For a inductor coil L = 0.04 H, then workdone by source to establish a current of 5A in it is -
(a) 0.5 J (b) 1.00 J (c) 100 J (d) 20 J

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 work done in an inductor:

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

### Step-by-Step Solution:

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

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

3. **Calculate \( I^2 \):**
\[ I^2 = 5^2 = 25 \]

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

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

6. **Final answer:**
The work done by the source to establish a current of 5 A in the inductor coil is \( 0.5 \, \text{J} \).

### Conclusion:
The correct answer is (a) 0.5 J.