Variables
Input:
- Length of wire.
- Material of wire.
- Width of wire.
- Starting temperature of wire.
Output:
- Voltage across wire.
- Current in circuit.
- Temperature of wire.
The lengh of wire will be the variable I will varie, the other input variables will be kept constant. The output variable that will be measured is the resistance of the wire.
Predictions
- The longer the wire, the higher the resistance. This is because the longer the wire, the more collisions the free electrons will cause with other free electrons, the particles making up the metal in the wire, and any impurities in the metal. Therefore, more energy is going to be lost in these collisions (as heat).
- 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, so doubling the amount of energy lost in these collisions.
Method
This circuit was used to perform the investigation:
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. Then we used a Jockey connector to place in the relevant position of the wire where we want to measure to.
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:
After performing these rough trials, it was decided that 4V would be used in the proper experiment, as it provided results from 10cm up to 100cm and the higher voltage provided no additional ease of measurement.
Furthermore, it was 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 in 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 voltage of 4V was chosen so that overheating was at low enough to be safe enough do the experiment but lengths lower than 10cm were not tried, which helped to avoid overheating.
Results
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.
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.
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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 we used batteries instead.
NB: If one were to assume that Ohm’s Law applies, then another possible explanation could be that at some points (more likely in the lower lengths), the wire was not allowed to cool completely so that the temperature was higher for that measurement. Whilst unlikely (due to the two sets of results), this would cause a higher resistance as explained previously. However, it is now known, after researching the metal alloy “constantan,” that the resistivity (the electrical resistance of a conductor of particular area and length) of this alloy is not affected by temperature. Therefore, in these experiments Ohm’s Law does not apply.
