Two pure inductors each of self-inductance `L` are connected in parallel but are well separted from each other. The total inductance is

Options

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

Explanation

To find the total inductance of two pure inductors, each with self-inductance \( L \), connected in parallel, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Inductors**: We have two inductors, both with the same self-inductance \( L \).

2. **Use the Formula for Inductors in Parallel**: The formula for the equivalent inductance \( L_{\text{equiv}} \) of inductors in parallel is given by:
\[ \frac{1}{L_{\text{equiv}}} = \frac{1}{L_1} + \frac{1}{L_2} \]
Since both inductors have the same inductance \( L \), we can substitute \( L_1 = L \) and \( L_2 = L \):
\[ \frac{1}{L_{\text{equiv}}} = \frac{1}{L} + \frac{1}{L} \]

3. **Combine the Terms**: This simplifies to:
\[ \frac{1}{L_{\text{equiv}}} = \frac{2}{L} \]

4. **Take the Reciprocal**: To find \( L_{\text{equiv}} \), we take the reciprocal of both sides:
\[ L_{\text{equiv}} = \frac{L}{2} \]

5. **Conclusion**: The total inductance of the two inductors connected in parallel is:
\[ L_{\text{equiv}} = \frac{L}{2} \]

### Final Answer:
The total inductance is \( \frac{L}{2} \).

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