The mutual inductance between two coils is `0.5 H`.It the current in one coil is changed at the rate of `5 A//s`,what will be the `emf` induced in the other coil?

Answer

To solve the problem, we will use the formula for the electromotive force (emf) induced in one coil due to a change in current in another coil, which is given by:

\[ \text{emf} = -M \frac{dI}{dt} \]

Where:
- \( M \) is the mutual inductance between the two coils (in Henrys),
- \( \frac{dI}{dt} \) is the rate of change of current in the first coil (in Amperes per second).

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Mutual inductance \( M = 0.5 \, H \)
- Rate of change of current \( \frac{dI}{dt} = 5 \, A/s \)

2. **Substitute the Values into the Formula:**
\[ \text{emf} = -M \frac{dI}{dt} \]
Substituting the values we have:
\[ \text{emf} = -0.5 \times 5 \]

3. **Calculate the Induced EMF:**
\[ \text{emf} = -2.5 \, V \]
The negative sign indicates the direction of the induced emf according to Lenz's law, but the magnitude of the induced emf is:
\[ |\text{emf}| = 2.5 \, V \]

4. **Final Answer:**
The emf induced in the other coil is \( 2.5 \, V \).