Discussion
The combined inductance of two coils connected in series is 1.2 H or 0.2 H, depending on the relative directions of the currents in the coils. If one of the coil, when isolated, has a self-inductance of 0.4 H, the value of mutual inductance will be
Answer: C
The mutual inductance is 0.25 H.
Two coils in series have a total inductance \(L_{1} + L_{2} \pm 2M\), the sign depending on whether their fluxes aid or oppose. So the two given values are:
\[ \begin{aligned} L_{1} + L_{2} + 2M &= 1.2 \\ L_{1} + L_{2} - 2M &= 0.2 \\ 4M &= 1.0,\quad M = 0.25\ \text{H} \end{aligned} \]
The 0.4 H of one coil is not needed for M; it only gives the other coil as 0.3 H. 1.0 H is 4M, not M, and 1.4 H is the sum of the two series values.
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