The resistance of a rod in terms of its length 'l' and cross-sectional area 'A' is given as,

\(R=\rho\frac lA\), where ρ (rho) is the resistivity of the rod.

Or, \(R=\frac{\rho l}{\displaystyle\frac{\pi d^2}4}=\left(\frac{4\rho}\pi\right)\frac l{d^2}\)

When l and d are doubled, the resistance becomes,

\(R'=\left(\frac{4\rho}\pi\right)\frac{2l}{(2d)^2}=\frac{4\rho}\pi\frac l{2d^2}\)

Or, \(\frac{R'}R=\frac12\)

Or, \(R'=\frac12R\)

∴ The new resistance of the rod is R' = 1/2 R