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The resistance of a wire is a measure of the opposition that it offers to the flow of electric current to it. Greater the resistance of a wire, greater is the opposition offered by the wire to the flow of current across it.

The resistance of a wire can be mathematically written in terms of its dimensions, that is, length and cross sectional area, and the resistivity of the material of which the wire has been made.

The resistance $R$ of a body of length $l$ and cross sectional area $A$ is given by

$R=\rho \dfrac{l}{A}$ --(1)

Where $\rho $ is the specific resistance or the resistivity of the material of which the wire is made.

Therefore, from (1) we can see for a wire, the resistance can be written as inversely proportional to the cross sectional area.

$\therefore R\propto \dfrac{1}{A}$

Therefore, the resistance of a wire varies inversely with the cross sectional area.