A parallel plate condenser is filled with two dielectrics as shown. Area of each plate is A metre² and the separation is t metre. The dielectric constants are k₁ and k₂ respectively. Its capacitance in farad will be:

      

1. $\frac{{\epsilon }_{0}A}{t}(k_1+k_2)$

2. $\frac{{\epsilon }_{0}A}{t}.\frac{k_1+k_2}{2}$

3. $\frac{2{\epsilon }_{0}A}{t}(k_1+k_2)$

4. $\frac{{\epsilon }_{0}A}{t}.\frac{k_1-k_2}{2}$

In the connections shown in the adjoining figure, the equivalent capacity between A and B will be:

1. 10.8 μF

2. 69 μF

3. 15 μF

4. 10 μF

The diagrams below show regions of equipotentials.

A positive charge is moved from A to B in each diagram. Then:

A capacitor of 2 $\mu F$ is charged as shown in the figure. When the switch S is turned to position 2, the percentage of its stored energy dissipated is:
       

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?
 

\(\mathrm{A}\), \(\mathrm{B}\) 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?