The secondary sources I used to research my experiment were; the Internet, several physics websites, GCSE Physics cd-rom by DK.
The two factors that I have chosen & my prediction:
I have chosen wire length and the cross sectional area because they are the most effective and easiest factor to measure. The material could not be tested, as there is not a wide range of materials or equipment to test this factor. The temperature of the equipment is not going to be tested because we did not have the equipment and it was more complex.
“Wire length: If the length of the wire is increased then the resistance will also increase as the
electrons will have a longer distance to travel and so more collisions will occur. Due to this
the length increase should be proportional to the resistance increase.
Wire width: If the wires width is increased the resistance will decrease. This is because of the
increase in the space for the electrons to travel through. Due to this increased space between
the atoms there should be fewer collisions “
I am going to conduct some small experiments to find out what lengths and widths of wire are best to achieve the best range of results and to help me on my big experiment. I predict that if the length increases then the resistance will also increase in proportion to the length. I think this because the longer the wire, the more atoms and therefore more likely the electrons are going to collide with the atoms. So if the length is doubled the resistance should also double. This is because if
the length is doubled the numbers of atoms will also double resulting in twice the number of collisions slowing the electrons down and increasing the resistance. If the length was halved the resistance should also half, as the amount of collisions of atoms & electrons should half. My graphs should show that the
length is proportional to the resistance.
Preliminary Test
I shall use an 18 SWG (set Wire Gauge) in this preliminary test and I will use 3 different voltages such as 3V, 6V & 9V. I will connect the equipment as shown in the diagram on the next page. Then I will place the crocodile clip that is connected to the Ammeter and Voltmeter on 10 cm and turn the power pack on at 3 volts and quickly but accurately write down the readings and turn the power pack off as soon as possible to the temperature does not rise, as this will affect my readings. However, the temperature will rise once the current is passing through it, which will cause the atoms in the wire to vibrate, and so obstruct the flow of electrons, so the resistance will increase creating an error. I will try and make sure the wire does not get to hot for safety precautions. I will then turn the power pack onto 6 volts and take the readings again off each device. I will continue to move the crocodile clip further along the wire at every 10cm and at the 3 different voltages until I have 10 lengths – 10cm, 20cm, 30cm, 40cm, 50cm, 60cm, 70cm, 80cm, 90cm & 100cm. I will make sure that the crocodile clip is exactly on the centimetre mark, as this will make the results more accurate.
I will draw a graph from the results I got and set out a table. This preliminary test will help me decide what lengths and voltage to use in my main experiment.
I will use:
5 x Electric Wires
1 x Crocodile clips
5 x Metallic conductive wires
1 x Voltmeter
1 x Ammeter
1 x Power pack
Diagram:
Safety
- I will handle the power supply carefully.
- I am going to only use a voltage of 3 volts for the main experiments.
- I will be careful when handling live wires.
Method:
In the preliminary experiment I will test the voltage (3V, 6V & 9V) and current of the wire. We will collect our equipment and then set it out as shown in the diagram above, by connecting the power pack to an 18 SWG wire. We will not leave the power pack on for a long period of time as this may lead to a rise in temperature which will make the resistance rise un-proportional to the length as we predicted.
This experiment requires safety considerations. Only use low voltages, because the wire will not be able to cope with very high ones. Do not use more than 4V for very long at a time.
Set up the circuit as shown on the above diagram, excluding the voltmeter. Place the crocodile clip at 10cm on the metre stick. Make sure it is clipped firmly to the wire (i.e. the teeth are touching it). Turn on the power supply and test to see if it is working. If not check that all wires are connected correctly and that the bulb is not faulty. Also check that the ammeter is picking up some current. If not, again check to make sure the wires are properly connected and adjust accordingly. Turn off the power supply.
Now connect the voltmeter. Ensure that the wire is connected at 10cm. Turn on the power supply to approximately 3V. Take readings from the voltmeter and ammeter. Turn the power supply off. Repeat this again with 6V and 9V. We are using 3 different voltages in our preliminary experiments to see which voltage would be best.
Move the crocodile clip to 20cm. Make sure the teeth of the clip are firmly on the wire. Turn on the power supply to 3V. Take readings from the voltmeter and ammeter. Turn off the power supply and repeat this paragraph again with 6V and 9V.
Next, repeat the previous paragraph, except replacing "20cm" with "30cm", followed by "40cm", then "50cm", "60cm", "70cm", "90m", and finally "1.00m". Each time use 3V, 6V and 9V on the repeats. This is our preliminary experiments done.
It is important that you turn off the power supply in between readings because otherwise the wire will become too hot. Temperature would be another variable, and would make the test unfair. With heat a wire has more resistance, because the wire particles vibrate with the heat, making it more difficult for electrons to flow through the wire. There are more collisions, meaning less current for the same voltage and more resistance as a result.
We did some preliminary work to (a) find out how these factors affect resistance: temperature, cross-sectional area and resistivity and (b) to find out what material and width would be most suitable for this particular experiment. We needed to know what we would have to keep the same in order for our experiment to be a fair test; what our controlled variables would have to be.
