When a $0.75 \mu F$ capacitor is charged to a voltage of $20 \ V$,then the magnitude of charge on each plate is (in $\mu C$)

The capacity of an isolated sphere is increased $n$ times when it is enclosed by an earthed concentric sphere. The ratio of their radii 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.

If the circumference of a sphere is $2 \ m$,find the capacitance of the sphere in water in $pF$. (Take dielectric constant of water $K = 80$)

The Earth is assumed to be a charged conducting sphere having volume $V$ and surface area $A$. The capacitance of the Earth in free space is

Consider a spherical drop of mercury of radius $R$ with capacitance $C = 4 \pi \epsilon_0 R$. If two such droplets combine to form a larger one,what would be its capacitance in terms of $C$?