ISRO EC 2023 Q.73: solution and answer

ISRO 2023 · ECQ.73 · 1 mark · MCQ

Change in magnetic flux in coil of 30 turns is 0.1 weber/second. What is the value of induced EMF?

See the question in the paper

Answer and solution

ANSWER

The induced EMF is $- 3 V$ , option (b).

Faraday's law with Lenz's law for a coil of $N$ turns: $e = - N \frac{d ϕ}{d t}$ .
Substitute $N = 30$ and $\frac{d ϕ}{d t} = 0.1 Wb/s$ .
$e = - 30 \times 0.1 = - 3 V$
The negative sign (Lenz's law) shows that the induced EMF opposes the change in flux. The answer is $- 3 V$ , option (b).
The other options do not follow from the law. $- 300 V$ comes from dividing by $0.1$ instead of multiplying, and $30 V$ and $300 V$ have a wrong magnitude and also drop the sign.

KEY IDEA

Induced EMF in an $N$ -turn coil is $e = - N d ϕ / d t$ : multiply the turns by the flux rate, and keep the minus sign from Lenz's law.

WATCH OUT FOR

Dividing the flux rate into the turns (giving $300$ ) instead of multiplying, or leaving out the negative sign that Lenz's law requires.