## Resistivity

When we want to compare the resistance of different materials to the passage of electric current, it is not enough to measure the resistance of a piece of wire or a piece of wood and then find out as if we didn't know already that the piece of wood has a higher resistance than the piece of wire. We must standardise the wire and the wood in some way. We define a concept called the resistivity, labeled
$\rho$
.
The resisitivity of a material is the resistance between opposite faces of a im cube made of the material, so that the cube is 1m by 1m by 1m. We do not need to such a cube to find the resistivity of a material. The resistance between the ends of a block of material of length L, constant cross sectional area A is inversely proportional to that area, and proportional to the length of the block. In effect we can 'resize' any block of constant cross sectional area up to a 1m by 1m by 1m cube. The resistance between the ends of the block will then be
$R=\frac{\rho l}{A}$
.