Effects change of diameter has on to resistance.

There are a few controlled variables to be taken into consideration:

1.  The length of the wire, this must remain at 1 meter to make the test fair because the length of the wire directly affects the resistance.
2. The temperature of the wire must remain the same because temperature affects resistance.
3. The resistivity must be kept the same because this will affect the equation therefore change the resistance.

Now that I have an equation linking every thing I need I am able to make a prediction. If I plot resistance against diameter I will get a graph looking like below.

Due to the fact that the resistance is directly proportional to the inverse square of the diameter, I am able to plot resistance against (1/dm)^2 this should give me a graph as follows:

I am confident that I will get a graph similar to that of above, this shows a clear relationship between diameter and resistance.

Before I can carry out this experiment I will have to carry out some preliminary experiments. These were to find out how much current I could pass through the wire before it got hot enough to affect the resistance.

Equipment list

Battery: to apply current and voltage to the circuit.

Digital ammeter: to measure the current, a digital one was selected because it can measure to a far greater degree of accuracy.

Digital voltmeter: for the same reason as above.

Variable resistor: to alter the resistance in the circuit.

Connecting wires: these are made of copper and have only a very small resistance therefore not affecting my resistance much.

Micrometer: used to measure the diameter of the wires under test.

Results

Below is my raw data collected for my experiment.

From the above results I am able to plot these graphs:

This graph shows no direct relationship between resistance and diameter. There does however appear that there may be a link between the resistance and the inverse square of the diameter.

Here are the results for mean resistance, mean diameter and the inverse square of each diameter.

From these results I am able to plot a graph of resistance against 1/(d/m)^2 as follows:

This graph shows conclusively that there is a relationship between resistance and the inverse square of the diameter. This is a linear relationship between d^2 and the resistance.

There are lots of sources of error to be taken into a account, like when measuring out the meter of wire, this wont cause a lot of error but it builds up. Calculating 1/(d/)^2 will create a reasonable amount off error, these all have to be taken into consideration.

I took these sources of error into consideration and to reduce them you could, increase the size of measurement you are taking to reduce the percentage error. Also if I used a analogue ammeter and voltmeter I could have reduced the amount of error. Most of my uncertainties were about 1% so this isn’t massive but it will effect my line of best fit. If I was to reduce my uncertainty’s by taking more time and using more accurate measuring equipment I could have produced a more accurate line of best fit.

For my experiment the overall percentage uncertainty is about 2% calculated to 1 decimal place. This isn’t very big therefore I think my results are reasonably reliable and this relationship I have show is valid.