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(D) From the figure,the three capacitors of capacitance $2 C$ are connected in parallel between point $A$ and point $P$.Therefore,the equivalent capac

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$6$

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(D) From the figure,the three capacitors of capacitance $2 C$ are connected in parallel between point $A$ and point $P$.Therefore,the equivalent capacitance $C_{AP}$ is:$C_{AP} = 2 C + 2 C + 2 C = 6 C$Now,this equivalent capacitor $C_{AP}$ is in series with the capacitor $C^{\prime}$ between points $A$ and $B$.The equivalent capacitance $C_{AB}$ of two capacitors in series is given by:$\frac{1}{C_{AB}} = \frac{1}{C_{AP}} + \frac{1}{C^{\prime}}$Given $C_{AB} = 3 C$,we have:$\frac{1}{3 C} = \frac{1}{6 C} + \frac{1}{C^{\prime}}$$\frac{1}{C^{\prime}} = \frac{1}{3 C} - \frac{1}{6 C} = \frac{2 - 1}{6 C} = \frac{1}{6 C}$Therefore,$C^{\prime} = 6 C$.

If the equivalent capacitance between $A$ and $B$ of the combination of capacitors shown in the figure is $3 C$,then the capacitor $C^{\prime}$ is equal to: (in $C$)

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