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. **Understand the Inductor Division**:
- We start with an inductor coil that has an inductance \( L \).
- When this inductor is divided into two equal parts, each part will have an inductance of \( \frac{L}{2} \).

2. **Identify the Configuration**:
- The two parts of the inductor, each with inductance \( \frac{L}{2} \), are connected in parallel.

3. **Use the Formula for Parallel Inductance**:
- The formula for the total (or equivalent) inductance \( L_{eq} \) of inductors in parallel is given by:
\[ \frac{1}{L_{eq}} = \frac{1}{L_1} + \frac{1}{L_2} \]
- Here, \( L_1 = \frac{L}{2} \) and \( L_2 = \frac{L}{2} \).

4. **Substitute the Values**:
- Plugging in the values, we have:
\[ \frac{1}{L_{eq}} = \frac{1}{\frac{L}{2}} + \frac{1}{\frac{L}{2}} \]
- This simplifies to:
\[ \frac{1}{L_{eq}} = \frac{2}{L} + \frac{2}{L} = \frac{4}{L} \]

5. **Calculate the Equivalent Inductance**:
- To find \( L_{eq} \), we take the reciprocal:
\[ L_{eq} = \frac{L}{4} \]

6. **Conclusion**:
- Therefore, the net inductance of the two parts connected in parallel is:
\[ L_{eq} = \frac{L}{4} \]

### Final Answer:
The net inductance when the inductor coil of inductance \( L \) is divided into two equal parts and connected in parallel is \( \frac{L}{4} \).

---