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Two coils having self inductances L1 and L2 are joined in series so that their fluxes add up (series-aiding). If the mutual inductance between them is M, what is the equivalent inductance of the combination?

1. 1/L1 + 1/L2 + 1/M
2. L1 + L2 + M
3. L1 + L2 + 2M
4. L1 + L2 - 2M

Correct answer: L1 + L2 + 2M

Solution

When two mutually coupled coils are connected in series, the same current i passes through both. The total flux linkage is L1*i + L2*i plus the mutual contributions M*i from each coil acting on the other (two such terms). For series-aiding connection these add, giving L_eq = L1 + L2 + 2M. For series-opposing it would be L1 + L2 - 2M.

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