When the current in a coil charges from 2A to 4A in 0.5 s, emf of 8 volt is induced in the coil. The coefficient of self induction of the coil is -

Options

A. 1H
B. 2H
C. 4H
D. 8H

Explanation

To find the coefficient of self-induction (L) of the coil, we can use the formula for induced electromotive force (emf) in terms of self-inductance:

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

Where:
- emf is the induced electromotive force (8 volts in this case),
- L is the self-inductance (which we need to find),
- di is the change in current,
- dt is the change in time.

### Step-by-Step Solution:

1. **Identify the change in current (di)**:
- The current changes from 2 A to 4 A.
- Therefore, the change in current (di) is:
\[ di = I_{\text{final}} - I_{\text{initial}} = 4\,A - 2\,A = 2\,A \]

2. **Identify the change in time (dt)**:
- The time interval during which this change occurs is given as 0.5 seconds.
- Thus, \( dt = 0.5\,s \).

3. **Substitute the values into the emf formula**:
- We know that the induced emf is 8 volts. Substituting the known values into the formula:
\[ 8 = -L \frac{2}{0.5} \]

4. **Calculate \(\frac{di}{dt}\)**:
- Calculate \(\frac{di}{dt}\):
\[ \frac{di}{dt} = \frac{2\,A}{0.5\,s} = 4\,A/s \]

5. **Rearranging the equation to solve for L**:
- Substitute \(\frac{di}{dt}\) back into the equation:
\[ 8 = -L \cdot 4 \]
- Rearranging gives:
\[ L = -\frac{8}{4} = -2\,H \]

6. **Taking the absolute value**:
- The coefficient of self-induction is typically expressed as a positive value, so we take the absolute value:
\[ L = 2\,H \]

### Final Answer:
The coefficient of self-induction of the coil is \(2\,H\).