Question

A wire of resistance $R$ is elongated $n$-fold to make a new uniform wire. The resistance of new wire

• A. $nR$
• B. $n^2R$
• C. $2nR$
• D. $2n^2R$

Answer 1

Answer: (B)

$n^2R$

Answer 2

The resistance of a wire is directly proportional to the length of the wire.
Thus, $R \propto l$ so the length increases $n$-fold also since the volume of the wire remains constant, so the area of the wire decreases $n$-fold.
Hence the resistance increases to $n^{2} R$ as the area is inversely proportional to resistance.