The ratio of charge to potential of a body is known as

$A$ 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.

For the shown situation,in the steady state condition,the ratio of the charge stored in the first capacitor to the charge stored in the $n^{th}$ capacitor is:

$A$ cylindrical capacitor has inner and outer conductors whose radii are in the ratio $10:1$. The inner conductor is replaced by a wire whose radius is half of the original inner conductor. To obtain the same capacitance as the original capacitor,by what ratio should the length of the wire be increased?

If the energy stored in a spherical conductor having a charge of $12 \mu C$ is $6 \ J$,then the radius of the spherical conductor is (in $cm$)

The capacitance of a spherical capacitor is $1 \mu F$. If the spacing between the two spheres is $1 \text{ mm}$,the radius of the outer sphere is