If the length of a wire is doubled, the resistance is doubled and the current is halved. This is because twice the length of wire is equivalent to two equal resistances in series so having a long length of wire will just be the same as having 2 lengths of wire half the size. Current will decrease with length, therefore Current is inversely proportional to length.
Experimental Procedure
The key factor that I plan to investigate is the length of the wire; I will vary the length of the wire and record the effects of how varying the length will affect the current that flows through it. I will use 9 different lengths of wire ranging from 10cm to 90cm and measure the current that flows through the wire at each of these lengths, while trying to keep the voltage, cross sectional area of the wire and temperature as constant as possible. I chose to use a nickel-chrome wire with s.w.g 30, as I felt this was the best one to use. This is because it is neither too thick, nor too thin and so the current flowing through the wire should not be too greatly affected by the resistance. I am planning to take two readings at each of the 9 lengths to ensure the results are accurate and reliable.
I will do this by;
- I will set up a circuit
- I will use the variable resistor to vary the voltage to 1.20V and keep it constant.
- I will use a metre ruler to measure out 90 cm of nickel-chrome wire and then use crocodile clips to adjust the length of the wire.
- I will read the ammeter to find the current flowing through the wire.
- I must ensure that the wire does not heat up and I will do this by using the switch to switch the circuit off when it is not in use.
- Repeat the above for all the lengths of wire: 10, 20, 30, 40, 50, 60, 70, 80 and 90cm.
I conducted trial experiments and used the extremes; highest and lowest lengths of wire to ensure that the values were a good enough range for reasonable experiment. The results I got for the trial experiments at a fixed voltage of 1.20V and a nickel-chrome wire of 30s.w.g. were:
I found that the problem with these results were the fact that the current was too high and I feel the reason for this was that the voltage, at 1.20V was too high. However I had a problem, 1.20V was the only voltage I could find where I could get a current reading for both extremes. The only way I could think of, of reducing the voltage was to add in another variable resistor
Prediction
A metal consists of ions (metal cations) surrounded by electrons. These electrons are free to move through the structure of the metal. When there is no applied external electric field, the electrons move randomly. When an electric field is applied, however, the electrons will be attracted towards the more positive potential and the cations towards the more negative potential. It is only the electrons which are free to move, these travel towards the positive potential. The electrons are accelerated towards the positive potential and their kinetic energy increases. But as they move through the metal they collide with the metal ions, this has the effect of slowing the electrons down and transferring some of the electron’s energy to the metal. In addition to slowing the electrons down, energy is transferred to the metal and this acts to heat up the metal. As the metal gets hotter and hotter, the metal ions vibrate more and more and so the number of collisions between ions and electrons increase, in effect the resistance to current flow increases.
Based on the theory, I predict that if the length of the wire is doubled then the resistance doubles. This means that the shorter the length of wire, the more current will pass through as there are less positive ions for the electrons to collide with and lose their energy which means that there is more of a chance for the electrons to get through per second which would result in a larger current.
Results Table
Obtaining
I feel that my experiment worked very well, the results were what I expected as when I plotted the graph I got a smooth curve with a negative gradient. I had to modify my original plan on which I conducted my trial experiments; this was because the voltage was too high and the current was too high. To get the current lower I had to lower the voltage and I did this using a variable resistor. I had problems trying to find a voltage that gave both a low current and worked for both extremes of my wire. I eventually settled on a voltage of 1 Volt.
There were many precautions that I had to take. To begin with I had to ensure that the wire did not get too hot as if it did, the vibration of the atoms in the metal would be greater and the free electrons within the metal would be more likely collide with the vibrating atoms thus hampering the movement of the electrons. The more the atoms vibrate, the greater the chance of collision would be which would result in the current being less and the resistance being greater.
I also had to try to make sure that the voltage was as accurate as possible, I experienced problems whilst doing this as it was difficult to adjust the variable resistor and also stop the voltage fluctuating.
I had to try my best to ensure that the length of the wire as accurate as possible by measuring from the right of the crocodile clips each time.
Analysis
The graph to show how the length of a wire affects the current flowing through it has a negative gradient which proves that as the length of the wire increases, the current decreases. This is because as the length of the wire increases, the resistance increases and as a result of this the current decreases.
