Two charged spherical conductors of radii \(R_1\) and \(R_2\) are connected by a wire. The ratio of surface charge densities of spheres \(\left ( \frac{\sigma _{1}}{\sigma _{2}}\right )\) is:
1. \(\sqrt{\frac{R_1}{R_2}}\)
2. \(\frac{R^2_1}{R^2_2}\)
3. \(\frac{R_1}{R_2}\)
4. \(\frac{R_2}{R_1}\)

Twenty seven drops of same size are charged at \(220~\text{V}\) each. They combine to form a bigger drop. Calculate the potential of the bigger drop.
1. \(1520~\text{V}\)
2. \(1980~\text{V}\)
3. \(660~\text{V}\)
4. \(1320~\text{V}\)

The equivalent capacitance of the combination shown in the figure is: 

A parallel plate capacitor with cross-sectional area \(A\) and separation \(d\) has air between the plates. An insulating slab of the same area but the thickness of \(\frac{d}{2}\) is inserted between the plates as shown in the figure having a dielectric constant, \(K=4\). The ratio of new capacitance to its original capacitance will be:

The variation of electrostatic potential with radial distance \(r\) from the centre of a positively charged metallic thin shell of radius \(R\) is given by the graph:

1.		2.
3.		4.

A hollow metal sphere of radius \(R\) is given \(+Q\) charges to its outer surface. The electric potential at a distance \(\frac{R}{3}\) from the centre of the sphere will be:
1. \(\frac{1}{4\pi \varepsilon_0}\frac{Q}{9R}\)
2. \(\frac{3}{4\pi \varepsilon_0}\frac{Q}{R}\)
3. \(\frac{1}{4\pi \varepsilon_0}\frac{Q}{3R}\)
4. \(\frac{1}{4\pi \varepsilon_0}\frac{Q}{R}\)

Three capacitors, each of capacitance \(0.3~\mu \text{F}\) are connected in parallel. This combination is connected with another capacitor of capacitance \(0.1~\mu \text{F}\) in series. Then the equivalent capacitance of the combination is: