Between the plates of a parallel plate condenser, a plate of thickness t₁ and dielectric constant k₁ is placed. In the rest of the space, there is another plate of thickness t₂ and dielectric constant k₂. The potential difference across the condenser will be 

(1) $\frac{Q}{A{\epsilon }_0}\left(\frac{{\displaystyle t_1}}{{\displaystyle k_1}}+\frac{{\displaystyle t_2}}{{\displaystyle k_2}}\right)$

(2) $\frac{{\epsilon }_{0}Q}{A}\left(\frac{{\displaystyle t_1}}{{\displaystyle k_1}}+\frac{{\displaystyle t_2}}{{\displaystyle k_2}}\right)$

(3) $\frac{Q}{A{\epsilon }_0}\left(\frac{{\displaystyle k_1}}{{\displaystyle t_1}}+\frac{{\displaystyle k_2}}{{\displaystyle t_2}}\right)$

(4) $\frac{{\epsilon }_{0}Q}{A}(k_1{t}_1+k_2{t}_2)$

The true statement is, on increasing the distance between the plates of a parallel plate condenser -

(1) The electric intensity between the plates will decrease

(2) The electric intensity between the plates will increase

(3) The electric intensity between the plates will remain unchanged

(4) The P.D. between the plates will decrease

The capacity and the energy stored in a parallel plate condenser with air between its plates are respectively C_o and W_o. If the air is replaced by the glass (dielectric constant = 5) between the plates, the capacity of the condenser and the energy stored in it will respectively be -

(1) $5C_o,5W_o$

(2) $5C_o,\frac{W_0}{5}$

(3) $\frac{C_o}{5},5W_o$

(4) $\frac{C_o}{5},\frac{W_o}{5}$

Force of attraction between the plates of a parallel plate capacitor whose dielectric constant is K will be -

(1) $\frac{q^2}{2{\epsilon }_{0}AK}$

(2) $\frac{q^2}{{\epsilon }_{0}AK}$

(3) $\frac{q}{2{\epsilon }_{0}A}$

(4) $\frac{q^2}{2{\epsilon }_0{A}^{2}K}$

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