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, $R ??$, 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 $n^2R$ as the area is inversely proportional to resistance.