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. The same
• D. Doubled

Answer 1

Answer: (D)

Doubled

Answer 2

The correct answer is (D) : 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 R/8 and if previous emf is E then new emf will be E/2 so
$P_i=\frac{E_2}{R}$
$P_f=\frac{(\frac{E}{2})^2}{\frac{R}{8}}$
$=\frac{2E^2}{R}=2P_i$
Because of the changes in answer key, students can challenge this question.