When a current changes from 2A to 4A in `0.05` sec . In a coil , induced emf is 8 V . The self inductance of coil is :

Options

A. `0.1 ` H
B. `0.2` H
C. `0.4` H
D. `0.8` H

Answer

To find the self-inductance of the coil, we can use the formula for induced electromotive force (emf) in terms of self-inductance. The formula is given by:

\[ E = -L \frac{\Delta I}{\Delta t} \]

Where:
- \(E\) is the induced emf (in volts),
- \(L\) is the self-inductance (in henries),
- \(\Delta I\) is the change in current (in amperes),
- \(\Delta t\) is the time interval over which the change occurs (in seconds).

### Step-by-Step Solution:

1. **Identify the change in current (\(\Delta I\))**:
The current changes from 2A to 4A.
\[ \Delta I = 4A - 2A = 2A \]

2. **Identify the time interval (\(\Delta t\))**:
The time interval during which this change occurs is given as:
\[ \Delta t = 0.05 \, \text{seconds} \]

3. **Identify the induced emf (\(E\))**:
The induced emf is given as:
\[ E = 8V \]

4. **Rearrange the formula to solve for self-inductance (\(L\))**:
From the formula \(E = L \frac{\Delta I}{\Delta t}\), we can rearrange it to find \(L\):
\[ L = \frac{E \cdot \Delta t}{\Delta I} \]

5. **Substitute the known values into the equation**:
\[ L = \frac{8V \cdot 0.05s}{2A} \]

6. **Calculate \(L\)**:
\[ L = \frac{0.4}{2} = 0.2 \, \text{H} \]

### Final Answer:
The self-inductance of the coil is \(0.2 \, \text{H}\) (Henries).

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