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# Two coils are mutually coupled, with L1=50 mH, L2=120 mH, and k=0.5. Calculate the maximum possible equivalent inductance if the coils are connected in parallel

Solution

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b) There are also two possibilities.

1. The polarity of the mutually-induced voltage is positive and in that case

\begin{align*} L_{eq} &=\frac{L_1L_2-M^2}{L_1+L_2-2M} \ \text{like we show in the previous problem (13.4) .} \end{align*}

1. The polarity of the mutually-induced voltage is negative and in that case

\begin{align*} L_{eq} &=\frac{L_1L_2-(-M)^2}{L_1+L_2-2(-M)} \\ L_{eq} &=\frac{L_1L_2-M^2}{L_1+L_2+2M} \end{align*}

$L_{eq}$ is greater in first case

\begin{align*} L_1+L_2-2M\frac{L_1L_2-M^2}{L_1+L_2-2M} \\ \end{align*}

So

\begin{align*} L_{eq}=\boxed{48.63\mathrm{~mH}} \end{align*}

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