Q. A current $i$ passes through a wire of length $l,$ radius of cross-section $r$ and resistivity $\rho.$ The rate of heat generation is
A) $\frac{i^{2}l\rho}{\pi r^{2}}$
B) $i^{2}\left( \frac{l\rho}{\pi r^{2}} \right)^{2}$
C) $i^{2}l\ \rho/r$
D) $il\ \rho/r$
Explanation
(a) $H = i^{2}Rt \Rightarrow \frac{H}{t} = i^{2}R = \frac{i^{2}\rho l}{\pi\ r^{2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.