Short Note

**Answer in brief:**

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

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#### Solution 1

Assuming that their mutual inductance can be ignored, the equivalent inductance of a parallel combination of two coils is given by

`1/"L"_"parallel" = 1/"L"_1 + 1/"L"_2` or `"L"_"parallel" = ("L"_1"L"_2)/("L"_1 + "L"_2)`

Hence, the equivalent inductance is less than the inductance of either coil.

#### Solution 2

- For a parallel combination of two coils, the current through each parallel inductor is a fraction of the total current and the voltage across each parallel inductor is the same.
- As a result, a change in total current will result in less voltage dropped across the parallel array than for any one of the individual inductors.
- There will be less voltage drop across parallel inductors for a given rate of change in current than for any of the individual inductors.
- Less voltage for the same rate of change in current results in less inductance.
- Thus, the total inductance of two coils is less than the inductance of either coil.

Concept: Inductance - Self-Inductance

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