In a smaller length of wire, there are fewer collisions between the fewer number of stationary particles and electrons so the wire is cooler, as shown by the path of the electron.
A piece of wire double of that at the start, means double the number of stationary particles. An electron has to travel further and bump into more electrons, losing more heat energy and heating up the wire more. The longer the wire gets, the more resistance there would be. This is why the graph is a straight line.
Setting out the results: - In order to handle the collected data easily, I would need to draw a table in which to write all the settings and results of the experiment.
Method: - I set up the following circuit –
The wire with ruler, will be connected into the circuit with crocodile clips. The clips will be at 0 and 10 cm on the ruler. I will turn the voltage up to 2V and record the Amps in my table. I will then move the crocodile clips apart another ten centimetres so 1 is on 0 and another is on 20. Again I will record the amps and volts. I will do this all the way up to 80 cm – making sure not to touch the wire, because by my predictions it should be quite hot. Once the graph is filled, I will go about finding the resistance with the formula V/I = volts/current. I will record the resistance in the table.
Preliminary work: - Before the actual experiment, I carried out a dummy experiment in order to get to know how to set up the circuit and also to see what problems could arise through doing the main experiment. I recorded the lengths, volts and amps and worked out the resistance. My table was as follows: -
As I was doing the experiment, I looked back at my results constantly, and constantly, I found I had put the wrong thing due to misreading the ammeter. I would have to be more careful in reading it in the real thing, if I can insure a fair test. Also in the experiment, the resistance didn’t look accurate. To resolve this problem, for the real experiment, I would need to do the experiment twice, then find the average of the two resistances.
After the dummy experiment, nothing much has changed for the method, except double-checking all the readings and equipment before I use them, and repeat the experiment for more accurate results. The sign that this experiment had worked correctly was the increasing resistance. I was ready for my real experiment.
The experiment: - I set up the circuit as before, placed the crocodile clips ten centimeters apart – one at 0 and one at 10, and continued to take ten readings, each with the crocodile clips a further 10 centimeters apart. This was the table I came up with-
The colours show the two tests and the final column is the average resistance from the two experiments. At this stage, there didn’t seem to be any strange readings. All went according to plan. Also, since I carefully checked the equipment before hand, nothing went wrong in that department.
Results: - The results in the table show a very strong pattern which almost proves my theory of the length being directly proportional to the resistance, for example, at length 20cm, the resistance is 3.7, and at 40cm it is 7.3 – being one decimal place out from being double the original.
As the length of the wire increases, so does the resistance, however, the amps decreases, because more of the energy is lost as heat by the colliding electrons. As said by my prediction, the length of the wire directly affects the resistance, because of the increased number of stationary particles causing it.
The graph: - The line of best fit I have drawn, begins at the origin, because that is when the experiment started, although it is not recorded, because when the length is 0, all other factors would be zero as well. The straight line went through the origin, as well as passing through 3 points.
From the black lines drawn on the graph (taken from the line of best fit) the length of wire is directly proportional to the resistance. At 20cm, the line of best fit is at 3.7 ohms, whilst at 40cm, the line is at 7.4 ohms. However, although most points are quite close to the line, the anomalies occur towards the end, where the resistance jumps up suddenly at length 70-80cm. This is because, as the electrons need to bump into more particles, they transfer more energy and heat up. This extra heat makes the stationery particles to vibrate, further slowing down the electrons. Increasing resistance. However, I only did the lengths up to 80, so the full effect of what the temperature had on the experiment is unknown.
The sloping gradient means that the resistance is rising almost steadily. The steeper the line, the lower the resistance. The gradient of this graph is 10.7. This means that the resistance of the wire we used is about average compared to other materials.
In the end, this graph, and my table, proved my original hypothesis to be exactly right, as well as my prediction of how the final graph would look.
Evaluation of experiment: - Overall my experiment went well. I managed to find out how the length affected the resistance, and also why the wire heated up. In addition, I also learnt that the length is actually directly proportional to resistance. The points formed a strong positive correlation, and all of them were close to the line of best fit, including the anomalies at the end that were caused by the heat.
However, although most of the crosses fit neatly onto or around the line, they could have been a lot more accurate. For example, the voltmeter we used would keep flicking between two or three decimal points, so in the end we just had to pick one and do with it. Although it might only be a miscalculation by a few tenths, it can have a large affect on the final layout of the graph. Also, a factor contributing to the inaccuracy of the experiment was the wire. As it was stuck onto the ruler, it was loose and slack. As a result the lengths we said we measured, might not have been the true lengths of the wire at the time, and could have been even a centimetre out. As a result, many more pieces of cello-tape had to be stuck onto the ruler, and the wire constantly pulled into place. The crocodile clips we used also weren’t ideal for the experiment. When clipped on to the wire, they might be either past or before the mark they were supposed to be, thus if this happened every time, each length could be nearly ½ a centimetre out. This means the amps and volts could be different for each length, meaning the end result of the resistance is different.
I could not do anything about the flicking amp and volt meter, but I could about making the wire tighter, and checking it was perfectly straight, and also by making sure I put the main part of the crocodile clip on the number of the length I intend to measure.
As well as this, too make the experiment a lot more accurate, would be, instead of taking measurements every 10cm, to take measurements every 5 cm. This would fill in the gaps between the points so I could make a better line of best fit. Also I could continue my measurements up to the area of about 200 – 250 cm, so I could see any extreme temperatures the heat and length have on the resistance.
Although my graph is not perfect, it gives the basis for me to say that it proves my prediction to be right, and any alterations to the experiment, will not have such an effect on the graph, that it will change it. I think my graph is relatively reliable, because even with any changes to the method, the graph will still remain in near enough the same shape.