Question

A short-circuited coil is placed in a time-varying magnetic field. Electrical power is dissipated due to the current induced in the coil. If the number of turns were to be quadrupled and the wire radius halved, the electrical power dissipated would be:

• A. Halved
• B. The same
• C. Doubled
• D. Quadrupled

Answer 1

Answer: (B)

$P=\frac{{\epsilon }^2}{R}$

where,$\epsilon =inducedemf=-\frac{d\varphi }{dt}$

$\varphi =NBA$

$\epsilon =NA\frac{dB}{dt}$

also, $R\propto \frac{l}{r^2}$

where ,R=resistance and r=radius of wire

$P\propto \frac{N^2{r}^2}{l^2}$

$\frac{P_1}{P_2}=1$

$P_1=P_2$

This means if the number of turns were quadrupled and the wire radius halved, the electrical power dissipated would be remains same.