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

Four equal charges Q are placed at the four corners of a square of each side is ‘a’. Work done in removing a charge – Q from its centre to infinity is 

(1) 0

(2) $\frac{\sqrt{2}{Q}^2}{4\pi {\epsilon }_{0}a}$

(3) $\frac{\sqrt{2}{Q}^2}{\pi {\epsilon }_{0}a}$

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

100 capacitors each having a capacity of 10 μF are connected in parallel and are charged by a potential difference of 100 kV. The energy stored in the capacitors and the cost of charging them, if electrical energy costs 108 paise per kWh, will be 

(1) 10⁷ joule and 300 paise

(2) 5 × 10⁶ joule and 300 paise

(3) 5 × 10⁶ joule and 150 paise

(4) 10⁷ joule and 150 paise

Two identical metal plates are given charges $Q_1 and Q_2\left(<Q_1\right)$ respectively. If they are now brought close to form a parallel plate capacitor with capacitance $C$, the potential difference between them is :

1. $\frac{Q_1+Q_2}{2C}$

2. $\frac{Q_1+Q_2}{C}$

3. $\frac{Q_1-Q_2}{C}$

4. $\frac{Q_1-Q_2}{2C}$

A condenser of 2μF capacitance is charged steadily from 0 to 5 Coulomb. Which of the following graphs correctly represents the variation of potential difference across its plates with respect to the charge on the condenser?

(1)

(2)

(3)

(4)

In the given circuit if point \(C\) is connected to the earth and a potential of \(+2000~\text{V}\) is given to the point \(A\), the potential at \(B\) is:
             

A point charge Q is placed at a distance d from the centre of an uncharged conducting sphere of radius R. The potential of the sphere is (d > R) –

1. $\frac{1}{4\mathrm{\pi } {\in }_0}.\frac{\mathrm{Q}}{\left(\mathrm{d}-\mathrm{R}\right)}$                     

2. $\frac{1}{4\mathrm{\pi } {\in }_0}.\frac{\mathrm{Q}}{\mathrm{d}}$

3. $\frac{1}{4\mathrm{\pi } {\in }_0}.\frac{\mathrm{Q}}{\mathrm{R}}$                             

4. zero

Two identical capacitors are joined in parallel, charged to a potential V and then separated and then connected in series i.e. the positive plate of one is connected to negative of the other 

(1) The charges on the free plates connected together are destroyed

(2) The charges on the free plates are enhanced

(3) The energy stored in the system increases

(4) The potential difference in the free plates becomes 2V

Figure shows an electric line of force which curves along a circular arc.

The magnitude of electric field intensity is same at all points on this curve and is equal to E. If the potential at A is V, then the potential at B is –

1. $\mathrm{V}-\mathrm{ER\theta }$                             

2. $\mathrm{V}-2\mathrm{ER} \sin \frac{\mathrm{\theta }}{2}$

3. $\mathrm{V}+\mathrm{ER\theta }$                             

4. $\mathrm{V}+2\mathrm{ER} \sin \frac{\mathrm{\theta }}{2}$

If W be the amount of heat produced in the process of charging an uncharged capacitor then the amount of energy stored in it is

(1) 2W

(2) $\frac{W}{2}$

(3) W

(4) zero