At a higher temperature, a wire is more resistant. So we then knew that we would have to keep the temperature constant throughout the experiment, to keep it a fair test. I managed to do this by quickly switching off the power pack supply every time I had recorded my set of readings. I then left the power pack to rest for a small interval of time before switching it on again to record the next set of readings.
* I also kept the diameter of the wire constant by using the same piece of wire throughout the whole experiment.
Since we also knew that the cross-sectional area of the wire and the resistivity affected resistance in a wire, we decided to tackle both these factors in one experiment. We wanted to find out how those two factors affected resistance so we would know what to control in our coursework experiment. The other aim of the experiment was to find out which material and thickness of wire would be the most suitable for our experiment. We used nichrome wires and copper wires, with one thin, one medium and one thick in each material. We found that the nichrome wire was much more resistant than copper, and that the thinnest wires also had the most resistance. The reason that the copper wire had a very low resistance is due to a large amount of loose, or free electrons in the wire. These electrons are more easily able to carry electricity, therefore needing less push (provided by the voltage) to produce the same current as a different material. We also found out that a thicker wire has less resistance. This is because in a thin wire there is not very much space for the electrons to space out in. This leads to more collisions between wire particles and electrons, meaning a higher resistance.
So we then knew what our controlled variables would have to be: temperature, the thickness of the wire and the material of the wire. We also knew what the most suitable material and thickness were for the wire. We decided that it was most suitable to use a thin nichrome wire, as this had the highest resistance. Having a high resistance means needing a lot of push (provided by the potential difference) for the same amount of current as a different material (such as copper). This way more P.D would show up on the voltmeter, making our results more accurate. Because we will be using an analogue voltmeter, it is very difficult for them to pick up such low voltages, and the thin nichrome wire requires a higher voltage to produce the same current as copper, meaning more reliable readings.
We will use a range of 10cm to 1.00m, with 10cm increments. On our preliminary experiment, we will repeat each reading once with 3V, once with 3V, 6V and 9V. This is to make our readings more accurate. If we just used the same voltage for all 3 readings and then took an average all the readings would be the same, so we will vary it. We will repeat our results 3 times to ensure accuracy.
The independent variable is the resistance of the wire.
The dependant variable is the length of the wire.
The controlled variables are the potential difference, the power pack, the voltmeter, the ammeter, the piece of wire used, the temperature.
Results of 1st wire tested: 18 SWG
To collect the data for my graphs I have chosen to take a range of 10 lengths. I have chosen a range of 10
as to plot an accurate graph I will need at least 10 points to mark on the graph. I will repeat each experiment three times to make sure that my readings are correct and that there will be no Rhode points. I will take the average of the two readings and then plot them on a graph. I have chosen this so that if I have any
anomalous results they will not show when I plot the averages on the graph. I will take measurements at intervals of ten centimetres. I have chosen these lengths because they are easily measured by the meter ruler and give a good range. We chose to do the rest of the experiments at 3 volts because it was much more safer, easier and the wire did not heat up as much as 6 volts or 9 volts. Therefore it is a more compatible wire.
The rest of the wires that we measured:
Table & Graph for 18 SWG (including resistance this time and only at 3 volts)
[Hand drawn graph here]
Table & Graph for 26 SWG
Table & Graph for 28 SWG
Table & Graph for 32 SWG
Table & Graph for 36 SWG
Conclusion
I conclude that the longer the wire, the higher the resistance. This is because in a longer wire, there are more wire particles. Resistance is caused by electrons colliding with wire particles. Where there are more particles electrons are obviously more likely to have collisions, leading to a higher resistance In a longer circuit, it is more of a struggle for electrons to get around the circuit without any collisions. There are lots more particles to avoid. Less electrons were able to get past at any one time in the wire, meaning that less current showed up on the ammeter. This means higher resistance.
The wire with the highest resistance was the longest one - 1m long. This had a mean average resistance of 13.27Ω. This was as expected in my prediction. I said that the longer the wire the higher the resistance, and this was the case. Also, the wire with the lowest resistance was the 0.1m one. This had a resistance of 1.3Ω. The reason for this is that there are not so many particles in a short wire. This means that there were fewer collisions between the electrons and the wire particles. A low resistance translates as not many collisions, and therefore lower resistance.
Metals conduct electricity due to a large amount of "loose" or "free" electrons in their atoms. These free electrons can carry electricity easily. When there is no electric field in a wire the electrons stay still, but as soon as you put an electric field there the electrons will move from the negative to the positive. I have illustrated this below.You could compare resistance to a high street. If you walk down one street and bump into a certain amount of people, in a street twice the length you are likely to bump into twice that certain amount of people. It is in this way that resistance works.
On my graph you can see that it is a steady, straight line of best fit. This suggests that length is directly proportional to resistance. This is not too surprising, because if you double the length of a wire, you would expect there to be double the amount of collisions and double the resistance. Likewise, if you triple the wire length there should be three times the amount of collisions and three times the resistance. It is logical. I have demonstrated this through illustrations below.
