In the given figure,the equivalent capacitance $C_{AB}$ is equal to ...... $C$.

In the given circuit,three capacitors $C_1$,$C_2$,and $C_3$ are connected to a battery of potential $V$. Which of the following conditions is correct?

Two capacitors,each having a capacitance of $2 \mu F$,are connected in series. What will be the effective capacitance of these capacitors (in $\mu F$)?

When two identical capacitors are in series,they have $3\,\mu F$ capacitance,and when in parallel,they have $12\,\mu F$ capacitance. What is the capacitance of each capacitor in $\mu F$?

What is the equivalent capacitance between $A$ and $B$?

$A$ 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 $\mu F$)