Three parallel plate air capacitors are connected in parallel. Each capacitor has plate area $\frac{A}{3}$ and the separation between the plates is $d, 2d$ and $3d$ respectively. The equivalent capacity of the combination is ($\varepsilon_0 =$ absolute permittivity of free space).

The combination of capacitors with $C_1 = 3\,\mu F$,$C_2 = 4\,\mu F$,and $C_3 = 2\,\mu F$ is charged by connecting $A$ and $B$ to a battery. Consider the following statements:
$I.$ Energy stored in $C_1$ $=$ Energy stored in $C_2$ $+$ Energy stored in $C_3$
$II.$ Charge on $C_1$ $=$ Charge on $C_2$ $+$ Charge on $C_3$
$III.$ Potential drop across $C_1$ $=$ Potential drop across $C_2$ $=$ Potential drop across $C_3$
Which of these is/are correct?

Three capacitors,each of $3\,\mu F$,are provided. These cannot be combined to provide the resultant capacitance of.........$\mu F$

Find the equivalent capacitance across $A$ and $B$ in $\mu F$.

Three capacitors $C_1$, $C_2$ and $C_3$ are connected to a voltage source $V$ as shown in the figure. The voltage across $C_3$ will be:

The combined capacity of the parallel combination of two capacitors is four times their combined capacity when connected in series. This means that: