For a inductor coil L = 0.04 H, then workdone by source to establish a current of 5A in it is -

Options

A. 0.5 J
B. 1.00 J
C. 100 J
D. 20 J

Explanation

To find the work done by the source to establish a current of 5 A in an inductor coil with inductance \( L = 0.04 \, \text{H} \), we can use the formula for the energy stored in an inductor, which is given by:

\[ W = \frac{1}{2} L I^2 \]

where:
- \( W \) is the work done (or energy stored),
- \( L \) is the inductance,
- \( I \) is the current.

### Step-by-step solution:

1. **Identify the values**:
- Inductance \( L = 0.04 \, \text{H} \)
- Current \( I = 5 \, \text{A} \)

2. **Substitute the values into the formula**:
\[ W = \frac{1}{2} \times 0.04 \, \text{H} \times (5 \, \text{A})^2 \]

3. **Calculate \( (5 \, \text{A})^2 \)**:
\[ (5 \, \text{A})^2 = 25 \, \text{A}^2 \]

4. **Substitute back into the equation**:
\[ W = \frac{1}{2} \times 0.04 \times 25 \]

5. **Calculate \( 0.04 \times 25 \)**:
\[ 0.04 \times 25 = 1 \]

6. **Calculate \( W \)**:
\[ W = \frac{1}{2} \times 1 = 0.5 \, \text{J} \]

Thus, the work done by the source to establish a current of 5 A in the inductor coil is \( 0.5 \, \text{J} \).

### Final Answer:
The work done by the source is \( 0.5 \, \text{J} \).