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(C) When two coils of inductance $L_1$ and $L_2$ are connected in series,the equivalent inductance $L_{eq}$ is given by $L_{eq} = L_1 + L_2 \pm 2M$,wh

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(C) When two coils of inductance $L_1$ and $L_2$ are connected in series,the equivalent inductance $L_{eq}$ is given by $L_{eq} = L_1 + L_2 \pm 2M$,where $M$ is the mutual inductance between the coils.Since the coils are identical,$L_1 = L_2 = L$.Because the winding directions are exactly opposite,the magnetic flux produced by one coil opposes the flux produced by the other,resulting in a negative mutual inductance effect.For two identical coils placed very close to each other,the mutual inductance $M$ is equal to the self-inductance $L$ (i.e.,$M = L$).Substituting these values into the formula: $L_{eq} = L + L - 2M = 2L - 2L = 0$.

Two identical coils of inductance $L$ joined in series are placed very close to each other such that the winding direction of one coil is exactly opposite to that of the other. The net inductance is

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