The resistance of a length of wire is calculated by measuring the current present in the circuit (in series) and the voltage across the wire (in parallel). These measurements are then applied to this formula:
V = I x R where V = Voltage, I = Current and R = Resistance
This can be rearranged to:
R = V
I
This prediction is also supported by Ohm’s Law, which states that the current through a metallic conductor (e.g. wire) at a constant temperature is proportional to the potential difference (voltage). Therefore V and I are constants. This means that the resistance of a metallic conductor is constant providing that the temperature also remains constant. Furthermore, the resistance of a metal increases as its temperature increases. This is because at higher temperatures, the particles of the conductor are moving around more quickly, thus increasing the likelihood of collisions with the free electrons.”
So, we can deduce from this that the temperature will also affect the experiment and therefore must remain constant. This will be another controlled variable.
The current must also be kept constant, and the material of the wire.
So, below is a revised list of variables: -
My independent variable will be the length of wire.
My dependant variable will be the resistance of the wire, found by measuring the voltage (volts – V) and the current (amps – I) and using the following formula: -
V = R
I
My controlled variables will be the area of the wire, the starting temperature of the wire, the current passed through the wire and the material the wire is made of, all which I will keep the same as far as is realistically possible.
Apparatus
Constantan Wire (126 cm so that ½ cm could be used in each of the crocodile clips without too much difficulty, to avoid as much as possible inaccurate results.)
2 crocodile clips
Power supply
Ammeter
Voltmeter
6 insulated wires
Permanent marker
Meter rule
The equipment will be set out as shown below: -
Preliminary Method.
In this preliminary experiment I will try and ensure a fair test by using a constant voltage of 5 volts for the lengths 25, 65 and 125 cm. Also, to try and maintain the temperature, which can increase resistance, I will allow the wire to cool between measurements.
- I will firstly measure out 126cm constantan wire using the meter rule.
- The circuit will then be set up as shown.
- I will mark on our lowest and highest lengths, 25cm and 125cm, using the permanent marker.
- I will clip one crocodile clip to the end of the wire.
- The other I will clip onto the wire at 25cm.
- Having made sure that the insulated wires are not touching the constantan wire as it will get hot and may melt the insulation, I will turn on the ammeter voltmeter and power supply, which I will set to 5 volts.
- I will take readings from both the ammeter and the voltmeter and repeat at each measurement three times to ensure accuracy and check for anomalous results.
- I will then repeat the points 5 to 7 at 65cm and 125cm.
- To find the resistance, I should use the equation: -
V = R
I
‘V’ being the reading from the voltmeter, ‘I’ being that of the ammeter and ‘R’ being the overall resistance measured in Ohms.
Preliminary Results: -
I have found from the trial run that three more items are necessary to this experiment and should therefore be added to the apparatus list. Two are for safety purposes. They are: -
Cellotape and several drawing pins to secure loose wires to prevent the risk of burning if the live and insulated wires come into contact.
The final one is for convenience. As we are measuring the resistance at regular intervals of 10cm, a meter rule is inappropriate for measuring. Therefore, we will employ a conventional 15cm ruler.
Revised method.
- I will firstly measure out 126cm constantan wire using the meter rule.
- The circuit will then be set up as previously shown, with the wire pinned down to avoid any accidents.
- I will mark on all our lengths, 23 –125 cm at intervals of 10cm, using the permanent marker and the 15cm ruler.
- I will secure one crocodile clip to the board using cellotape, and use it to hold the end of the wire.
- The other I will clip onto the wire at 25cm.
- Having made sure that the insulated wires are not touching the constantan wire as it will get hot and may melt the insulation, I will turn on the ammeter voltmeter and power supply, which I will set to 5 volts.
- I will take readings from both the ammeter and the voltmeter and repeat at each measurement three times to ensure accuracy.
- I will then repeat the last three points at 65cm and 125 cm.
- To find the resistance, I should use the equation: -
V = R
I
‘V’ being the reading from the voltmeter, ‘I’ being that of the ammeter and ‘R’ being the overall resistance measured in Ohms.
Safety: -
The power supply must be handled with care
A low voltage (5V) is used so that overheating is minimised.
Lengths lower than 25cm should not be attempted, again to avoid overheating.
Make sure insulated wires do not touch the live wire, as they could burn.
Pin the live wire to a wooden board, and all other loose components should be secured, to avoid potential accidents.
Results: -
Conclusion.
As stated in my prediction, an increase in the length of the wire is equal to an increase in the resistance of the wire. Also, from the graph on the previous page, we can see that the statement ‘the length of a wire is directly proportional to its resistance’ is true, as the line of best fit is straight. This statement implies that, if the length of the wire is doubled, the resistance will double also.
I would like to restate here the initial theory: -
“Electricity is conducted through a conductor, in this case wire, by means of free electrons. The number of free electrons depends on the material and more free electrons means a better conductor, i.e. it has less resistance. For example, gold has more free electrons than iron and, as a result, it is a better conductor. The free electrons are given energy and as a result move and collide with neighbouring free electrons. This happens across the length of the wire and thus electricity is conducted. Resistance is the result of energy loss as heat. It involves collisions between the free electrons and the fixed particles of the metal, other free electrons and impurities. These collisions convert some of the energy that the free electrons are carrying into heat.”
This proves that there is more resistance over a longer stretch of wire, and that energy is lost through heat. The longer the wire, the more space and opportunity there is for the energy to be lost as heat along the length.
Evaluation.
There were several limitations in this experiment, other than those which I have already discussed. Those which I have already mentioned included temperature and area of the wire. These are both hard limitations to monitor. To maintain the temperature we allowed the wire to cool before each reading, but had no way of knowing if it had cooled to the same temperature as it initially had been, and getting new wire each time would have been very uneconomical. The area of the wire was impossible to measure, as is it such a small distance, we do not have the equipment to perform such enquiries and we cannot tell if the wire has the same area all the way along its length. Another possible cause of anomalous results would be any small kinks in the wire, although we tried to straighten these out as much as possible.
My results were reliable as I took a wide range and took three at each length to try and prevent anomalies from occurring.
The experiment could be improved by trying to remove some of the limitations present. For example, being able to measure the temperate and diameter of wire quickly, easily and efficiently would make the experiment a lot more accurate. Also, a bigger board would be useful as we found it necessary to pin the wire down in a large coil so it would fit on the board, and this made it difficult to measure the 10cm lengths as several measurements went round corners. If the wire had been in a straight line it would have made it a lot easier to measure the individual lengths and would have prevented the potential short circuits present in our experiment. Also, more readings could be taken to prove that ‘the length of a wire is directly proportional to its resistance’, for example, every 5cm instead of every 10. Finally, more readings could be taken at each individual length to improve levels of accuracy.
Using different types of wire in the same experiment to test the theory behind this experiment further would further prove whether or not the theory is true.
Further research has shown that in the metal alloy “constantan,” 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.
Bibliography.
The following Websites were useful sources of information in the writing of this investigation: -
Channel 4: Homework High – Science
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Freestudentstuff.co.uk
Sci-journal.org
Essaybank.co.uk