My theory is that if you increase the length of the wire, there are more free electrons, but the electrons have less space to move in, so thy collide more often with the atoms, creating more resistance.
However, if you increase the cross sectional area, there are still more free electrons, but there is more room for them to move, therefore decreasing the collisions with the atoms, and in turn decreasing the resistance. This is my reason for my aforementioned prediction.
Method: To keep the experiment as fair as possible, the only variable shall be the cross-sectional area of the wire. The other variables shall be kept as similar as possible in every test. Firstly, the length of the wire shall always be 0.5 metres, the temperature will be kept as constant as possible, and the wire used shall be Nichrome wire, which is
1.1 x 10^-6 /Ωm
The following diagram shows the circuit I shall use to gather results from my experiments:
Volts, V
As Resistance, R = Amps, I, I will find the resistance of each wire using this formula.
I will test each wire three times, and then find an average resistance. This will make my results more accurate and fair.
Observations
Wire 1 (Nichrome 32)
Wire 2 (Nichrome 30)
Wire 3 (Nichrome 28)
Wire 4 (Nichrome 26)
Wire 5 (Nichrome 24)
For this final wire, I will try to use the formula:
Resistivity, ρ (ohm metres) x length, l (metres)
Resistance, R (ohms) = Cross-sectional area, A (square metres)
To predict the resistance of this wire.
The cross sectional area of a wire, 0.57mm in diameter = 2.551758633 x 10^-7 m^2
Resistivity of nichrome = 1.1 x 10^-6 /Ωm
Length of wire = 0.5m
(1.1 x 10^-6) x 0.5
R = (2.551758633 x 10^-7) = 2.155376268 Ω
Due to this formula, I predict that the resistance from a wire with the diameter of 0.57mm will be 2.156 Ω
To check my prediction, I will run the experiment with this wire.
My prediction was only about 0.331 Ω incorrect, but this may have been caused by experimental error, from the heat increasing the resistance, or imprecise measurements of diameter and length.
The above graph shows the results of my experiment. The results are roughly accurate, although some stray from the line of best fit, most likely due to human error. From these results, it is made obvious that the cross sectional area of a wire and the resistance of a wire are clearly inversely proportionate.
This also proves that my prediction was correct – as the cross sectional area of a wire increases, the resistance of that wire decreases.
Because there is exponential decay in the graph, I suspected that the formula for this graph included resistance = 1/ cross sectional area. To test my theory, I plotted the same results, except I put 1/cross sectional area as the x axis.
As the line is now straight, I have proved that my suspicions were correct. As the scatter is small, this proves that my data is reliable. From this graph I have found that, for a Nichrome wire, the formula for resistance is:
_ 0.37 .
Resistance = cross sectional area + 0.5
In my experiment, there were no glaringly anomalous results. This proves that my experiment was carried out very fairly. However, problems that may have arisen could have been that the circuit would have risen in temperature, which would have increased the resistance in the wire. Also, the crocodile clips may have been misplaced or could have slipped on the wire, causing the wire being tested to be a different length, which would also affect the resistance of the wire.
I could have made my results more accurate by installing some form of temperature stabilizer, to keep the temperature of the wire constant, or by making my measurements more accurate.
I could also further this experiment by using a different type of wire (with a different resistivity) or by experiment with different lengths of wire.
