Question

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

• A. \( 5 \times 10^4 \) V
• B. \( 1 \times 10^5 \) V
• C. \( 25 \times 10^5 \) V
• D. \( 5 \times 10^6 \) V

Hint:

The induced emf in the secondary coil is proportional to the rate of change of current in the primary coil and the mutual inductance.

Answer 1

The Correct Option is B

Step 1: Formula for induced emf.
The emf induced in the secondary coil is given by: \[ \text{emf} = -M \frac{dI}{dt} \] where \( M \) is the mutual inductance, \( dI \) is the change in current, and \( dt \) is the time interval. Substituting the given values, we get the induced emf.

Step 2: Conclusion.
Thus, the induced emf in the secondary coil is \( 1 \times 10^5 \) V. Hence, the correct answer is option (B).

Final Answer: \[ \boxed{1 \times 10^5 \, \text{V}} \]