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How does the length of a wire affect the resistance?

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Nazifa Musa                                                               Physics Coursework

How does the length of a wire affect the resistance?


Background Knowledge


Resistance is the opposition of electron flow in a circuit and is based on the physical size of the conductors. Since current is the movement of free electrons in a circuit then the number of atoms in a wire make a big difference as to how many electrons can flow at any given time. The bigger the diameter a wire is, the more atoms there are in the wire, so the more free electrons. The smaller the diameter of wire the fewer the number of atoms so the fewer the number of free electrons.

The factors that affect the resistance of a wire are:

  • As the length increases the resistance increases
  • As cross- sectional area increases, resistance decreases
  • It depends on the material of the wire, example: nichrome
  • As the temperature increases, the resistance of a wire increases.

Theory: George Ohm discovered that the current flowing through a metal wire is proportional to the potential difference across it (providing the temperature remains constant.

From this the following equation was derived:

  Resistance = Potential difference across the wire (V)        

                          Current through the wire (I)                        

It can also be written in symbols where resistance = R, potential difference = V and current = I.

  • R = V / I
  • V = I x R
  • I  = V / R
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The results were as expected because as the length of the wire increased the resistance increased too. The link between the wire length and the resistance was directly proportional.

As my preliminary results did not provide a very wide range of results, when I carry out my experiment I will take results from 20-100 in intervals of 20.


I predict that the longer the piece of wire, the greater the resistance will be. This is due to the idea of the free moving electrons being resisted by the atoms in the wire. In a longer piece of wire, there would be more atoms for the electrons to collide with and so the resistance would be greater. The relationship between the wire length and the resistance should be directly proportional. This is because in a wire twice the length of another wire there would be double the amount of atoms causing the resistance.

An example of this would be in a 20cm wire. The electrons would have to travel double to distance if it have to go through a 10cm wire. This would in turn double the amount of atoms that the electrons would collide with and then resistance would double.

Expected Graph




  • Constatine Wire
  • Ammeter
  • Voltmeter
  • Powerpack
  • Metre ruler
  • Variable resistor
  • Crocodile clips
  • Connecting leads



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Overall the method used was suitable for my experiment. However, in order to obtain more reliable and accurate results, improvements could be made.

To improve on my results I would:

  • Use a digital voltmeter instead of an analogue meter. I would do this because a digital voltmeter is a lot more accurate than an analogue meter. Also if the needle in the analogue voltmeter is bent then the readings given off will be incorrect whereas a digital voltmeter does not rely on a needle or any other manual movements.
  • Use pointers instead of crocodile clips, I would do this because pointers would be more accurate. The pointers tips have a much smaller area than the crocodile clips giving a more accurate measurement of the length of wire.

As well as making these modifications I could also extend my investigation by testing the same wire but different thickness of that wire, in order to see the effect on the resistance of the wire. The method would be the same except instead of the length of the wire being the variable that is controlled, this time the variable would be the thickness of the wire.

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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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