Capacitance of an isolated conducting sphere of radius $R_{1}$ becomes $n$ times when it is enclosed by a concentric conducting sphere of radius $R_{2}$ connected to earth. The ratio of their radii $\left(\frac{R_{2}}{R_{1}}\right)$ 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?

The graph shows the variation of voltage $V$ across the plates of two capacitors $A$ and $B$ versus the charge $Q$ stored in them. Then:

The stratosphere acts as a conducting layer for the Earth. If the stratosphere extends up to $50 \ km$ from the Earth's surface,calculate the capacitance of the spherical capacitor formed between the Earth's surface and the stratosphere in $F$. Take the radius of the Earth as $6400 \ km$.

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 $C$?

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 $times$)