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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 as shown in the 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} - M

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C

L_{1} + L_{2} + 3 M

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D

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

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Solution

The correct option is C $L_{1} + L_{2} + 2 M$
if a current $i$ passes through the series combination,
induced emf in $L_{1} = L_{1} \frac{d i}{d t} + M \frac{d i}{d t}$
induced emf in $L_{2} = L_{2} \frac{d i}{d t} + M \frac{d i}{d t}$
total induced emf $= (L_{1} + L_{2} + 2 M) \frac{d i}{d t}$

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