The coefficient of mutual inductance between the primary and secondary of the coil is 5H .A current of 10 A is cut - off in 0.5 s . The induced emf is :

Options

A. 1 V
B. 10 V
C. 5 V
D. 100 V

Answer

To solve the problem, we will use the formula for induced electromotive force (emf) due to mutual induction. The formula is given by:

\[ \text{Induced emf} (E) = -M \frac{\Delta I}{\Delta t} \]

Where:
- \( M \) is the coefficient of mutual inductance,
- \( \Delta I \) is the change in current,
- \( \Delta t \) is the change in time.

### Step-by-step Solution:

1. **Identify the values given in the problem:**
- Coefficient of mutual inductance, \( M = 5 \, \text{H} \)
- Initial current, \( I_i = 10 \, \text{A} \)
- Final current, \( I_f = 0 \, \text{A} \)
- Change in time, \( \Delta t = 0.5 \, \text{s} \)

2. **Calculate the change in current (\( \Delta I \)):**
\[ \Delta I = I_f - I_i = 0 \, \text{A} - 10 \, \text{A} = -10 \, \text{A} \]

3. **Substitute the values into the induced emf formula:**
\[ E = -M \frac{\Delta I}{\Delta t} \]
\[ E = -5 \, \text{H} \cdot \frac{-10 \, \text{A}}{0.5 \, \text{s}} \]

4. **Calculate the induced emf:**
\[ E = -5 \cdot \frac{-10}{0.5} = -5 \cdot (-20) = 100 \, \text{V} \]

5. **Conclusion:**
The induced emf is \( 100 \, \text{V} \).

### Final Answer:
The induced emf is \( 100 \, \text{V} \).

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