Eight drops of mercury, each of same radius and same charge, combine to form a bigger drop. The ratio of the capacitance of the bigger drop to that of each smaller drop is: (in $ : 1$)

The conducting spherical shells shown in the figure are connected by a conductor. The capacitance of the system is

The capacitance of an isolated sphere of radius $r_1$ is increased by $5$ times,when it is enclosed by an earthed concentric sphere of radius $r_2$. The ratio of their radii is

$A$ spherical capacitor consists of two concentric spherical conductors. Find the capacitance of the spherical capacitor if the outer radius is $2 R$ and the inner radius is $R$.

Four capacitors,each of $25\,\mu F$,are connected as shown in the figure. The $dc$ voltmeter reads $200\,V$. The charge on each plate of the capacitor is

Two spherical conductors of capacities $3 \mu F$ and $2 \mu F$ are charged to the same potential,having radii $3 \ cm$ and $2 \ cm$ respectively. If $\sigma_1$ and $\sigma_2$ represent the surface charge density on the respective conductors,then $\frac{\sigma_1}{\sigma_2}$ is: