$A$ spherical drop of capacitance $1\,\mu F$ is broken into eight drops of equal radius. Then,the capacitance of each small drop is ......$\mu F$.

$A$ spherical capacitor consists of two concentric spherical conductors,held in position by suitable insulating supports. Show that the capacitance of a spherical capacitor is given by $C = \frac{4 \pi \varepsilon_{0} r_{1} r_{2}}{r_{1} - r_{2}}$,where $r_{1}$ and $r_{2}$ are the radii of outer and inner spheres,respectively.

Two spherical conductors $A$ and $B$ of radii $a$ and $b$ $(b > a)$ are placed in air concentrically. $B$ is given a charge $+Q$ and $A$ is grounded. The equivalent capacitance of this system is:

The radii of the inner and outer spheres of a spherical capacitor are $9\,cm$ and $10\,cm$ respectively. If the dielectric constant of the medium between the two spheres is $6$ and the charge on the inner sphere is $18 \times 10^{-9}\,C$,calculate the potential of the inner sphere,given that the outer sphere is earthed.

$A$ conductor is connected to a battery of $5\, V$. It acquires a charge of $50\ \mu C$. Calculate the capacitance of the conductor in $\mu F$.

Match the following types of capacitors with their respective capacitance formulas:

Capacitor Type	Capacitance Formula
$A$. Cylindrical capacitor	$i$. $4\pi \epsilon_0 R$
$B$. Spherical capacitor	$ii$. $\frac{K A \epsilon_0}{d}$
$C$. Parallel plate capacitor with dielectric	$iii$. $\frac{2\pi \epsilon_0 \ell}{\ln(r_2/r_1)}$
$D$. Isolated spherical conductor	$iv$. $\frac{4\pi \epsilon_0 r_1 r_2}{r_2 - r_1}$