What is the Electrical Resistance in a Wire ?

The electrical resistance of a wire is greater for a longer wire and less for a wire of larger cross sectional area. The resistance depend on the material of which it is made and can be expressed as:

    R = ρ L / A                       (1)

    where

    R = resistance (ohm, Ω)

    ρ = resistivity coefficient (ohm m, Ω m)

    L = length of wire (m)

    A = cross sectional area of wire (m2)

The factor in the resistance which takes into account the nature of the material is the resistivity. Since it is temperature dependent, it can be used to calculate the resistance of a wire of given geometry at different temperatures.

The inverse of resistivity is called conductivity and can be expressed as:

    σ = 1 / ρ                          (2)

    where

    σ = conductivity (1 / Ω m)

Example - Resistance in an Aluminum Wire

Resistance of an aluminum cable with length 10 m and cross sectional area of 3 mm2 can be calculated as

R = (2.65 10-8 Ω m) (10 m) / ((3 mm2) (10-6 m2/mm2))

   = 0.09 Ω

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