The coefficient of mutual inductance of the two coils is 0.5 H. if the current is increased form 2 to 3 A in 0.1 sec. in one of them, then find the induced e.m.f in the second coil in Volts.

Answer

To solve the problem, we need to find the induced electromotive force (e.m.f) in the second coil when the current in the first coil changes. We will use the formula for mutual inductance and the relationship between current change and induced e.m.f.

### Step-by-Step Solution:

1. **Identify Given Values:**
- Coefficient of mutual inductance (M) = 0.5 H
- Initial current (I1_initial) = 2 A
- Final current (I1_final) = 3 A
- Time interval (Δt) = 0.1 s

2. **Calculate the Change in Current (ΔI):**
\[ \Delta I = I1_{final} - I1_{initial} = 3 A - 2 A = 1 A \]

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

4. **Use the Formula for Induced e.m.f (ε):**
The induced e.m.f in the second coil is given by:
\[ \epsilon = -M \frac{dI}{dt} \]
where M is the mutual inductance.

5. **Substitute the Values:**
\[ \epsilon = -0.5 \, \text{H} \times 10 \, \text{A/s} = -5 \, \text{V} \]

6. **Determine the Magnitude of the Induced e.m.f:**
The magnitude of the induced e.m.f is:
\[ |\epsilon| = 5 \, \text{V} \]

### Final Answer:
The induced e.m.f in the second coil is 5 Volts.

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