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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

...read more.

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

...read more.

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.

...read more.

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