Q. The resistance of a wire of uniform diameter $d$ and length $L$ is $R.$ The resistance of another wire of the same material but diameter $2d$ and length $4\ L$ will be
A) $2R$
B) $R$
C) $R/2$
D) $R/4$
Explanation
(b) $R \propto \frac{l}{A} \propto \frac{l}{d^{2}} \Rightarrow \frac{R_{1}}{R_{2}} = \frac{l_{1}}{l_{2}} \times \left( \frac{d_{2}}{d_{1}} \right)^{2} = \frac{L}{4L}\left( \frac{2d}{d} \right)^{2} = 1$
$\Rightarrow R_{2} = R_{1} = R$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.