I will investigate how the length of a wire affects the resistance in the wire.
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Prediction: I think that when the length of the wire is increased the resistance in the wire will also increase. This is because there are more atoms in a longer piece of wire than a smaller piece of wire. This means that the free electrons traveling through the wire will collide with the atoms of the wire more. This means that the free electrons are continually giving off some of their kinetic energy in the collisions, so as there are more collisions there is more resistance in the wire.
Another reason for the resistance increasing with the length is that when the
wire is lengthened it is like adding another resistor in series, to find the total resistance of the resistors in series you add up the resistance of each resistor together. This means as it is like adding another resistor the resistance must increase.
The line on the graph of resistance against the length of wire will be a straight-line showing it is in proportion.
Preliminary Results: For these I will measure the resistance using a multimeter.
Even though each wire seems to have a definite pattern. I have decided to use Nickel Chrome wire as its resistance goes higher than that of Constantan at 100cm. This means that if a mistake was made in measuring the resistance of Nickel Chrome it would not matter as much because it would be a smaller percentage error. As there were some slightly anomalous readings I will have to repeat the experiment three times to make the results more reliable.
Apparatus:
Meter rule, (able to measure to 1/2 mm) Nickel chrome wire, Multimeter (to
measure Ω’s), Circuit leads, Crocodile clips, sellotape.
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Method:
1) Set up the circuit shown below.
2) Attach one crocodile clip to the nickel chrome wire level with 0cm and the other one 10cm away.
3) Set the multimeter to the 200Ωs setting.
4) Record the Ωs reading.
5) Move the 2nd crocodile clip 20cm away from the 1st clip and record the Ωs reading again.
6) Record the Ωs reading when the 2nd clip is 30, 40, 50, 60, 70, 80, 90, 100cm away from the 1st clip on the wire.
7) Repeat the experiment twice more to make the results more reliable.
8) Using the formulae:
Resistance = Voltage
Current
Work out the resistance at the wire at each length. Then take an average resistance reading by adding the three results and dividing the total by three.
Safety: Do not put the crocodile clips too close together or the circuit will short circuit.
To ensure a fair test the circuit leads must stay the same throughout, because these add resistance themselves. If the lead was changed for a longer lead more resistance would be added make the results unreliable. The setting on the multimeter must be kept the same or the results will be unreliable. The wire that I am measuring (Nickel Chrome) must be kept the same as well as the diameter of the wire. The temperature must be kept the same too.
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Results:
Analysis: As the length of the wire increases the resistance also increases. In my prediction I stated on the graph of the length of the wire against the resistance in the wire would go up in proportion. This statement was correct because the line on the graph was a straight line proving proportionality. The line on the graph shows that when the length was 10cm the resistance was 9.3Ω, when the length is doubled to 20cm, the resistance is doubled to 1.86Ω, so when the length is doubled so is resistance; when the length is multiplied by four to 40cm the resistance was multiplied by four to 3.72Ω. This proves proportionality. This statement is also correct because of the rule of resistors in series.
10cm of wire has 0.93Ω of resistance, when 10cm more of wire is added to it, it is like adding an identical resistor with the resistance of 0.93Ω. When resistors are set up in series to find the total resistance, the resistance of the
resistors is added together. This means when 10cm of wire is added, 0.93Ω are added to the total resistance meaning the resistance will double if the length is doubled.
The length of wire increased with resistance because, as I said in my prediction, when the wire is lengthened there are more atoms present in the wire. This means that there will be more collisions between electrons and atoms. When the electrons collide with the atoms they give off some of their kinetic energy, slowing them down; this means there is more resistance.
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Evaluation: The method I used was fairly hard to use because the connection between the crocodile clips and the wire was not as good as it could have been. This meant that the multimeters were waving about a bit and I had to wait for it to settle down before taking results. Even though this was the case the results still came out accurate and seemed to be correct and fit a pattern of proportionality. All the points on the graph were all very close if not touching the line of best fit, there were only two slightly anomalous results but even these were only 1/2 Ω away from the best fit line; these were at 80cm and 100cm these may have been slightly wrong due to the bad connection.
Also the wire that I was measuring became twisted so that the length of the wire may have been slightly wrong. Another criticism is that when the wire was short it became hot this may have caused the resistance to increase so it would not be very accurate. This meant that the experiment is limited to longer lengths of wire.
To make this experiment more reliable I would have to take even more check readings to ensure consistency and find another way of connecting the wire up. My results were reliable as the check readings were consistent almost through out my results.
My results show that resistance increases with length proportionally, but that may only be true for my wire so my conclusion may be wrong for other wires so it would be necessary to test some other wires to know that my conclusion is correct for all wires. Also it may be useful to test the other input variables such as width and the temperature.
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