Question

Two coils \(P\) and \(Q\) are separated by some distance. When a current of \(3A\) flows through coil \(P\), a magnetic flux of \(10^{-3}\) Wb passes through \(Q\). No current is passed through \(Q\). When no current passes through \(P\) and a current of \(2A\) passes through \(Q\), the flux through \(P\) is \(x\times 10^{-3}\) Wb. The value of \(x\) is

• A. \(6.67\)
• B. \(0.667\)
• C. \(3.67\)
• D. \(0.367\)

Hint:

Mutual inductance is the same in both directions, so find M from the first case and reuse it.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
Flux linked with a coil is \(\Phi=MI\). The mutual inductance \(M\) is the same whichever coil carries the current.

Step 2: Find M
\(M=\dfrac{\Phi_Q}{I_P}=\dfrac{10^{-3}}{3}\) H.

Step 3: Flux through P
\(\Phi_P=MI_Q=\dfrac{10^{-3}}{3}\times2=0.667\times10^{-3}\) Wb.

Step 4: Result
So \(x=0.667\), option (B).

Final Answer:
The value of x is 0.667. \[ \boxed{\text{(B) }0.667} \]