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 was to be quadrupled and the wire radius halved, the electric power dissipated would be

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

Answer 1

The correct option is B The same

Power dissipated, $P=\frac{e^2}{R}$

where,

$e=$ Induced emf $=-\left(\frac{d\varphi }{dt}\right)$

and

$\varphi =NBA$

Therefore,

$e=-NA\left(\frac{dB}{dt}\right)$

Also,

$R\propto \frac{1}{a}\propto \frac{1}{r^2}$

Therefore,

$P=\frac{e^2}{R}\propto \frac{N^2{A}^2{r}^2}{l}\propto \frac{N^2{r}^4}{l}$

As $r$ is halved, then $N$ is quadruples.

Therefore, $P$ remains the same.