Question

The mutual inductance between a pair of coils is 3 H. If the current in one coil changes from 0 A to 2 A in 0.5 s, the induced emf produced in the other coil is

• A. 5 V
• B. 2 V
• C. 6 V
• D. 12 V
• E. 3 V

Hint:

Induced emf depends on the rate of change, not just the magnitude of change. Changing current faster (smaller \(\Delta t\)) always leads to higher induced voltages.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Mutual induction is the phenomenon of producing induced emf in a secondary coil due to a change in current in a primary coil placed near it.

Step 2: Key Formula or Approach:
Induced emf: \(e = M \left| \frac{dI}{dt} \right|\)

Step 3: Detailed Explanation:
Given:
\(M = 3 \text{ H}\)
Initial current \(I_1 = 0 \text{ A}\)
Final current \(I_2 = 2 \text{ A}\)
Time interval \(\Delta t = 0.5 \text{ s}\)
Calculating the rate of change of current:
\[ \frac{dI}{dt} = \frac{2 - 0}{0.5} = 4 \text{ A/s} \]
Calculating induced emf:
\[ e = 3 \times 4 = 12 \text{ V} \]

Step 4: Final Answer:
The induced emf is 12 V.