The capacitance $(C)$ of an isolated conducting sphere of radius $(a)$ is given by $4\pi \varepsilon_0 a$. If this sphere is enclosed by an earthed concentric sphere of radius $(b)$,and the ratio of the radii of the spheres is $\frac{b}{a} = n$,then the capacitance of such a system will be increased by a factor of:

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 ($\epsilon_{0} =$ permittivity of free space).

Which one of the following is the correct dimensional formula for the capacitance in $F$? $M, L, T$ and $C$ stand for units of mass,length,time,and charge respectively.

Given below are two statements: One is labelled as Assertion $A$ and the other is labelled as Reason $R$.
Assertion $A:$ Two metallic spheres are charged to the same potential. One of them is hollow and another is solid,and both have the same radii. The solid sphere will have a lower charge than the hollow one.
Reason $R:$ Capacitance of metallic spheres depends on the radii of the spheres.
In the light of the above statements,choose the correct answer from the options given below.

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

The capacitance of a capacitor depends on: