# Answer in brief: Explain why the inductance of two coils connected in parallel is less than the inductance of either coil. - Physics

Short Note

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

#### 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

1. 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.
2. 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.
3. There will be less voltage drop across parallel inductors for a given rate of change in current than for any of the individual inductors.
4. Less voltage for the same rate of change in current results in less inductance.
5. Thus, the total inductance of two coils is less than the inductance of either coil.
Concept: Inductance - Self-Inductance
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