An inductor coil of inductance L is divided into two equal parts and both parts are connected in parallel. The net inductance is :

Options

A. L
B. 2L
C. `L//2`
D. `L//4`

Answer

To solve the problem of finding the net inductance when an inductor coil of inductance \( L \) is divided into two equal parts and connected in parallel, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Inductor Division**:
- When the inductor coil of inductance \( L \) is divided into two equal parts, the inductance of each part becomes half of the original inductance.
- Therefore, the inductance of each part is:
\[ L_1 = L_2 = \frac{L}{2} \]

2. **Using the Formula for Parallel Inductance**:
- When inductors are connected in parallel, the formula for the equivalent inductance \( L_{eq} \) is given by:
\[ \frac{1}{L_{eq}} = \frac{1}{L_1} + \frac{1}{L_2} \]

3. **Substituting the Values**:
- Substitute \( L_1 \) and \( L_2 \) into the formula:
\[ \frac{1}{L_{eq}} = \frac{1}{\frac{L}{2}} + \frac{1}{\frac{L}{2}} \]
- This simplifies to:
\[ \frac{1}{L_{eq}} = \frac{2}{L} + \frac{2}{L} = \frac{4}{L} \]

4. **Finding the Equivalent Inductance**:
- Now, take the reciprocal to find \( L_{eq} \):
\[ L_{eq} = \frac{L}{4} \]

5. **Conclusion**:
- The net inductance when the inductor coil is divided into two equal parts and connected in parallel is:
\[ L_{eq} = \frac{L}{4} \]

### Final Answer:
The net inductance is \( \frac{L}{4} \).

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