Experiment
The equation used to find the resistance from current and voltage is:
Resistance (R) = Voltage (V) / Current (I)
So to test this theory I need to measure the voltage and current passing through different thicknesses of wire. As I know that resistance is affected by length of the wire these need to be the same length. To check this is the only factor affecting the resistance I need to use different current/voltages to see if the resistances are the same. I intend to do this by setting the variable resistor in the circuit diagram below at three different points and measuring the voltage and current for each of the different thicknesses of wire at each point on the variable resistor.
The results I would expect are that there would be a lower resistance in a thicker wire than a thinner one.
Apparatus
: Battery
: Variable Resistor
: Ammeter
: Voltmeter
: Different thickness of wire
: Crocodile clips
In the circuit below I intend to place wires of different thicknesses but the same length between the crocodile clips.
How am I going to conduct the experiment?
- For six different thickness of wire I am going to record three different measurements for both voltage across and current passing through the wire.
- I am going to do this by varying the current passing through the test circuit. It is important to do this so as to ensure the thickness of the wire is the only factor affecting the results.
- To do this I am are going to adjust the position of the variable resistor in the test circuit.
- For each different thickness of wire I am going to record in a table both the voltage across and the current passing through the wire using the ammeter and voltmeter as shown in the test apparatus.
- From these recordings I am going to calculate the resistance using the formula above.
- To ensure the test results are fair I am going to analyse the average of the three measures of resistance I have calculated for each thickness of wire.
- The results are to be analysed using both tables and graphs.
- I intend to order the results in increasing diameter/thickness.
- If my theory is correct the table and graph should show that the thinner the wire the greater the resistance and vice-versa.
Table 1:
Resistance in the above table is calculated using the following formula:
Resistance = Voltage/ Current
e.g.: For the 0.15mm wire in Experiment 1 the calculation is as follows: 10.89/.09 = 9.89
Table 2:
The Average Resistance in the above table is calculated as follows:
e.g. For diameter wire 0.15 (mm): (9.89 + 10.45 + 10.28)/3 = 10.21
My table of results is broadly as I predicted, with the resistance falling as the wire gets thicker. However, the results for the wires of both diameter 0.31m and 0.38m appear anomalous. As the three results for each of diameter of wire are closely in line with the average resistance it is more likely there is a problem with my experiment than with my theory as all other results appear to back my theory up.
= Anomalous result
The line of best fit as predicted shows there is a clear linear relationship between resistance and the diameter of the wire - the thicker the wire the less resistance. In the thicker wire atoms are less densely packed so the electrons are less likely to collide with them so the resistance is less and vice versa.
The results recorded for the wire with cross sectional area of 0.31mm and 0.38mm appear anomalous as can be seen from both the table and graph. The most surprising result was for the 0.38mm wire. If you look at the table 2 you would expect this thickness of wire to have a lower resistance but it does not.
As for each of these wire thickness the results for each experiment are broadly similar the problem must be in the design of the experiment. The most likely cause is that these wires were not the same length as the others however there is a small chance the temperature of the wires could also have affected the results or I mistakenly inserted the wrong thickness of wire. All of these would affect the resistance.
To improve the experiment I first, must take care to ensure that each thickness of wire is exactly the same length and I insert the correct thickness into the apparatus. I could also improve the experiment by repeating the exercise for each thickness/diameter of wire using two different lengths of wire.
Another way I could make the experiment more reliable is to ensure the room temperature is the same before each measurement is taken.
