To find the uncertainty for each measurement according to the thickness I will have to subtract the lowest result from the highest result to determine the uncertainty. For example 0.15-0.13 would yield an uncertainty of ±0.02. I will also keep the uncertainties to two decimal places to ensure it is consistent with the results.
To find the averages of each measurement (voltage/current) according to thickness I will add each trial and then divide them by the amount of trials ((t₁+t₂+t₃)/3). For example ((0.41+0.42+0.43)/3)=0.42.
I do not need to average the thickness of the wire as it was the same one used in all trials and it did not change at all.
To find the resistance of the wire, I took the voltage and divided it by the current. I did it for each trial and the average to keep the results consistent. To find the percentage uncertainty of the Resistance, I had to divide the uncertainty of the voltage by one of the values and multiply it by 100 to find the percentage, and the same with current; finally adding them together to find the total percentage error/uncertainty. For example: ((0.02/0.53)*100=3.773584906)+((0.10/0.67)*100=14.92537313)=18.70%
To find the cross sectional area of the wire, I will take the diameter, halve it, then square it and then finally multiply it by Pi. This will ensure I find the correct cross-sectional area of the wire. For example; Diameter = 10mm
((10/2)^2)*Pi=78.54mm²
Conclusion & Evaluation
From the graph created through the results, we can see that the result does in fact support the theory that as you increase the thickness of the wire the resistivity will decrease. As dictated by the graph, there is a proportional relation between the points, however the line of best fit is not as optimal as it does not pass through all the points. This was probably caused by some faulty measurement. However I cannot remove this point and plot the line again, since I need the point to gain a faint idea on what the co-relation is and I have five points only which is the bare minimum.
The graph is not that reasonable because as you can see in the graph, only 2-3 points are proportional to each other, however because of the first and last point the graph has shifted upwards leaving us with an unreasonable line of best fit. I believe there are several errors while I proceeded with my experiment; this is because the equipment used in the experiment such as the voltmeter and ammeters have small errors. The readings from these two equipments were used to calculate the resistance. An error for the area is inevitable as it is extremely hard to measure the thickness of the wire and could have affected the total area when using the equation.
The results from this experiment could have been more accurate if a wider range of wire thicknesses had been used, there could have been more points created on the graph which would reduced the error of the line of best fit, also if more points were used then any errors and anomalies could have been removed/ignored. It would also be beneficial if there was another way of measuring the thickness and area of the wire as the margin of error is huge for humans like us. Also in the experiment the wires that are used to connect up the circuit could have been cleaned before the experiment as oxidation of the wire may have caused unnoticeable errors which could have affected the resistance of the wire.
