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As seen from the graph, the relationship between my independent and dependent quantities is linear and they are inversely proportional. This means that the thicker the wire is, the lower the resistance. In other words, the larger the cross-sectional area is of the constantan wire, the lower the electrical resistance gets across the circuit.
Although the best-fit curve passes through the all the error bars, the error on the graph is fairly significant since there aren’t enough points to identify any anomalous outliers to confirm this relationship. However, as the graph (graph B) that shows the cross-sectional area is inversely proportional to area is a curve, it is not easy to tell the gradient of the graph using the maximum and the minimum gradients. Although, I believe that if my graph was a best-fit line the gradient would have given me the resistivity (this is my initial expectation) and hence I decided to plot Graph A that shows the slopes of the lines in y=mx+c form. The gradient of my graph tells me how much the electrical resistance changes as the cross-sectional area gets bigger. However, Graph A clearly proves that resistance is proportional to 1/Cross-sectional Area. Although it is seen that the Line of Best Fit is fairly close to the max and the min steepest gradient lines, the LOBF misses put on several points by a small margin which means that my experiment would be reasonable if my error bars are were slightly bigger and hence my uncertainty has to be bigger. Graph A is given in the form: y=mx+c and the value of the gradient is 0.1613, seen directly from the graph.
The major uncertainty tends to come from the resistance of the wire which was calculated using the potential difference and the current. This may be unreliable as heat may build up across the circuit and hence result in an increase in resistance across the circuit. As afore mentioned, the cross-sectional area uncertainty is only (0.01 mm) which is insignificant and hence can be negligible.
Despite the limitations to this experiment, I believe that my results were fairly reasonable which proves the distinct relationship between the cross sectional area and the Resistance. This is because the instruments used to measure the quantities were fairly accurate and had a very small degree of uncertainty which didn’t give me a systematic error as they weren’t wrongly calibrated. My graph doesn’t show any anomalies either as I kept my controlled variables constant such as: the 6 different constantan wires I used were 100 cm for all the readings and was coiled up using a pencil. In addition, the voltage on the power supply was kept on 6V throughout the experiment.
I repeated my measurements for the dependent and independent variables 3 times – Diameter, Potential Difference and Current as this would allow me to scrap any misreading and mistakes.
Limitations and ways of improvements: The only limitation was that there was insufficient time to test the validity of this experiment by using more wires of different thicknesses. More data, using more thicknesses of wires, would have helped to justify the inversely proportional relationship between the cross-sectional area and the resistance (electrical resistance, in this case) – this could have been done by using different materials of wires and also different lengths of the wires. I could have also used a different voltage on the power supply.
However, one way to improve my experiment would be by using shorter lengths of wire since the relationship between the length of the wires and resistance is proportional; the longer the wire, the greater the resistance. However, this would not be a major problem since it would be the same throughout the entire experiment. Another improvement would be to use a switch in the circuit; this would make the readings on the Voltmeter and Ammeter more accurate as the circuit will not remain heated after each reading.
