A 6 μF capacitor is charged from 10 volts to 20 volts. Increase in energy will be 

(1) 18 × 10^–4 J

(2) 9 × 10^–4 J

(3) 4.5 × 10^–4 J

(4) 9 × 10^–6 J

Twenty seven drops of water of the same size are equally and similarly charged. They are then united to form a bigger drop. By what factor will the electrical potential changes 

(1) 9 times

(2) 27 times

(3) 6 times

(4) 3 times

The dielectric constant k of an insulator cannot be 

(1) 3

(2) 6

(3) 8

(4) ∞

A parallel plate capacitor is charged and the charging battery is then disconnected. If the plates of the capacitor are moved further apart by means of insulating handles, then 

(1) The charge on the capacitor increases

(2) The voltage across the plates decreases

(3) The capacitance increases

(4) The electrostatic energy stored in the capacitor increases

A spherical condenser has inner and outer spheres of radii a and b respectively. The space between the two is filled with air. The difference between the capacities of two condensers formed when outer sphere is earthed and when inner sphere is earthed respectively will be 

(1) Zero

(2) $4\pi {\epsilon }_{0}a$

(3) $4\pi {\epsilon }_{0}b$

(4) $4\pi {\epsilon }_{0}a\left(\frac{{\displaystyle b}}{{\displaystyle b-a}}\right)$

The intensity of electric field at a point between the plates of a charged capacitor 

(1) Is directly proportional to the distance between the plates

(2) Is inversely proportional to the distance between the plates

(3) Is inversely proportional to the square of the distance between the plates

(4) Does not depend upon the distance between the plates

In a spherical condenser radius of the outer sphere is R. The difference in the radii of the outer and inner sphere is x. Its capacity is proportional to

(1) $\frac{xR}{(R-x)}$

(2) $\frac{x(R-x)}{r}$

(3) $\frac{R(R-x)}{x}$

(4) $\frac{R}{x}$

A parallel plate condenser with oil between the plates (dielectric constant of oil K = 2) has a capacitance C. If the oil is removed, then capacitance of the capacitor becomes 

(1) $\sqrt{2}C$

(2) 2C

(3) $\frac{C}{\sqrt{2}}$

(4) $\frac{C}{2}$

Two identical charged spherical drops each of capacitance C merge to form a single drop. The resultant capacitance is -

(1) Equal to 2C

(2) Greater than 2C

(3) Less than 2C but greater than C

(4) Less than C