# What is meant by electrical resistivity of a material? Derive its S.I. unit.

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What is meant by electrical resistivity of a material? Derive its S.I. unit.

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Mathematically, resistivity of the conducting material is given by

ρ = R x A/J

If l = 1 m, A = 1 m2, then ρ = R

Hence, the resistivity of the material is defined as the resistance offered by a metallic wire having a unit length and a unit area of cross-section. Since unit length and unit area of cross-section forms a cube, the specific resistance or resistivity can also be defined as the resistance offered by a cube of a material of side 1 m when current flows perpendicularly through the opposite faces. In

SI system, its units is

Unit of ρ = Unit of R X Unit of area of cross -Section/Unit of length of Conductor

= Ω x m2/m = Ωm