The current decays from 5A to 2A in 0.01s in a coil. The emf induced in a coil nearby it is 30V. Calculate the mutual inductance of the coil.

Options

A. 0.1H
B. 0.2H
C. 0.5H
D. 0.01H

Answer

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

\[ \text{emf} = -M \frac{\Delta I}{\Delta t} \]

Where:
- \( \text{emf} \) is the induced emf (in volts),
- \( M \) is the mutual inductance (in henries),
- \( \Delta I \) is the change in current (in amperes),
- \( \Delta t \) is the change in time (in seconds).

### Step-by-step Solution:

1. **Identify the given values**:
- Initial current, \( I_1 = 5 \, \text{A} \)
- Final current, \( I_2 = 2 \, \text{A} \)
- Change in time, \( \Delta t = 0.01 \, \text{s} \)
- Induced emf, \( \text{emf} = 30 \, \text{V} \)

2. **Calculate the change in current (\( \Delta I \))**:
\[ \Delta I = I_1 - I_2 = 5 \, \text{A} - 2 \, \text{A} = 3 \, \text{A} \]

3. **Substitute the values into the formula**:
Rearranging the formula to solve for mutual inductance \( M \):
\[ M = -\frac{\text{emf} \cdot \Delta t}{\Delta I} \]

4. **Plug in the values**:
\[ M = -\frac{30 \, \text{V} \cdot 0.01 \, \text{s}}{3 \, \text{A}} \]

5. **Calculate \( M \)**:
\[ M = -\frac{0.3}{3} = -0.1 \, \text{H} \]

Since mutual inductance is a positive quantity, we take the absolute value:
\[ M = 0.1 \, \text{H} \]

### Final Answer:
The mutual inductance of the coil is \( 0.1 \, \text{H} \).