Three coils of inductance L_1 = 2 H, L_2 = 3 | vedclass

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(C) For a parallel connection, the equivalent inductance $L_{eq}$ is given by $\frac{1}{L_{eq}} = \frac{1}{L_1} + \frac{1}{L_2} + \frac{1}{L_3} = \fra

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(C) For a parallel connection, the equivalent inductance $L_{eq}$ is given by $\frac{1}{L_{eq}} = \frac{1}{L_1} + \frac{1}{L_2} + \frac{1}{L_3} = \frac{1}{2} + \frac{1}{3} + \frac{1}{6} = \frac{3+2+1}{6} = 1 \ H$, so $L_{eq} = 1 \ H$.For a series connection, $L_{eq} = L_1 + L_2 + L_3 = 2 + 3 + 6 = 11 \ H$.For a mixed connection, let us check the configuration where $L_1$ is in parallel with the series combination of $L_2$ and $L_3$:$L_{23} = L_2 + L_3 = 3 + 6 = 9 \ H$.Now, $L_1$ is in parallel with $L_{23}$:$\frac{1}{L_{eq}} = \frac{1}{L_1} + \frac{1}{L_{23}} = \frac{1}{2} + \frac{1}{9} = \frac{9+2}{18} = \frac{11}{18} \ H^{-1}$.Therefore, $L_{eq} = 18/11 \ H$.This corresponds to the circuit where $L_1$ is in parallel with the series combination of $L_2$ and $L_3$. Looking at the provided options, this configuration is represented by Figure $Q$.

Three coils of inductance $L_1 = 2 \ H$, $L_2 = 3 \ H$, and $L_3 = 6 \ H$ are connected such that they are separated from each other. To obtain an effective inductance of $18/11 \ H$ between points $A$ and $B$, which of the following figures is correct?

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