Question

Two coils have a mutual inductance of \(0.005 \text{H}\). The current changes in the first coil according to equation \(I = I_0sinωt\), where \(I_0 = 10 \text{A}\) and \(ω = 60π \text{rad s}^{-1}\). The maximum values of e.m.f. in the second coil in volt will be

• A. \(2π\)
• B. \(3π\)
• C. \(4π\)
• D. \(6π\)

Hint:

The induced emf is M times the rate of change of current.

Answer 1

The Correct Option is B

Step 1: Peak rate of change:
$\left|\frac{dI}{dt}\right|_{max} = 10 \times 60\pi = 600\pi$ A/s.

Step 2: Multiply by M:
$0.005 \times 600\pi = 3\pi$ V.

Final Answer:
The maximum emf is $3\pi$ V, option (B). \[ \boxed{3\pi\ \text{V}} \]