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Physics-

General

Easy

Question

Two identical induction coils each of inductance L joined in series are 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?

$L^{2}$
$2 L$
$L / 2$
Zero

The correct answer is: Zero

When the two coils are joined in series such that the winding of one is opposite to the other, then the emf produced in first coil is 180 $degree$ out of phase of the emf produced in second coil. Thus, emf produced in first coil is negative and the emf produced in second coil is positive, so net inductance is
$L equals L subscript 1 end subscript plus L subscript 2 end subscript equals L plus L$
From Faraday’s law of electromagnetic induction
$ϕ equals L i comma$ where $ϕ$ is flux and $i$ the current
$therefore L equals negative fraction numerator ϕ over denominator i end fraction plus fraction numerator ϕ over denominator i end fraction$
$rightwards double arrow L$ =0

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