the wire to be connected. Once this was all set up we proceded with the actual experiment. This consisted of turning the mains on and adjusting the voltage to 4volts (which I was able to check by looking at the reading on the voltmeter) and taking the readings from the ammeter. I used the same three pieces of wire throughout the experiment in order to try and make it as fair as possible. This was done by first cutting three pieces of wire from the same reel all exactly one meter long.

In order to test my variable and in turn my hypothesis I started with three pieces wire all 1m as I stated earlier making sure the wire doesn’t touch itself when connected because if it did it would short circuit. I then cut and took the readings of progressively shorter lengths of wire, this was done by cutting off five centimetres of the wire after every reading. I used three sets of the same wire so that I could take three readings from which I could then take the average, making the experiment much more accurate as any inaccuracies or mistakes can be spotted and corrected if necessary. This process was repeated all the way down to 10 cm, I was unable to go all the way down to 5 cm because it would simply have been to short to stretch across the terminals and so the circuit would have been incomplete and so I took three sets of nineteen readings ie 57 readings in total. As the lengths of wire got shorter and shorter the wire started to heat up due to the current with increasing magnitude and so it was extremely easy to melt the wire and oneself. Also in order to keep the results as accurate as possible I had to take the readings very quickly and switch of the mains in between each reading as the heat of the wire was likely to effect the resistance. In order to obtain good results I needed to keep all the other factors that could have an effected the restistance constant ie due to the converter I had plugged into the mains I was able to keep the voltage at 4 volts at all times and as for the thickness I have to rely on the company which made the wire to have made it with the same thickness all the way through.

When I had taken all the 57 results I put them in an excel spreadsheet was therefore able to calculate the current averages for each different length with great ease. As the aim of the experiment was to see how the resistance was effected by the length of wire I needed to find the resistance. This was done by using the formula resistance=voltage divided by the current; R=V / I, once this had been done for all the different lengths I plotted the resistance against the lengths on a graph. Therefore once I had drawn line of best fit throught he points on the graph I was able to see whether my hypothesis had been correct ie if the length was directly proportional to the resistance I would have expected to see a straight line graph going through he origin: “y=x” looking roughly like this;

The reason why it goes through the origin is that if there is no wire there is no resistance.

Results

*resistance is measured in ohms

Conclusion

My hypothesis that the length is directly proportional to the resistance has been shown to be true. The following backs up my hypothesis:

Resistance of wire (R) = Constant (K) x Length of Wire (L)

To check my hypothesis I have made this table and if my hypothesis is correct then the constant should remain the same. Note the readings are taken from the best fit line however in order to prove this I have only used 5 readings at intervals of ten cms.

And so this proves my hypothesis to be correct as the constant is more or less the same and the By observation, it is obvious that the constant is pretty much the same throughout, varying only by 0.43. Also, it is also very close to the gradient that I have calculated in the previous section. (Gradient = 11.4).

Therefore, I conclude that the resistance of the wire is directly proportional to the length of the wire.

Analysis

Due to the fact that I took three readings for each length and used a different piece of wire for each length the experiment were very accurate and in turn so were the results. This is simply manifested by the fact that none of the three readings vary by more than 0.05A. And so the results showed a very straight line thus proving my hypothesis; the length is directly proportional to the resistance.

There was a problem with the experiment however and that was that as the lengths of wire got shorter they became increasingly hot. This was due to the large current that was being forced through the wire causing a huge amount of friction; friction produces heat, and as more current flows through the wire more friction is produced. Because of the immense heat of the wire (we were able melt through a plastic pen with it) it became very unstable and the readings varied drastically. The resistant greatly increases when the wire is hot because it is heated to the extent that the atoms in the wire start shaking which makes it increasingly hard for the electrons to get through the wire.

In order to solve this problem I had to leave the wire to cool down between each reading by turning the mains off and then turning it on for a slight second to quickly take the readings. Another way of getting round this problem would be to lower the voltage being put in thus lowering the current, this would still give the same result ie the same resistance reading due to ohm’s law.

However if I were to be given the chance to redo the experiment there would be certain things which I would change. The first thing that I would change would be the connection terminal which connected the wire to the circuit. The problem was that there were nearly always different amounts of wire sticking out the other end of the terminal, therefore varying the proper lengths of wire and so compromising the accuracy of the results.

I would also find it interesting to look further into the investigation by looking at the effect of some of the other variables. By this I mean that I would like to look at the effect of the diameter of the wire and the thickness.