Question

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

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

Answer 1

The correct option is C Doubled

As number of turns are halved so, length of wire is halved, and radius is doubled, then area will be $4$ times the previous one.
If previous resistance is $R$ then new resistance is $\frac{R}{8}$ and if previous emf is $E$ then new emf will be $\frac{E}{2}$
Therefore,
$P_i=\frac{E^2}{R}$
$P_f=\frac{{\left(E/2\right)}^2}{R/8}=\frac{2E^2}{R}=2P_i$
Hence, option $\left(D\right)$ is correct.