Three parallel plate capacitors of capacitances $4 \mu F$,$6 \mu F$ and $12 \mu F$ are first connected in series and then in parallel. The ratio of the effective capacitances in the two cases is

Two parallel plate capacitors are connected in series. Each capacitor has a plate area $A$ and a separation $d$ between the plates. The dielectric constants of the media between their plates are $2$ and $4$. The separation between the plates of a single air capacitor of plate area $A$ which effectively replaces the combination is:

Four identical capacitors are connected in series with a battery of $emf$ $10 \ V$. Point $X$ is grounded. Find the potential at point $A$ in $V$.

What is a series connection of capacitors? Obtain the formula for the effective capacitance in the series combination of two different capacitors.

The equivalent capacitance of the combination shown in the figure is:

$A$ 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 $\mu F$)