The value of self inductance of a coil is 5H. The value of current changes from 1A to 2A in 5 sec., then value of induced emf in it :-

Options

A. 10V
B. 0.1V
C. 1.0V
D. 100V

Answer

To find the induced electromotive force (emf) in a coil due to a change in current, we can use the formula for self-inductance:

\[ \text{emf} = -L \frac{di}{dt} \]

Where:
- \( L \) is the self-inductance of the coil (in henries),
- \( di \) is the change in current (in amperes),
- \( dt \) is the change in time (in seconds).

### Step-by-step Solution:

1. **Identify the values given:**
- Self-inductance \( L = 5 \, \text{H} \)
- Initial current \( I_1 = 1 \, \text{A} \)
- Final current \( I_2 = 2 \, \text{A} \)
- Time interval \( dt = 5 \, \text{s} \)

2. **Calculate the change in current (\( di \)):**
\[ di = I_2 - I_1 = 2 \, \text{A} - 1 \, \text{A} = 1 \, \text{A} \]

3. **Calculate the rate of change of current (\( \frac{di}{dt} \)):**
\[ \frac{di}{dt} = \frac{di}{dt} = \frac{1 \, \text{A}}{5 \, \text{s}} = 0.2 \, \text{A/s} \]

4. **Substitute the values into the emf formula:**
\[ \text{emf} = -L \frac{di}{dt} = -5 \, \text{H} \times 0.2 \, \text{A/s} \]

5. **Calculate the induced emf:**
\[ \text{emf} = -5 \times 0.2 = -1 \, \text{V} \]

6. **Interpret the result:**
The negative sign indicates that the induced emf opposes the change in current (according to Lenz's law). However, the magnitude of the induced emf is \( 1 \, \text{V} \).

### Final Answer:
The value of the induced emf in the coil is \( 1 \, \text{V} \).

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