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# How does the diameter or cross-sectional area of a wire affect its resistance?

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Introduction

Physics

How does the diameter or cross-sectional area of a wire affect its resistance?

Aim:

I am going to investigate how the diameter, or gauge, of a wire affects its resistance. In order for me to do this, I will need to find as many different diameters of wire as I can. I will cut each one to a reasonable length (probably about 10cm), then connect it to a battery pack and measure the current and voltage (with an ammeter and voltmeter respectively). From these readings I will calculate the resistance, using the formula:

R = V / I                           (Resistance = Voltage / Current)

The scale by which the diameter of wires is measured is called SWG (standard wire gauge) which confusingly goes up as the wire gets thinner. However I shall not use this in my graphs, as I do not know enough about SWG to make any worthwhile observations. The gauge of wires can also be measured by their cross-sectional area.

Scientific Theory:

Some factors affecting the resistance of a wire are:

• its temperature
• the metal it is made from
• its diameter/cross-sectional area
• its length

Middle

 Run 1 Run 2 SWG Diameter Voltage (V) Amps (A) Resistance R=V/I Voltage (V) Amps (A) Resistance R=V/A 20 0.9 0.25 1.6 0.15625 0.25 1.6 0.15625 22 0.71 0.16 1 0.16 0.175 1.5 0.11666667 24 0.56 0.6 1.45 0.4137931 0.6 1.4 0.42857143 26 0.45 0.8 1.25 0.64 0.8 1.25 0.64 28 0.4 0.9 1.2 0.75 0.9 1.2 0.75 30 0.31 1.1 1 1.1 1.1 1 1.1 32 0.28 1.2 0.95 1.2631579 1.2 1 1.2 Run 3 Average SWG Diameter Voltage (V) Amps (A) Resistance R=V/A

Conclusion

x-axis and Resistance (Ω, or Ohms) on the y-axis. It showed a negative correlation, but had this weird thing going on at the end – an anomaly. I was able to draw quite a clear curve of best fit. The graph proved my theory correct, because as the diameter increased so the resistance of the wire decreased.

Evaluation:

I believe the experiment was a success, as it proved my theory correct and my graph showed a clear curve of best fit. However there was an anomalous reading, right at the end. This may have been a mistake in reading the meters, or a mistake in calculating the resistance.

To improve the accuracy and fairness of my experiment, I could have done the following things:

• used a more reliable power source (the power flow from battery packs weakens with use),
• cleaned the connections within the battery pack (corroded or dirty connections can affect power flow),
• used more accurate am- and volt- meters (i.e. with a greater number of decimal places),
• widen my range of results by connecting the circuit to more than one cell of the battery pack,
• cut more lengths of wire from different rolls (one roll alone may not be representative of that particular gauge) as defects etc. may affect the results.

This student written piece of work is one of many that can be found in our GCSE Electricity and Magnetism section.

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