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: Understanding the Concept:
The emf induced in the second coil is \(\varepsilon = M\frac{dI}{dt}\) in magnitude.

Step 2: Key Formula or Approach:
\(I = I_0\sin\omega t\) gives \(\frac{dI}{dt} = I_0\omega\cos\omega t\), with maximum value \(I_0\omega\).

Step 3: Detailed Explanation:
\[ \varepsilon_{max} = M I_0\omega = 0.005 \times 10 \times 60\pi = 3\pi\ \text{V} \]
Options A, C and D differ by a wrong factor in the arithmetic.

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