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 the inductor given that 0.1 J of energy is stored for a current of 0.2 A, we can use the formula for energy stored in an inductor:

### Step-by-Step Solution:

1. **Write down the formula for energy stored in an inductor**:
\[ U = \frac{1}{2} L I^2 \]
where:
- \( U \) is the energy stored (in joules),
- \( L \) is the inductance (in henries),
- \( I \) is the current (in amperes).

2. **Substitute the known values into the formula**:
Given:
- \( U = 0.1 \, \text{J} \)
- \( I = 0.2 \, \text{A} \)

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

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

4. **Substitute \( I^2 \) back into the equation**:
\[ 0.1 = \frac{1}{2} L (0.04) \]

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

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

7. **Perform the division**:
\[ L = 5 \, \text{H} \]

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

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