Question

# How does the resistance of a wire vary with its cross sectional area?

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Hint: This problem can be solved by recalling the formula for the resistance of a body at a specific temperature in terms of the specific resistance or resistivity of the material at that temperature, the length of the body and the cross sectional area of the body.

Formula used: $R=\rho \dfrac{l}{A}$

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