Question

If the coefficient of mutual induction of the primary and secondary coils of an induction coil is 5 H and a current of 10 A is cut-off in $5\times {10}^{-4}$ s, the emf inducted (in volt) in the secondary coil is

• A. $5\times {10}^4$
• B. $1\times {10}^5$
• C. $25\times {10}^5$
• D. $5\times {10}^6$

Answer 1

The correct option is B

$1\times {10}^5$

Step 1: Given data

Coefficient of mutual induction, M = 5 H

Change in current, di = 10 A

Change in time, dt = $5\times {10}^{-4}$ s

Step 2: Formula used

Induced emf in the secondary coil = $\epsilon s=-M\frac{di}{dt}$

Step 3: Calculation

$\epsilon s=-M\frac{di}{dt}$

$=-5\frac{10}{5\times {10}^{-4}}$

$=1\times {10}^5$ V [The negative sign only indicates that the emf opposes the change.]

The emf induced in the secondary coil is $1\times {10}^5$ V.

Hence option B is the correct answer.