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

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Aicharya · Accepted Answer

Consider figure below. Equivalent capacitance between AP is: $\mathrm{C}_{\mathrm{AP}}=3(2 \mathrm{C})$ As capacitors are connected parallel, the equivalent capacitance of AB is: $\frac{1}{\mathrm{C}_{\mathrm{AB}}}=\frac{1}{\mathrm{C}^{\prime}}+\frac{1}{6 \mathrm{C}}=\frac{6 \mathrm{C}+\mathrm{C}^{\prime}}{6 \mathrm{CC}^{\prime}}$ We know $\mathrm{C}_{\mathrm{AB}}=3 \mathrm{C}$, $\begin{aligned} & \Rightarrow C_{A B}=\frac{6 C^{\prime}}{6 C+C^{\prime}}=3 C \ & \Rightarrow 2 C^{\prime}=6 C+C^{\prime} \ & \Rightarrow C^{\prime}=6 C \end{aligned}$

If the equivalent capacitance between $\mathrm{A}$ and $\mathrm{B}$ of the combination of capacitors shown…

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