Question

Two coils \(P\) and \(Q\) are kept near each other. When no current flows through coil \(P\) and current increases in coil Q at the rate of \(10 \mathrm{~A} / \mathrm{S}\), the e.m.f. in coil P is 15 mV . When coil Q carries no current and current of 1.8 A flows through coil \(P\), the magnetic flux linked with coil Q is

• A. 1.8 mWb
• B. 2.7 mWb
• C. 1.5 mWb
• D. 1 mWb

Hint:

First find the mutual inductance from the induced e.m.f., then multiply by the current in P.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
Induced e.m.f. in P is \(e=M\dfrac{dI_Q}{dt}\), and flux linked with Q due to current in P is \(\phi=M I_P\).

Step 2: Mutual inductance
\(M=\dfrac{15\times10^{-3}}{10}=1.5\times10^{-3}\text{ H}\)

Step 3: Flux
\(\phi=M I_P=1.5\times10^{-3}\times1.8=2.7\times10^{-3}\text{ Wb}=2.7\text{ mWb}\)

Final Answer:
The magnetic flux linked with coil Q is 2.7 mWb. \[ \boxed{\text{(B) }2.7\ \text{mWb}} \]