When the length of wire is 10cm the average current is 0.672A. The current here is fairly high and this is because as the wire is short, there are less positive ions for the electrons to collide with and lose their energy. This results in there being more electrons passing through every second and so the current is higher.
For a length of 20cm, the first result I got was anomalous and I knew this because when I repeated the result a further two times, I got a reading from the ammeter stating that the current was 0.349A, so when I calculate the average current for 20cm, I did not use the value of 0.282 as it was inconsistent with the other readings for the same length of wire.
At a length of 90cm, the average current is 0.077, which is considerably less then that of 10cm. This is what I would expect, as the longer the length of the wire, the more difficult it is for current to flow as there is more material for the current to pass through and so there are more positive ions for the electrons to collide with and lose their energy. This results in there being less of a chance for the electrons to get through and so the current is less.
Overall this graph shows that as the length of the wire increases from 10cm to 90cm, the current decreases from an average of 0.672A to 0.077A.
For the second graph I plotted ‘1 / Current’ to show that the relationship between current and length was inversely proportional – as the length doubles, the current halves.
In plotting 1/current and getting a straight line through the origin, it shows that current and length is inversely proportional because if 1/current against length is a straight line through the origin, then current against length must be inversely proportional. If two variables are inversely proportional, then the variable y is inversely proportional to the variable x if there is a non-zero constant k so that y = _k_ x
In this case y = length and x = current.
For this graph I had an inaccurate result, this was the one for 10cm length of wire; however I feel that this is probably because the wire is getting hot despite my efforts to keep it cool and so this may have affected the result. I did not however have any anomalous results.
Evaluation
I feel that I obtained good results which gave me an accurate conclusion. The final method I used to collect the results also worked very well.
I was extremely pleased with the results that I obtained. By looking at the results table, I can see that the all my repeats were very similar and gave me a smooth line through all the points on my graph. There was one result I recorded for 20cm of wire that was very different to all the other results for the same length. As a result of this I had to ensure I did not use that value when calculating the average. I did not have any anomalous results as they all followed the trend and I got a smooth curve through all my points.
I feel that although my results were good I could have improved the experimental procedure to make them more accurate. At some points during the experiment the crocodile clips had been difficult to clip on to the wire with. It was also difficult to ensure that they were measured from the same point each time. Next time this could be avoided by aid of a device, which is more steady and stable when clipped on, in comparison to the crocodile clips. Also I could use thinner crocodile clips which would be only a few millimetres long ensuring that the contact was thinner and so the length was more accurate.
The wires may have not been able to cool down properly before each reading, so that if the temperature were higher, that would make the resistance higher. To solve this, I could make sure that the power supply is switched off after and before each reading, for approximately 20/30 seconds. However doing this may not make the wire cool down completely, so I could use a device which can take the temperature of the wire, before the experiment, and then after each reading, wait for it to cool down and resume its original temperature. The voltage also continuously fluctuated, to control this I could use a finer variable resistor also I could use 2 variable resistors; one of which would make the large changes and the second of which would make the small changes ensuring accuracy.
I feel that I controlled the fixed variable such as temperature and voltage very well. As I explained earlier I experienced problems when trying to keep the voltage constant as it kept fluctuating however I found that this problem can be solved by using two variable resistors. I tried to keep the temperature as constant as possible by switching the circuit off every time I was not using it. I feel this may have helped as my results are accurate and there is no evidence of temperature affecting the results greatly as seen from the graph.
My conclusion is a very limited one, it is only suitable a wire of length up to 90cm. This conclusion may not necessarily be the same for other lengths of wire. Also the results are only for one type of wire. The results and therefore the conclusion would be different for another type of wire as it may conduct better resulting in a larger current. The results are at a constant voltage of 1 volt. If the voltage was higher there would be a larger current as the electrons would be provided with more energy giving them more of a chance of passing through the wire. The cross sectional area of the wire was also the same in all the wires, this means that the conclusion that I have reached is only suitable for a nickel-chrome wire of cross sectional area 30 with a voltage supply of 1 volt.
To expand on my conclusion, I could expand on the experimental procedure. I could use the same experiment on different wire cross sectional areas and different voltages to see if they gave me a similar conclusion. I could also experiment with wires mad of different materials to see if my conclusion related to any other material of wire.
