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How does the length of a wire affect its resistance?

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Introduction

Physics Investigation

How does the length of a wire affect its resistance?

Aim:

        The aim of this investigation is to determine how the length of a wire can affect its resistance.

Scientific Knowledge:

Resistance means the ‘opposition to the flow of current.’ Electric current is defined as the movement of free electrons; therefore resistance is the opposition to the motion of free electrons.

        Ohm’s law shows the relationship between the voltage across a given piece of metal and the current flowing through it. The law states the following:

For a metal conductor at constant temperature, the current flowing through it is directly proportional to the voltage across it.

        It is also relevant to know of Ohm's Law, which states that the current through a metallic conductor (e.g. wire) at a constant temperature is proportional to the potential difference (voltage). Therefore V ¸ I is constant. This means that the resistance of a metallic conductor is constant providing that the temperature also remains constant. Furthermore, the resistance of a metal increases as its temperature increases. This is because at higher temperatures, the particles of the conductor are moving around more quickly, thus increasing the likelihood of collisions with the free electrons.

        As voltage divided by current is resistance, this law tells us that the resistance of a piece of metal (at constant temperature) is constant. It can easily be shown that the resistance of a piece of metal increases as its temperature increases.

        Resistance is important because it has a controlling effect on the amount of current which flows with an applied voltage.

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Middle

        The formula for the resistance of a wire is as follows:

R = r*L/A

        (L is the length of the wire, A is the cross-sectional area of the wire, and r is the ‘resisivity’ of the material).  

Prediction:

I predict that if the length increases then the resistance will also increase in proportion to the length. I think this because, the longer the wire the more atoms and then it is most likely that the electrons will collide with the atoms. Furthermore, doubling the length of the wire will result in double the resistance. This is due to the fact that, by doubling the length of the wire one is also doubling the collisions that will occur, therfore doubling the amount of energy lost in these collisions.

        My prediction is also supported by Ohm’s Law, which says that the current throught a metal conductor at a constant emperature is proportional to the potential difference (the voltage). Therefore, the voltage and the current are both constants.

        I, also, predict that my results and my graph should show that the length is proportional to the resistance.

Equipment List:

        The apparatus that I am going to use to conduct the experiment are as follows:

  • 4 volt battery.
  • 0.45 thick nichrome wire.
  • Standard Wire Gage 24 (SWG).
  • Crocodile clips are going to be used to connect the wire to the rest of the circuit.
  • Ammeter is going to be used to measure the current flowing through the circuit.
  • Voltmeter is going to be used to measure the voltage flowing through the circuit.
  • Positive and negative wires are going to be used to connect the above items and to complete the circuit.

Safety Aspects:

The experiment must be carried out in a safe way. The safety aspects that I am going to consider to make my experiment are as follows:

  • All long hair must be tied back so that it does not get caught on anything or so that it is not in the way of carrying out the experiment.
  • Do not put the crocodile clips at the 5cm point on the wire as it will burn the wire and create a spark.
  • Keep all apparatus away from the edge of the table as it may fall off and cause an injury.
  • Make sure that your hands are not wet when using electricity, in case of an electric shock.

Variables:

The variables for this experiment are as follows:

  • The independent variable for this experiment is the resistance of the wire.
  • The dependant variable for this experiment is the length of the wire.
  • The control variables for this experiment are the voltage of the battery, the material of the wire and the thickness of the wire.
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Conclusion

  • I kept the material of the wire the same.
  • I kept the thickness of the wire the same.
  • I kept the voltage on the battery the same.

        If I did this experiment again I would make some changes to ensure that I did not get any anomaly results. Firstly, I would not have kept the crocodile clip on the wire for a long period of time as that was one of the main reasons that the first set of results did not have the length proportional to the length.

        I believe that my investigation was a fair test, I certainly tried to ensure that it was.

        I was not pleased with my first set of results as it did not show that my prediction was correct. Nevertheless, I was pleased with my second set of results as they proved Ohms Law; that the length of a conductor is proportional to its length.

         Further experiments I could do related to the resistance in a wire would be to see whether the following factors would make a difference in the resistance of a wire; if the thickness of the wire was changed, I think that the resistance would be decrease as the wire got wider, because there would be more room for the electrons to move through the wire.

        Another way that I would improve the experiment would be to use pointers instead of crocodile clips; I would do this because pointers are more accurate. The pointers are more accurate because the tips have a much smaller surface area than the crocodile clips giving an accurate measurement of the resistance of the wire.

Amrit Bagha

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