Resistivity
What does the resistance of a wire depend on?
We can use the apparatus below to investigate the effect of length. We can also find the effect of cross sectional area and investigate different materials.
What we find is that:
Resistance is directly proportional to length
Resistance is inversely proportional to cross sectional area.
The property of a material that effects the resistance of things made from it is called resistivity. The resistance of a wire is proportional to the resistivity of the material it is made from. Also the conductance of a wire is proportional to the conductivity of the material it is made from where conductivity is the inverse of resistivity.
Example;
Calculate the resistance of an aluminum cable ( resistivity = 3.2 x 10-8 ohm m ) of length 25m and diameter 4cm.
R = rho l / A = (3.2 x 10-8 x 25) / (pi x ( 2 x 10-2 )2) = 6.37 x 10-4 ohms
What about temperature?
When a metal is heated its atoms vibrate more (faster and with greater amplitude). Because of this the free electrons in the wire find it harder to travel through the material so its resistance increases.
This is why the resistance of a bulb increases as we increase the voltage across it.