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

A 12pF capacitor is connected to a 50V battery. How much electrostatic energy is stored in the capacitor ?

1. 1.5 × 10^–8 Joule

2. 2.5 × 10^–7 Joule

3. 3.5 × 10^–5 Joule

4. 4.5 × 10^–2 Joule

The capacity of a parallel plate condenser is 15 μF, when the distance between its plates is 6 cm. If the distance between the plates is reduced to 2 cm, then the capacity of this parallel plate condenser will be?
1. 15 μF
3. 30 μF
4. 45 μF
5. 60 μF

The capacity of a parallel plate capacitor with no dielectric substance but with a separation of 0.4 cm is 2 μF. The separation is reduced to half and it is filled with a dielectric substance of value 2.8. The final capacity of the capacitor is 

1. 11.2 μF

2. 15.6 μF

3. 19.2 μF

4. 22.4 μF

Two insulated metallic spheres of 3 μF and 5 μF capacitances are charged to 300 V and 500V respectively. The energy loss, when they are connected by a wire is 

1. 0.012 J

2. 0.0218 J

3. 0.0375 J

4. 3.75 J

A charge of 40 μC is given to a capacitor having capacitance C = 10 μF. The stored energy in ergs is 

1. 80 × 10^–6

2. 800

3. 80

4. 8000

A parallel plate capacitor has plate area A and separation d. It is charged to a potential difference V₀. The charging battery is disconnected and the plates are pulled apart to three times the initial separation. The work required to separate the plates is 

1. $\frac{3{\epsilon }_{0}A{V}_0^2}{d}$

2. $\frac{{\epsilon }_{0}A{V}_0^2}{2d}$

3. $\frac{{\epsilon }_{0}A{V}_0^2}{3d}$

4. $\frac{{\epsilon }_{0}A{V}_0^2}{d}$