Q. Two conductors are made of the same material and have the same length. Conductor $A$ is a solid wire of diameter $1.0\ mm.$ Conductor $B$ is a hollow tube of outside diameter $2.0\ mm$ and inside diameter $1.0\ mm.$ The resistance ratio $R_{A}/R_{B}$ will be
A) 1
B) 2
C) 3
D) 4
Explanation
(c) For conductor $A,\ R_{A} = \frac{\rho l}{\pi r_{1}^{2}},$
For conductor $B,\ R_{B} = \frac{\rho l}{\pi(r_{2}^{2} - r_{1}^{2})}$
$\Rightarrow \frac{R_{A}}{R_{B}} = \frac{r_{2}^{2} - r_{1}^{2}}{r_{1}^{2}} = \left( \frac{r_{2}}{r_{1}} \right)^{2} - 1 = \left( \frac{d_{2}}{d_{1}} \right)^{2} - 1 = \left( \frac{2}{1} \right)^{2} - 1 = 3$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.