Five capacitors, each of capacitance value $C$ are connected as shown in the figure. The ratio of capacitance between $P$ and $R$, and the capacitance between $P$ and $Q$ is

Between the points $P$ and $Q$, a capacitor $C_1$ and series combination of $C_2, C_3, C_4, C_5$ are connected in parallel. $\therefore \frac{1}{C_s}=\frac{1}{C_2}+\frac{1}{C_3}+\frac{1}{C_4}+\frac{1}{C_5}$
$$ =\frac{1}{C}+\frac{1}{C}+\frac{1}{C}+\frac{1}{C}=\frac{4}{C} $$ or, $C_s=C / 4$. The equivalent capacitance between $P$ and $Q$ is $$ C^{\prime}=C_1+C_s=C+\frac{C}{4}=\frac{5 C}{4} \text {. } $$ Between the points $P$ and $R$ a series combination of $C_1, C_2$ and a series combination of $C_3, C_4, C_5$ are connected in parallel. $$ \begin{aligned} & \therefore \quad \frac{1}{C_s^{\prime}}=\frac{1}{C_1}+\frac{1}{C_2}=\frac{1}{C}+\frac{1}{C}=\frac{2}{C} \text { or, } C_s^{\prime}=\frac{C}{2} \\ & \frac{1}{C_s^{\prime \prime}}=\frac{1}{C_3}+\frac{1}{C_4}+\frac{1}{C_5}=\frac{1}{C}+\frac{1}{C}+\frac{1}{C}=\frac{3}{C} \text { or, } C_s^{\prime \prime}=\frac{C}{3} \end{aligned} $$ The equivalent capacitance between $P$ and $R$ is $$ \begin{aligned} & C^{\prime \prime}=C_s^{\prime}+C_s^{\prime \prime}=\frac{C}{2}+\frac{C}{3}=\frac{5 C}{6} \\ & \therefore \quad \frac{C^{\prime \prime}}{C^{\prime}}=\frac{(5 C / 6)}{(5 C / 4)}=\frac{4}{6}=\frac{2}{3} \end{aligned} $$