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Physics IA - DCP CE - Resistance vs cross-section area

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Introduction

Investigating the relationship between resistance and cross-sectional areas

Research:

The aim of this experiment is to investigate the relationship between resistance and different cross-sectional areas of constantan wires. This is done by setting up a circuit that consists of a constantan wire, Voltmeter, Ammeter and a power supply. The cross-sectional area is found by measuring the diameter of constantan wires of different thicknesses by using a micrometer thereby using the formula: A=π (½d).  The resistance is found by using the readings of the potential difference and the current on

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Middle

0.30

0.30

32

0.26

0.27

0.26

0.26

34

0.22

0.22

0.22

0.22

36

0.17

0.17

0.18

0.17

Raw Data: The uncertainties for the Diameters were arrived from the smallest reading on the micrometer screw gauge. I think it is reasonable to neglect them since the micrometer is fairly accurate and the numbers are pretty small.

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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

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Conclusion

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.

By Janam Shah, 6U1

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