In the given circuit,if the equivalent capacitance between $A$ and $B$ is $1\,\mu F$,what is the value of $C$?

$A$ thin metallic partition of negligible thickness is inserted between two shaded metallic plates as shown. The remaining ends are then packed with insulating plates to form a container-like structure. Two taps shown are opened at $t = 0$ and finally closed at $t = 5 \ s$. Find the capacitance of the system between $A$ and $B$ after closing the taps. (Assume the liquid to be non-conducting). Volumetric flow rates and dielectric constants of the liquid are given.

The ratio of potential difference that must be applied across parallel and series combination of two capacitors $C_1$ and $C_2$ with their capacitance in the ratio $1: 2$ so that energy stored in these two cases becomes same is

The switch $S_w$ is shifted from position $1$ to position $2$ as shown in the figure. Heat generated in the circuit is

How many $6 \mu F, 200 \ V$ capacitors are needed to make a capacitor of $18 \mu F, 600 \ V$?

Three charged capacitors,$C_1 = 17 \ \mu F$,$C_2 = 34 \ \mu F$,$C_3 = 41 \ \mu F$ and two open switches,$S_1$ and $S_2$ are assembled into a network with initial voltages and polarities,as shown in the figure. The final status of the network is attained when the two switches,$S_1$ and $S_2$ are closed. In the figure,the final charge on capacitor $C_3$ in $mC$ is closest to: