Two conductors of the same length and material are compared. The smaller wire has a resistance of 40 Ω. If the larger wire has twice the cross-sectional area, what is its resistance?

Resistance of a conductor is given by $R = \rho \frac{L}{A}$. For two conductors of the same material (identical $\rho$) and same length ($L$), resistance is inversely proportional to cross-sectional area: $R \propto \frac{1}{A}$. If the larger conductor has twice the cross-sectional area of the smaller one ($A_2 = 2 A_1$), its resistance is halved: $R_2 = \frac{R_1}{2} = \frac{40\,\Omega}{2} = 20\,\Omega$.

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