Electrical resistivity

Electrical resistivity is a concept in electrical engineering. It is a measure of how much a material stops the flow of electric current through it. Most metals have very low electrical resistivity.

More precisely, "the resistivity of a material of conductor is the resistance of its unit area of cross section and per unit of its length". The International System of Units uses the ohm metre for measuring how much electrical resistivity there is. Electrical resistivity is the inverse of electrical conductivity. This term is more used for semiconductors and insulators.

A piece of resistive material with electrical contacts on both ends.

The name of this formula, is Pouillet's law. (It is named after Claude Pouillet):

$$R=\rho {\frac {\ell }{A}}.$$The resistance of a given element is proportional to the length, but inversely proportional to the cross-sectional area. For example, if A = 1 m², $\ell$ = 1 m (forming a cube with perfectly conductive contacts on opposite faces), then the resistance of this element in ohms is numerically equal to the resistivity of the material it is made of in Ω⋅m.

The resistivity of a substance is equal to the resistance of a rod of that substance which is 1 metre long and 1 square metre in cross-section. This can be a 1 cubic Metre cube. So we can also say that the resistivity of a substance is equal to he resistance between the opposite faces of a 1-metre cube of the substance.