$A$ cylindrical capacitor has two cylinders of radii $1.4\,cm$ and $1.5\,cm$ and length $15\,cm$. The outer cylinder is earthed and the inner cylinder is given a charge of $3.5\,\mu C$. Determine the capacitance of the system and the potential of the inner cylinder.

$64$ small drops of water having same charge and same radius are combined to form one big drop. The ratio of capacitance of the big drop to the small drop is . . . . . . .

$A$ spherical capacitor has an inner sphere of radius $12 \;cm$ and an outer sphere of radius $13 \;cm$. The outer sphere is earthed and the inner sphere is given a charge of $2.5 \;\mu C$. The space between the concentric spheres is filled with a liquid of dielectric constant $32$.
$(a)$ Determine the capacitance of the capacitor.
$(b)$ What is the potential of the inner sphere?
$(c)$ Compare the capacitance of this capacitor with that of an isolated sphere of radius $12 \;cm$. Explain why the latter is much smaller.

Eight drops of mercury of equal radii combine to form a big drop. The capacitance of a bigger drop as compared to each smaller drop is (in $times$)

$A$ drop of capacitance $1 \ \mu F$ is divided into $8$ identical drops. The capacitance of each small drop is .... $\mu F$.

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