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Combination of Inductors

A circuit con...

Question

A circuit contains two inductors of self-inductance $L_{1}$ and $L_{2}$ in series (see figure). If $M$ is the mutual inductance, then the effective inductance of the circuit shown will be

A

L_{1} + L_{2}

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B

L_{1} + L_{2} - 2 M

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C

L_{1} + L_{2} + M

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D

L_{1} + L_{2} + 2 M

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Solution

The correct option is D $L_{1} + L_{2} + 2 M$
Series connection of 2 inductors can be divided into two categories.
Case 1: When current through both the inductors is in same direction.
Effective inductance of the circuit, $L = L_{1} + L_{2} + 2 M$

Case 2: When current through both the inductors is in opposite direction.
Effective inductance of the circuit, $L = L_{1} + L_{2} - 2 M$

Since for the circuit given in he question belongs to 1st case.
Therefore effective inductance of the circuit, $L = L_{1} + L_{2} + 2 M$

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