Question

A short circuited coil is placed in magnetic field at any time. Power loss in coil occurs due to generated induced current. If number of turns becomes $4$ times and radius of wire becomes half, then the loss of electric power will be

• A. half
• B. equal
• C. two times
• D. four times

Answer 1

Answer: (C)

Power $P=\frac{e^2}{R}$ and $e=-\frac{d\varphi }{dt}$
Here, $\varphi =NBA$
$\therefore$ $e=-NA\left(\frac{dB}{dt}\right)$ and $R\propto \frac{1}{r^2}$
$P\propto N^2{r}^4$
$\therefore$ $\frac{P_1}{P_2}=1$