Physics - Capacitor Question with Solution | TestHub

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 ${\mathrm{C}}_{\mathrm{AB}}=3\mathrm{C}$, $\begin{array}{rl}& \Rightarrow C_{AB}=\frac{6C^{\prime }}{6C+C^{\prime }}=3C\\ & \Rightarrow 2C^{\prime }=6C+C^{\prime }\\ & \Rightarrow C^{\prime }=6C\end{array}$