Q. A uniform wire of resistance $R$ is uniformly compressed along its length, until its radius becomes $n$ times the original radius. Now resistance of the wire becomes
A) $\frac{R}{n^{4}}$
B) $\frac{R}{n^{2}}$
C) $\frac{R}{n}$
D) $nR$
Explanation
(a) $\frac{R_{1}}{R_{2}} = \left( \frac{r_{2}}{r_{1}} \right)^{4} \Rightarrow \frac{R}{R_{2}} = \left( \frac{nr}{r} \right)^{4} \Rightarrow R_{2} = \frac{R}{n^{4}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.