Find the equivalent capacitance between $A$ and $B$ of the following arrangement:

$A$ network of $4$ capacitors is connected to a battery as shown. The ratio of the charges on capacitors $C_{2}$ and $C_{4}$ is

Consider the combination of $2$ capacitors $C_{1}$ and $C_{2}$,with $C_{2} > C_{1}$. When connected in parallel,the equivalent capacitance is $\frac{15}{4}$ times the equivalent capacitance of the same capacitors connected in series. Calculate the ratio of the capacitors,$\frac{C_{2}}{C_{1}}$.

In the following circuit,the equivalent capacitance between terminal $A$ and terminal $B$ is: (in $\mu F$)

Four identical metal plates are arranged in air at equal distances from each other as shown in the figure. Each plate has an area $A$. Find the equivalent capacitance of the system between points $A$ and $B$.

$A$ series combination of $10$ capacitors,each of value $C_1$,is charged by a source of potential difference $4V$. When another parallel combination of $8$ capacitors,each of value $C_2$,is charged by a source of potential difference $V$,it has the same total energy stored in it as in the first combination. The value of $C_2$ is