Show that if two inductors with equal inductance `L` are connected in parallel then the equivalent inductance of combination is `L//2`.The inductors are separated by a large distance.

Explanation

To show that if two inductors with equal inductance \( L \) are connected in parallel, the equivalent inductance of the combination is \( \frac{L}{2} \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Configuration**: We have two inductors, both with inductance \( L \), connected in parallel.

2. **Formula for Equivalent Inductance in Parallel**: The formula for the equivalent inductance \( L_{eq} \) of two inductors in parallel is given by:
\[ \frac{1}{L_{eq}} = \frac{1}{L_1} + \frac{1}{L_2} \]
where \( L_1 \) and \( L_2 \) are the inductances of the individual inductors.

3. **Substituting Values**: Since both inductors have the same inductance \( L \), we can substitute \( L_1 = L \) and \( L_2 = L \) into the formula:
\[ \frac{1}{L_{eq}} = \frac{1}{L} + \frac{1}{L} \]

4. **Simplifying the Equation**: This simplifies to:
\[ \frac{1}{L_{eq}} = \frac{2}{L} \]

5. **Finding the Equivalent Inductance**: To find \( L_{eq} \), we take the reciprocal of both sides:
\[ L_{eq} = \frac{L}{2} \]

6. **Conclusion**: Therefore, the equivalent inductance of the two inductors connected in parallel is:
\[ L_{eq} = \frac{L}{2} \]

### Final Result:
The equivalent inductance of two inductors with equal inductance \( L \) connected in parallel is \( \frac{L}{2} \).

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