Question

Explain why the equivalent inductance of two coils connected in parallel is less than the inductance of either of the coils.

Hint:

In parallel inductors, the total inductance is always less than the smallest inductance in the group, just like resistances in parallel.

Answer 1

Step 1: Understanding parallel connection of inductors.
When two inductors are connected in parallel, the total current splits between the two inductors. The inductance opposes changes in current, and in parallel circuits, the inductive reactance (opposition to AC) behaves in a manner similar to resistances in parallel.
Step 2: Formula for equivalent inductance.
The formula for the equivalent inductance \( L_{\text{eq}} \) of two inductors \( L_1 \) and \( L_2 \) connected in parallel is: \[ \frac{1}{L_{\text{eq}}} = \frac{1}{L_1} + \frac{1}{L_2} \] This shows that the reciprocal of the total inductance is the sum of the reciprocals of the individual inductances.
Step 3: Conclusion.
Since \( \frac{1}{L_{\text{eq}}} \) is the sum of the reciprocals of \( L_1 \) and \( L_2 \), the equivalent inductance is always less than either \( L_1 \) or \( L_2 \).