Three condensers of capacities $C_1$,$C_2$,and $C_3$ are connected in series with a source of e.m.f. $V$. The potentials across the three condensers are in the ratio:

Four capacitors with capacitances $C_1 = 1\ C$,$C_2 = 2\ C$,$C_3 = 3\ C$,and $C_4 = 4\ C$ are connected to a battery of potential $V$ as shown in the figure. Find the ratio of charges on $C_2$ and $C_4$.

$A$ finite ladder is constructed by connecting several sections of $2\,\mu F$ and $4\,\mu F$ capacitor combinations as shown in the figure. It is terminated by a capacitor of capacitance $C$. What value should be chosen for $C$ such that the equivalent capacitance of the ladder between the points $A$ and $B$ becomes independent of the number of sections in between? (in $\mu F$)

Four capacitors of equal capacitance have an equivalent capacitance $C_1$ when connected in series and an equivalent capacitance $C_2$ when connected in parallel. The ratio $\frac{C_1}{C_2}$ is:

The effective capacitance between points $A$ and $B$ shown in the figure is (in $\mu F$)

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 $C$)