Resistivity

We find from experiments that

The resistance of a wire is proportional to its length, L.
The resistance of a wire is inversely proportional to its cross-sectional area, A.

In combination, these two statements mean: R is proportional to L / A

The proportionality constant is called resistivity, $\rho$:

R =	$\rho$ $\cdot$ L

	A

$\rho$ =	R $\cdot$ A

	L

The unit of resistivity is $\Omega$ $\cdot$ m.
The inverse of the resistivity is called the conductivity, $\sigma$:

$\sigma$ =	1

	$\rho$

Caution: The symbol that is typically used for the conductivity is the same as for the surface charge density. Please be sure to understand which is used in which situation in order to avoid confusion. Unfortunately, there is only a finite number of letters, and there are more physics quantities than letters.

The resistivity depends, of course, on the material the wire is made out of, but also on the temperature. Naturally, good conductors have low resistivity or high conductivity. To give you a feeling what distinguishes conductors, insulators, and semiconductors, here are some typical values for ranges of the resistivity, $\rho$:

metals	10^-8 to 10^-6 $\Omega$ $\cdot$ m
insulators	10¹²to 10¹⁶ $\Omega$ $\cdot$ m
semiconductors	10^-4to 10⁺⁴ $\Omega$ $\cdot$ m