\begin{array}{l} R \propto l\\ R \propto \frac{1}{a}\\ So,\,\,R = \frac{l}{a}\\ R = \rho \times \frac{l}{a}........(i) \end{array}

where ρ(rho) is called resistivity of the material of conductor.

If,             l = 1 m and a = 1 m2

Then          R = ρ                           …(ii)

Thus, if we take 1 metre long piece of a substance having a cross-sectional area of 1 meter2, then the resistance of that piece of the substance is called its resistivity.

Resistivity of a substance can also be defined as follows :

The resistance offered by a cube of a substance having side of 1 metre, when current flows perpendicular to the opposite faces, is called its resistivity.

Units of resistivity

From equation (i), we can write

\rho = \frac{{R \times a}}{\ell }

So,{\rm{ }}SI{\rm{ }}unit{\rm{ }}of{\rm{ }}resistivity{\rm{ }}(\rho ){\rm{ }} = \frac{{ohm\, \times \,{m^2}}}{m} = {\rm{ }}ohm.m

Thus, the SI unit of resistivity is ohm. m (or Ω . m)

Classification of Material on Basis of Resistivity

Substances showing very low resistivities : The substances which show very low resistivities allow the flow of electric current through them. these type of substances are called conductors.

For example, copper, gold, silver, aluminium and electrolytic solutions are conductors.

Substances having moderate resistivity: The substances which have moderate resistivity offer appreciable resistance to the flow of electric current through them. Therefore, such substances are called resistors. For example, alloys such as nichrome, manganin, constantan and carbon are typical resistors.

Substances having very high resistivity: The substances which have very high resistivities do not allow electricity to flow through them. The substances which do not allow electricity to pass through them are called insulators. For example, rubber, plastics, dry wood, etc. are insulators.