Does the length of wire effect resistance

Michael Hyatt

Does the length of wire effect resistance?

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. The more free electrons in a particular metal means that it is a better conductor. The better the conductor the less its resistance. Gold has more free electrons than iron and, as a result, it is a better conductor. Free electrons are given energy and move because of electromagnetic currents. Movement of these free electrons means that they will collide with neighbouring free electrons. This happens across the length of the wire and thus electricity is conducted. Resistance is the result of energy lost. 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 into heat.

Investigation

To find out how resistance changes if the length of a wire in changed.

Prediction

I predict that the longer the wire, the higher the resistance. This is because there will be more collisions in a longer piece of wire. Therefore, more energy is going to be lost in these collisions. Furthermore, doubling the length of the wire will result in double the resistance. This is because by doubling the length of the wire, you are doubling the amount of collisions, meaning you are doubling the loss of energy.

Preliminary Work

For our preliminary work, we measured the current passing through a copper wire of lengths 10cm and 50cm at 1 volt and 5 volts. There was an ammeter in parallel to the circuit to take readings from each voltage.

The results were as below:

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Preliminary Work

The results were as below:

The 10cm wire at a voltage of 5 volts, simply melted as a result of the testing. If I did have a value for that particular test, it would sway the results, as the temperature would have heated up. Heat affects resistance therefore my results would e affected. As a result of the preliminary work, I have decided to change the material of the wire from copper to constantan. Constantan is a metal that does not change temperature or melt at 5 volts when 10cm long. I am also going to insulate the wire to ensure that my starting temperature is consistent throughout the experiment.

Equipment list

A lab pack, various lengths of wire of the same material, bulldog clips, Ammeter, voltmeter.

Risk assessment

Do not allow anything to come into contact with the hot wire. Make sure that the 3-pin plug is wired up correctly. Do not increase the voltage when the wire shows signs of incandescence.

Variables

Variables that could affect the results of the experiment are the cross sectional area of the wire, the metal used in the experiment, the resistance of the wire and the temperature of the wire. These entire variables will be controlled with the exception of resistance, as this is the dependent variable.

Method

I will clip the wire onto the lab pack wires. I will then put an ammeter in series with the circuit so that I can take a reading for the amperes and the voltage. This will give me the values to work out the resistance in the wires by using the formula V=IxR. I will record the data in a table and then draw a graph based on my results. I will then fin the gradient of the graphs.

Measure out and cut the appropriate lengths of constantan wire for the experiment make sure they have the same cross sectional area.
Clip the bulldog clips from the lab pack wires, to the length of wire.
Place the ammeter into the circuit in series as shown below.

Turn lab pack on and turn to the appropriate voltage.
Record the reading on the ammeter in a table
Repeat this for up to 5 volts and all lengths of wires.

Conclusion

From my graph I can see that as the voltage increases, the current decreases. It also shows that the shorter lengths of wire have a higher current than the longer wires. It also shows that most of the current is directly proportional to the voltage. The exception to this would be the 10cm piece of wire. This will be due to the fact that the wire would get to hot and sway the results. It also shows the resistance. I used the formula V=I/R. I have rearranged this to R (Ω)=V/I. It shows that the resistance increases as the length increases, and that although the resistance is a small amount higher or lower, that the resistance is same in the same wire. I have noticed that the points of my graphs follow the trend line almost perfectly. This shows that my results are very reliable.

This table shows the working of the gradient, using the formula above. It shows that there is an increase in the gradient as the wire length increases. This supports what I have said about the table above. The longer the wire, the greater the resistance. It also shows that resistance is directly proportional to length.

Evaluation

I think that my method was very good. I used the equipment safely and correctly. My results are very reliable because of the fact that they lie on the trend line in all wire lengths. I did not foresee any problems with the experiment during my method and did not encounter any problems when carrying out the experiment. If I were to investigate this subject further, I could try to find out how metal type and cross sectional area affect the resistance of the wire. For my results to be more reliable, I need to maintain the temperature of my wire. To do this I would need to insulate all of the wires very well and conduct the experiment in a controlled temperature environment. I would need to conduct the experiment with a variety of different metals to determine just how much length affects resistance however; I think the results would be very similar.