Question

Two coils P and Q are kept near each other. When current in coil Q increases at the rate 10 $A/s$, the emf in coil P is 12 mV. When current of 1.5 A flows through coil P, the magnetic flux linked with coil Q in mWb is

• A. 0.9
• B. 1.2
• C. 1.5
• D. 1.8

Hint:

Mutual inductance $M$ is the same whether you consider coil P affecting Q or Q affecting P.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
The problem involves mutual induction between two coils. The mutual inductance \( M \) is constant for a given arrangement regardless of which coil carries the current.

Step 2: Key Formula or Approach:
1. Induced emf in second coil: \( |e_p| = M \left( \frac{di_q}{dt} \right) \)
2. Flux linked with second coil: \( \phi_q = M i_p \)

Step 3: Detailed Explanation:
From the first case:
\[ e_p = 12 \text{ mV} = 12 \times 10^{-3} \text{ V} \] \[ \frac{di_q}{dt} = 10 \text{ A/s} \] Calculate mutual inductance \( M \):
\[ M = \frac{e_p}{di_q/dt} = \frac{12 \times 10^{-3}}{10} = 1.2 \times 10^{-3} \text{ H} = 1.2 \text{ mH} \] Now, for the second case:
Current in P, \( i_p = 1.5 \text{ A} \)
Flux in Q:
\[ \phi_q = M \times i_p \] \[ \phi_q = (1.2 \text{ mH}) \times (1.5 \text{ A}) = 1.8 \text{ mWb} \]

Step 4: Final Answer:
The magnetic flux linked with coil Q is \( 1.8 \text{ mWb} \).