I will measure the voltage using a voltmeter and calculate the resistance (in ohms) by dividing the voltage by the amperage.
Apparatus
0-5 amp analogue ammeter analogue voltmeter Power Pack 2 Crocodile clips Wire cutter SWG32 Constantan wire*
Meter ruler
* Constantan is a malleable alloy of nominally 60% copper and 40% nickel.
Predictions The longer the wire, the higher the resistance. This is because the longer the wire, the more times the free electrons will collide with other free electrons, the particles making up the metal, and any impurities in the metal. Therefore, more energy is going to be lost in these collisions (as heat). Furthermore, doubling the length of the wire will result in double the resistance. This is because by doubling the length of the wire one is also doubling the collisions that will occur, thus doubling the amount of energy lost in these collisions.
METHOD
The following circuit was constructed to perform the investigation:
The two dots represent the crocodile clips that were placed at the ends of the required length of wire.
1. One metre length of 0.4mm diameter “constantan” (a metal alloy) wire is fixed to a metre rule.
2. The first crocodile clip is clipped to the wire at the 0cm position on the metre rule.
3. The second crocodile clip is clipped to the relevant position depending on the required length of wire.
4. The power supply is turned on. The voltage and current are then read off the ammeter and voltmeter, and recorded.
5. The power supply is then turned off and the second crocodile clip is moved to the next position.
The above steps are completed for each length and then the entire investigation is repeated for accuracy.
Preliminary experiment
In order to decide upon the voltage and lengths of wire to use in the final experiment, the following rough trials were carried out:
At 3V:
At 5V:
After performing these rough experiments, it was decided that 3V would be used in the final experiment, as it provided results from 10cm up to 100cm and the higher voltage provided no additional ease of measurement. Furthermore, I also decided to allow the wire to cool between experiments as considerable heat was noticed at lower lengths and, as mentioned above, an increase in temperature results is an increase in resistance. By allowing the wire to cool between experiments a fair test could be assured.
Safety
In order to perform a safe experiment, a low of 3V was chosen so that overheating was minimilised. Furthermore, lengths lower than 10cm were not tried, which also helped to avoid overheating. I also kept the working area tidy and dry, to avoid short circuiting.
RESULTS
Wire 1, Set 1:
Wire 1, Set 2:
Having completed two sets of results for one wire, it was noticed that these was a large black mark towards one end of the wire, where it appeared that it had been melted to some degree at some point. It was therefore decided to conduct experiments on an additional piece of wire that was checked for integrity prior to investigation:
Wire 2, Set 1:
Wire 2, Set 2:
Averages for each wire were then calculated to give the following results, which were then graphed:
Conclusions
Having performed the investigation, the following conclusions were drawn:
• As predicted, an increase in length resulted in an increased resistance. This can be clearly said for both wires tested.
• Both wires show a strong trend of a straight line, i.e. the length of the wire is shown to be directly proportional to the resistance – double the length and the resistance doubles.
• The overall resistance of the two wires seems to differ considerably. Due to the strong correlation of the results, the explanation of this is unlikely to be the method used to obtain the results. The more likely explanation would be that the first wire was actually of a larger diameter than the second one. Obviously this is a rather important oversight and this will be discussed more in the Evaluation section. The reason why this is the likely explanation is because resistance is known to be inversely proportional to the cross-sectional area, i.e. if you increase the cross-sectional area (by increasing the diameter) then you decrease the resistance. This is because a wider wire means less likelihood of the free electrons having collisions and losing energy.
It is important to realise, however, that despite the fact that it would appear that the resistance of wire 2 is double that of wire 1, that does not mean that the diameter is half that of the wire 1. That is because if you halve the diameter then you decrease the area by a factor of about 3 (A = πr2)
Evaluation
• As mentioned previously, the biggest downfall of the investigation was the apparent mistakes when choosing the wire, in that they would appear to be of differing diameters. This did not, in this case, cause a big problem as the same wire was used for each set of results so it is known that the results for each wire are correct.
• Generally speaking, wire 1 would appear to contain the most accurate results due to the fact that all of its points bar one sit on the line of best fit for that wire. The only one that does not is the point at 90cm, which was exactly at the point that the black mark (mentioned previously) was found to be.
• Wire 2, on the other hand, had three main anomalous results: at 50, 80 and 90cm. They are by no means that far off but in an experiment such as this, which is generally a very accurate one anyway, such anomalous results should not be quite so common. Possible explanations for these anomalies are as follows:
The length of wire for that particular measurement was not correct. At 50 and 80cm it is possible that the length was shorter, causing a lower resistance, and at 90cm it is possible that it was longer, causing a higher resistance. The solution to this is to measure the lengths more carefully and ensure that the wire is pulled tight against the metre rule.
For a particular result, one or more of the connections could have been faulty, causing extra resistance at the connections. A solution to this would be to, before each experiment, connect the connections together without the wire in place and measure the resistance then. If it is higher than it should be then the connections could be cleaned.
Whilst extremely unlikely, it is conceivable that the power supply was providing a different voltage for some of the results. This is unlikely to be a problem in this investigation but it might have been an issue had I used batteries instead.
