The average `emf` induced in the secondary coil is `0.1 V` when the current in the primary coil changes from `1` to `2A` in `0.1 s`.What is the mutual inductance of the coils.

Explanation

To solve the problem, we need to find the mutual inductance (M) of the coils given the average induced electromotive force (emf) in the secondary coil, the change in current in the primary coil, and the time over which this change occurs.

### Step-by-Step Solution:

1. **Identify Given Values:**
- Average induced emf (E) = 0.1 V
- Initial current (I1) = 1 A
- Final current (I2) = 2 A
- Time interval (Δt) = 0.1 s

2. **Calculate Change in Current (ΔI):**
\[ \Delta I = I2 - I1 = 2 \, \text{A} - 1 \, \text{A} = 1 \, \text{A} \]

3. **Calculate Rate of Change of Current (ΔI/Δt):**
\[ \frac{\Delta I}{\Delta t} = \frac{1 \, \text{A}}{0.1 \, \text{s}} = 10 \, \text{A/s} \]

4. **Use the Formula for Mutual Inductance:**
The formula relating the induced emf (E) to mutual inductance (M) is given by:
\[ E = -M \frac{\Delta I}{\Delta t} \]
Rearranging this formula to find M gives:
\[ M = -\frac{E}{\frac{\Delta I}{\Delta t}} \]

5. **Substitute the Values:**
Substitute the values of E and ΔI/Δt into the formula:
\[ M = -\frac{0.1 \, \text{V}}{10 \, \text{A/s}} = -0.01 \, \text{H} \]
Since mutual inductance is a positive quantity, we can ignore the negative sign:
\[ M = 0.01 \, \text{H} \]

### Final Answer:
The mutual inductance of the coils is **0.01 Henry**.

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