Two coils of self inductance L 1 and L 2 are connected in series combination having mutual inductance of the coils as M . The equivalent self inductance of the combination will be

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Here self inductances are in series but their mutual inductances are linked oppositely.

As the inductors connected are in series opposition, hence magnetic flux will be opposing each other. Therefore,

$L_{e q} = L_{1} + L_{2} - 2 M$

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