$A$ metallic sheet is inserted between the plates of a parallel plate capacitor. The capacitance of the capacitor

In the given figure,three capacitors $C_1, C_2$ and $C_3$ are connected to a battery. With symbols having their usual meanings,the correct conditions are:

$A$ circuit is shown in the figure for which $C_1=(3 \pm 0.011) \mu F$,$C_2=(5 \pm 0.01) \mu F$,and $C_3=(1 \pm 0.01) \mu F$. If $C$ is the equivalent capacitance across $AB$,then $C$ is given by:

Assuming the drops to be spherical,$27$ identical drops of mercury are charged simultaneously to the same potential of $20 \ V$. If all the charged drops are made to combine to form one big drop,then the potential of the big drop will be: (in $V$)

The space between the plates of a parallel plate capacitor of plate area $4 \ cm^2$ and separation $d = 1.77 \ mm$ is filled with uniform dielectric materials with dielectric constants $k_1 = 5$ and $k_2 = 3$ as shown in the figure. Another capacitor of capacitance $7.5 \ pF$ is connected in parallel with it. The effective capacitance of this combination is . . . . . . $pF$. (Given $\varepsilon_0 = 8.85 \times 10^{-12} \ F/m$)

$A$ network of four capacitors with capacitances $C_1 = C$,$C_2 = 2C$,$C_3 = 3C$,and $C_4 = 4C$ is connected to a battery of potential $V$ as shown in the figure. The ratio of the charges on $C_2$ and $C_4$ is: