Find the equivalent capacitance between $A$ and $B$. (in $C$)

The equivalent capacitance between points $a$ and $b$ in the given circuit is ........ $\mu F$.

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

Three capacitors $C_1$,$C_2$,and $C_3$ are connected in parallel,and their equivalent capacitance is $12$ units. Given $C_1 \cdot C_2 \cdot C_3 = 48$ units. When $C_1$ and $C_2$ are connected in parallel,their equivalent capacitance is $6$ units. Find the individual capacitances $C_1, C_2, C_3$.

An electrical technician requires a capacitance of $2 \; \mu F$ in a circuit across a potential difference of $1 \; kV$. $A$ large number of $1 \; \mu F$ capacitors are available,each of which can withstand a potential difference of not more than $400 \; V$. Suggest a possible arrangement that requires the minimum number of capacitors.

In the given capacitor network,$C_1 = 10\,\mu F$,$C_2 = 5\,\mu F$,and $C_3 = 4\,\mu F$. What is the resultant capacitance between $A$ and $B$ in $\mu F$?