We discovered that -

• Resistance is proportional to length
• Resistance is inversely proportional to cross-sectional-area
• Resistance depends on the material the wire is made of

At A level we put these into an equation:

Here is an interactive Java application

where

r is the resistivity of the material (see below)

R is the resistance of the wire (the ratio of the potential difference across its end to the current that flows through it)

l is the length of the wire

A is the cross sectional area of the wire (if circular this will be pr² = pd²/4)

Unit of resistivity

We can discover the unit for resistivity from this equation

The unit of resistance multiplied by the unit for CSA divided by the unit for length

That gives us Wm as the unit for resistivity.

What is resistivity?

The electrical resistivity, or specific resistance, is the resistance between the opposite faces of a metre cube of a material.

We are used to thinking of resistance in wires. So, it would be the resistance of a metre of wire with a cross sectional area of 1 m²

Imagine a wire like that!

Wow! What dimensions, hardly a wire at all - more like a metal cylinder!

You would expect the resistivity of such a wire to be very small as the cross sectional area is so great.... and the values for resistivity of metals are very small.

Nichrome is quoted to have a resistivity of 103 X 10^-8 Wm in Kaye and Laby. All resistivities of metals are usually quoted in terms of X 10^-8 Wm so that comparisons between them can easily be made, but it has to be remembered that Most numbers are probably reasonably accurate to 2 significant figures where quoted but it is clear that you should expect values to depend upon your particular sample.

Values are affected by impurities. Values given in different sources vary considerably. Resistivity is temperature dependent.

The reciprocal of the electrical resistivity is the electrical conductivity s.

Click here to go to an excellent flash graphic of the periodic table and resistivity of elements!

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We can manipulate the equation to get R on the left

This equation is of the form Y=mx; it forms a straight line that goes through the origin. (See graphs section).

r is a constant for a particular material

R is the Y equivalent and what m is depends upon what you choose 'x' to be.

- If your variable 'x' is the length then m (the gradient) becomes r/A as A is kept constant to give a fair test

- If your variable 'x' is ¹/_A then m (the gradient) becomes rl as l is kept constant to give a fair test

Bibliography

G.W.C. Kaye and T.H. Laby in Tables of physical and chemical constants, Longman, London, UK, 15th edition, 1993.