Ohm's law states: "the current through a metal conductor is directly proportional to the voltage across its ends, as long as all other conditions are constant", so I would expect that this would not be the case, as we changed length in this experiment. The formula for resistance is V/I, and if you change one of these things (out of potential difference and current) then you vary the resistance. V/I is a constant (when no other factors are affecting it) known as resistance. However, we changed current by varying the length, and for the longer wires this meant less current (more collisions, less electron flow), and changing current changes resistance.
So my results support my prediction well. They have shown clearly, and with no anomaly, that as the length of a wire increases, so does the resistance. There is a very clear, steady pattern visible both in the results table and in the graph. On the graph I have labelled several points that make this clear. You can see that for 0.2m the resistance is approximately 2.7Ω, and for 0.4m (twice 0.2) the resistance is approximately 5.4Ω. This is exactly double the resistance of a 0.2m wire. Also, at 0.3m the resistance is 4Ω, and at 0.9m the resistance is 3 times that at 12Ω. So again my results are solid proof for my prediction.
Analysis
Although the graphs and tables prove that my prediction was correct, all except 32 SWG (that as the length increases, the resistance will also increase, proportion to the length), it was not a fair test. As we used different Ammeters for 32 SWG & 36 SWG wires. One of which showed more accurate readings to 3 or 4 decimal places, whereas we did it the 1st significant figure or any other decimal else for the rest of the wires in the experiment, and the power pack may have been left on longer than other measurements, so the temperature may have rose, (as the temperature rises, the resistance increases) And on the 32 SWG wire, the resistance did not increase proportional to the length of the wire at all. This may have been due to kinks or bends in the wire that were not visible. Or there may have been a fault with the equipment. The wire may not give an accurate reading due to frequent use.
To make my experiment more accurate I could have made sure hat I had the same equipment throughout the experiments, making sure I have more time to do it accurately, and making sure the temperature didn’t rise (use a thermometer to measure the temp) as this may have interfered with the resistance. Our accuracy was quite good and we didn’t get any big variations between the 3 tests we did in the Main experiments. I will also use a digital ammeter that gives the exact reading for accuracy.
All results that we collected fitted a certain pattern, i.e.; resistance is proportional to the length of the wire. All except the 32 SWG wire, which the resistance never increased, it always stayed at 1 Ω. This may have been due top faulty equipment, miss readings or incorrect calculations.
Our method was straightforward and simple to do so by measuring the voltage and current at every 10cm, we received more accurate readings and were therefore to show that our prediction was correct.
Most of our results are accurate, but the 36 SWG may be more accurate than the other wires as we used a different & more accurate Ammeter in that lesson to receive the results. And the 32 SWG did not increase at all.
Therefore this isn’t really a fair test. Also there may have been some kinks in the wires that we may not have known about that would have lead to the resistance reducing. The temperature may have risen slightly but nothing dramatic was shown in out tables/graphs.
If I was to collect further evidence to come up with a definite law relating the length of wire to its resistance, I think that I would have to measure the wire to every 1 centimetre or if possible every millimetre to get those vital accurate results.
For a 10 Ω resistor:
18 SWG wire, as 1 meter = 0.994444 Ω,
Therefore 10 meters = 10.05587042 Ω,
28 SWG = 66.5 cm,
32 SWG = unable to do as the resistance never rose above 1 Ω, due to some unknown fault.
36 SWG = 10.667 cm.
Evaluation
I think that the procedure used was fairly suitable, although not as much as I would have liked it to be, because we just used a crocodile clip to connect the wire at a certain length. Firstly, the crocodile clip is quite wide, and it is impossible to connect it at the exact length that you want. Secondly, the wire was not perfectly straight - it had several slight twists and bends in it, and this would have affected the accuracy of our results. We might not actually have been observing the results for the exact length we intended.
The only way we would be able to solve the problem of the bends and twists in the wire is to use a brand new piece of wire and look after it very carefully. We could solve the length problem by using a brand new piece of wire, which starts off at 1m in length, and we would cut it down to size for each result. This would make our observations closer to the exact length.
Our results were also made more accurate by the fact that we used a fairly wide range. Using just one or two increments is not reliable enough to draw a valid conclusion, so we used 10 increments. This way we would have been able to cope with any anomalous results using a line of best fit.
Anomalies could have been because the temperature became too high, creating an extra variable to make the test unfair. If the temperature did get too high it would have decreased the current, increasing the resistance. Similar to this idea, the wire could have had some impurities in it, varying the resistivity and increasing/decreasing the resistance. Any of the remaining three (I say this because we have already used one in our experiment - length) factors affecting resistance could have been varied - temperature, resistivity and thickness, leading to unreliable readings. The other reason for an anomaly could simply be that we misread the voltmeter/ammeter.
We could use an even wider range of results to increase the reliability of out results, or we could repeat the results more times. For further work, we could think about which material, length, width and temperature wire has the highest/lowest resistance. We could also use different kinds of resistors in the circuit, for example thermistors, so we could see how resistance varied with heat and that resistor, or we could instead use a light dependant resistor, to see how resistance would vary with that.
