Question

Two coils P and Q have mutual inductance 'M' H. If the current in the coil P is \(I = I_0sinωt\), then the maximum value of e.m.f. induced in coil Q is

• A. \(\frac{ω}{MI_0}\)
• B. \(\frac{Mω}{I_0}\)
• C. \(MωI_0\)
• D. \(\frac{MI_0}{ω}\)

Hint:

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

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
The emf induced in coil Q is \(e = -M\dfrac{dI}{dt}\), where \(I\) is the current in coil P.

Step 2: Differentiate.
\[ \frac{dI}{dt} = I_0\omega\cos\omega t \Rightarrow e = -MI_0\omega\cos\omega t \]

Step 3: Find the maximum.
The largest value of \(|\cos\omega t|\) is 1, so \(e_{max} = M\omega I_0\).

Step 4: Check the options.
Options (A), (B) and (D) put \(\omega\) or \(I_0\) in the denominator, which gives the wrong dimensions.

Final Answer:
The maximum emf is \(M\omega I_0\), option (C). \[ \boxed{M\omega I_0} \]