Four capacitors of capacitance $10\, \mu F$ and a battery of $200\, V$ are arranged as shown. How much charge will flow through $AB$ after the switch $S$ is closed?

$A$ composite parallel plate capacitor is made up of two different dielectric materials with different thicknesses ($t_{1} = 0.5 \text{ mm}$ and $t_{2} = 1 \text{ mm}$) and dielectric constants ($\epsilon_{r1} = 3$ and $\epsilon_{r2} = 4$) as shown in the figure. The two dielectric materials are separated by a conducting foil $F$. The voltage of the conducting foil is $.....V$.

$A$ parallel plate air capacitor is connected to a battery. The plates are pulled apart at uniform speed $v$. If $x$ is the separation between the plates at any instant,then the time rate of change of electrostatic energy of the capacitor is proportional to $x^\alpha$,where $\alpha$ is . . . . . . .

The resultant capacitance between $A$ and $B$ in the following figure is equal to.....$\mu F$

Three uncharged capacitors of capacitance $C_1$,$C_2$ and $C_3$ are connected as shown in the figure to one another and to points $A$,$B$ and $D$ at potentials $V_A$,$V_B$ and $V_D$. Then the potential at point $O$ will be

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