The mutual inductance between two coils is `1.25` henry. If the current in the primary changes at the rate of `80 ampere//second`, then the induced e.m.f. in the secondary is

Options

A. `12.5`V
B. `64.0`V
C. `0.016`V
D. `100.0`V

Answer

To find the induced e.m.f. in the secondary coil due to the changing current in the primary coil, we can use the formula for mutual inductance.

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Mutual inductance (M) = 1.25 henry
- Rate of change of current in the primary coil (ΔI/Δt) = 80 A/s

2. **Use the Formula for Induced e.m.f.**:
The induced e.m.f. (E) in the secondary coil can be calculated using the formula:
\[ E = -M \frac{ΔI}{Δt} \]
Here, the negative sign indicates the direction of the induced e.m.f. according to Lenz's law, but since we are interested in the magnitude, we can ignore the negative sign.

3. **Substitute the Values**:
Substitute the values of M and ΔI/Δt into the formula:
\[ E = 1.25 \, \text{H} \times 80 \, \text{A/s} \]

4. **Calculate the Induced e.m.f.**:
\[ E = 1.25 \times 80 = 100 \, \text{V} \]

5. **Final Result**:
The induced e.m.f. in the secondary coil is:
\[ E = 100 \, \text{V} \]