Question

A rectangular coil of $20$ turns and area of cross-section $25\, cm ^{2}$ has a resistance of $100\, \Omega$. If a magnetic field which is perpendicular to the plane of the coil changes at a rate of $1000\, T / s$, the current in the coil is

• A. 1.0 A
• B. 50 A
• C. 0.5 A
• D. 5.0 A

Answer 1

Answer: (C)

The emf of coil
$e=-\frac{d \phi}{d t}$ and current $I=\frac{e}{R}$
So, the current in the coil
$I =\frac{1}{R} \frac{d \phi}{d t}=-\frac{1}{R} \frac{d}{d t}(N B A)$
$=-\frac{N A}{R} \frac{d B}{d t}$
$=-\frac{20 \times\left(25 \times 10^{-4}\right)}{100} \times 1000$
$=-0.5\, A$