A parallel plate air capacitor of capacitance C is connected to a cell of emf V and then disconnected from it. A dielectric slab of dielectric constant K, which can just fill the air gap of the capacitor, is now inserted in it. Which of the following is incorrect?
 

1.	The potential difference between the plates decreases K times
2.	The energy stored in the capacitor decreases K times
3.	The change in energy stored is \({1 \over 2} CV^{2}(\frac{1}{K}-1)\)
4.	The charge on the capacitor is not conserved

\(\mathrm{A}\), \(\mathrm{B}\) and \(\mathrm{C}\) are three points in a uniform electric field. The electric potential is:

Two metallic spheres of radii 1 cm and 3 cm are given charges of -1$\times {10}^{-\mathrm{2 }}\mathrm{C}$ and $5\times {10}^{-\mathrm{2 }}\mathrm{C}$, respectively. If these are connected by a conducting wire, the final charge on the bigger sphere is:

1. $2\times {10}^{-\mathrm{2 }}\mathrm{C}$

2. $3\times {10}^{-\mathrm{2 }}\mathrm{C}$

3. $4\times {10}^{-\mathrm{2 }}\mathrm{C}$

4. $1\times {10}^{-\mathrm{2 }}\mathrm{C}$

A parallel plate condenser has a uniform electric field E(V/m) in the space between the plates. If the distance between the plates is d(m) and area of each plate is $\mathrm{A}\left({\mathrm{m}}^2\right)$, the energy (joule) stored in the condenser is:

1. $\frac{1}{2}{\mathrm{\epsilon }}_0{\mathrm{E}}^2$

2. ${\mathrm{\epsilon }}_0\mathrm{EAd}$

3. $\frac{1}{2}{\mathrm{\epsilon }}_0{\mathrm{E}}^2\mathrm{Ad}$

4. ${\mathrm{E}}^2\mathrm{Ad}/{\mathrm{\epsilon }}_0$

A series combination of n₁ capacitors, each of value C₁, is charged by a source of potential difference 4 V. When another parallel combination of n₂ capacitors, each of value C₂, is charged by a source of potential difference V, it has the same (total) energy stored in it as the first combination has. The value of C₂ in terms of C₁ is:

1.  $\frac{2C_1}{n_1{n}_2}$             

2. 16$\frac{n_2}{n_1}$C₁

3.  2$\frac{n_2}{n_1}$C₁           

4.  $\frac{16C_1}{n_1{n_2}_{}}$

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?

The equivalent capacitance between A and B is:

A parallel plate capacitor has capacitance \(C\). If it is equally filled with parallel layers of materials of dielectric constants \(K_1\) and \(K_2\), its capacity becomes \(C_1\). The ratio of \(C_1\) to \(C\) is:

Consider two points 1 and 2 in a region outside a charged sphere. Two points are not very far away from the sphere. If E and V represent the electric field vector and the electric potential, which of the following is not possible?

An elementary particle of mass m and charge +e is projected with velocity v at a much more massive particle of charge Ze, where Z > 0. What is the closest possible approach of the incident particle?