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(D) When two identical coils of inductance $L$ are connected in series,the total inductance is given by $L_{eq} = L_1 + L_2 \pm 2M$,where $M$ is the m

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(D) When two identical coils of inductance $L$ are connected in series,the total inductance 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 and placed very close to each other,the mutual inductance $M$ is equal to the self-inductance $L$ (i.e.,$M = L$).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.Therefore,the net inductance is $L_{eq} = L + L - 2M$.Substituting $M = L$,we get $L_{eq} = L + L - 2L = 0$.

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

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