Q. A wire of resistance $R$ is elongated $n -$ fold to make a new uniform wire. The resistance of new wire
A) $nR$
B) $n^{2}R$
C) $2nR$
D) ${2n}^{2}R$
Explanation
(b) Resistance of the wire, $R = \rho\frac{L}{A}$
When the wire is enlongated to $n -$fold, its length becomes $L' = nL$
As the volume of the wire remains constant
$\therefore A^{'}L^{'} = AL \Rightarrow A^{'} = \frac{AL}{L'} = \frac{A}{n}$
New resistance, $R^{'} = \rho\frac{L^{'}}{A'} = \rho\frac{(nL)}{(A/n)} = n^{2}\rho\frac{L}{A} = n^{2}R$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.