Two circular coils are kept in vicinity of each other. The current in primary coil changes from 10 A to 6 A in 0.3 sec. Calculate the coefficient of mutual inductance of the pair of emf of 1V induced in secondary coil.

Answer

To solve the problem, we will use the formula for the induced electromotive force (emf) in the secondary coil due to the changing current in the primary coil. The relationship is given by Faraday's law of electromagnetic induction.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Initial current in the primary coil, \( I_1 = 10 \, A \)
- Final current in the primary coil, \( I_2 = 6 \, A \)
- Time interval, \( \Delta t = 0.3 \, s \)
- Induced emf in the secondary coil, \( \text{emf} = 1 \, V \)

2. **Calculate the Change in Current:**
\[ \Delta I = I_2 - I_1 = 6 \, A - 10 \, A = -4 \, A \]

3. **Determine the Rate of Change of Current:**
\[ \frac{dI}{dt} = \frac{\Delta I}{\Delta t} = \frac{-4 \, A}{0.3 \, s} = -\frac{40}{3} \, A/s \]

4. **Use Faraday's Law to Relate Induced emf to Mutual Inductance:**
According to Faraday's law, the induced emf (\( \text{emf} \)) in the secondary coil is given by:
\[ \text{emf} = -M \frac{dI}{dt} \]
Here, \( M \) is the mutual inductance we need to find.

5. **Substituting the Values:**
\[ 1 \, V = -M \left(-\frac{40}{3} \, A/s\right) \]
Simplifying this gives:
\[ 1 = M \cdot \frac{40}{3} \]

6. **Solve for Mutual Inductance \( M \):**
\[ M = \frac{3}{40} \, H \]

### Final Answer:
The coefficient of mutual inductance \( M \) is \( \frac{3}{40} \, H \).

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