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:

The respective radii of the two spheres of a spherical condenser are $12 \; cm$ and $9 \; cm$. The dielectric constant of the medium between them is $6$. The capacity of the condenser will be

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:

$A$ 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?

Eight drops of mercury, each of the same radius and having the same charge, coalesce to form a single larger drop. The capacitance of the larger drop compared to each individual smaller drop is how many times greater?

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 $6400 \ km$.