If 0.1 J of energy is stored for the flow of the current of 0.2 A in an inductor, then its inductance value (in H) is

Answer

To find the inductance value \( L \) of an inductor given that 0.1 J of energy is stored for a current of 0.2 A, we can use the formula for the energy stored in an inductor:

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

where:
- \( E \) is the energy stored in the inductor (in joules),
- \( L \) is the inductance (in henries),
- \( I \) is the current flowing through the inductor (in amperes).

### Step-by-Step Solution:

1. **Identify the given values**:
- Energy \( E = 0.1 \, \text{J} \)
- Current \( I = 0.2 \, \text{A} \)

2. **Substitute the known values into the energy formula**:
\[ 0.1 = \frac{1}{2} L (0.2)^2 \]

3. **Calculate \( (0.2)^2 \)**:
\[ (0.2)^2 = 0.04 \]

4. **Rewrite the equation with the calculated value**:
\[ 0.1 = \frac{1}{2} L (0.04) \]

5. **Multiply both sides by 2 to eliminate the fraction**:
\[ 0.2 = L (0.04) \]

6. **Solve for \( L \)** by dividing both sides by 0.04:
\[ L = \frac{0.2}{0.04} \]

7. **Calculate the value of \( L \)**:
\[ L = 5 \, \text{H} \]

### Final Answer:
The inductance value \( L \) is \( 5 \, \text{H} \).

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