Q. The electric resistance of a certain wire of iron is $R.$ If its length and radius are both doubled, then
A) The resistance will be doubled and the specific resistance will be halved
B) The resistance will be halved and the specific resistance will remain unchanged
C) The resistance will be halved and the specific resistance will be doubled
D) The resistance and the specific resistance, will both remain unchanged
Explanation
(b) $R \propto \frac{l}{r^{2}} \Rightarrow \frac{R_{2}}{R_{1}} = \frac{l_{2}}{l_{1}} \times \frac{r_{1}^{2}}{r_{2}^{2}} = \left( \frac{2}{1} \right) \times \left( \frac{1}{2} \right)^{2} = \frac{1}{2}$
$\Rightarrow R_{2} = \frac{R_{1}}{2},\ $ specific resistance doesn’t depend upon length, and radius
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.