Question

A current $I$ passes through a wire of length $l$, radius $r$ and resistivity $\rho$. The rate of heat generated is :

• A. $\frac{I^2\rho l}{r}$
• B. $\frac{I^2\rho l}{\pi r^2}$
• C. $\frac{I^2\rho l}{\pi r}$
• D. None of these

Answer 1

The correct option is B $\frac{I^2\rho l}{\pi r^2}$

The rate of heat generation according to Joule's law is,

H$=i^{2}R$

By Ohm's law,

$R=\frac{\rho L}{A}⟹H=\frac{i^2\rho L}{\pi r^2}$