Resistance of a Wire

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GCSE Physics Coursework - Resistance of a Wire Coursework
Resistance of a Wire

Task

To investigate how the resistance of a wire is affected by the length of the wire.

Theory

What is resistance?

Electricity is conducted through a conductor, in this case wire, by means of free electrons. The number of free electrons depends on the material and more free electrons means a better conductor, i.e. it has less resistance. For example, gold has more free electrons than iron and, as a result, it is a better conductor. The free electrons are given energy and as a result move and collide with neighbouring free electrons. This happens across the length of the wire and thus electricity is conducted. Resistance is the result of energy loss as heat. It involves collisions between the free electrons and the fixed particles of the metal, other free electrons and impurities. These collisions convert some of the energy that the free electrons are carrying into heat.

How is it measured?

The resistance of a length of wire is calculated by measuring the current present in the circuit (in series) and the voltage across the wire (in parallel). These measurements are then applied to this formula:

V = I ´ R where V = Voltage, I = Current and R = Resistance

This can be rearranged to:

R = V

I

Ohm’s Law

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.

Variables

Input:

Length of wire. *
Material of wire.
Width of wire.
Starting temperature of wire.

Output:

and thus the resistance of the wire. †

Voltage across wire.
Current in circuit.
Temperature of wire.

The variable marked with a * will be varied, the other input variables will be kept constant. The output variable marked with a † will be measured.

Predictions

The longer the wire, the higher the resistance. This is because the longer t...

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... more of the connections could have been faulty, causing extra resistance at the connections. A solution to this would be to, before each experiment, connect the connections together without the wire in place and measure the resistance then. If it is higher than it should be then the connections could be cleaned.
Whilst extremely unlikely, it is conceivable that the power supply was providing a different voltage for some of the results. This is unlikely to be a problem in this investigation but it might have been an issue had we used batteries instead.

NB: If one were to assume that Ohm’s Law applies, then another possible explanation could be that at some points (more likely in the lower lengths), the wire was not allowed to cool completely so that the temperature was higher for that measurement. Whilst unlikely (due to the two sets of results), this would cause a higher resistance as explained previously. However, it is now known, after researching the metal alloy “constantan,” that the resistivity (the electrical resistance of a conductor of particular area and length) of this alloy is not affected by temperature. Therefore, in these experiments Ohm’s Law does not apply.

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