A capacitor of 2 µF charged as shown in the figure. When the Switch S is turned to position 2, the percentage of its stored energy dissipated is 

1. 20%
2. 75%
3. 80%
4. 0%

Three concentric spherical shells have radii a, b and c (a<b<c) and have surface charge densities $\mathrm{\sigma }, -\mathrm{\sigma }$ and $\mathrm{\sigma }$ respectively. If ${\mathrm{V}}_{\mathrm{A}}, {\mathrm{V}}_{\mathrm{B}}$ and ${\mathrm{V}}_{\mathrm{C}}$ denote the potential of the three shells, if c=a+b, we have

(1) ${\mathrm{V}}_{\mathrm{C}}={\mathrm{V}}_{\mathrm{A}}\ne {\mathrm{V}}_{\mathrm{B}}$                                       

(2) ${\mathrm{V}}_{\mathrm{C}}={\mathrm{V}}_B\ne {\mathrm{V}}_{\mathrm{A}}$

(3) ${\mathrm{V}}_{\mathrm{C}}\ne {\mathrm{V}}_B\ne {\mathrm{V}}_A$                                       

(4) ${\mathrm{V}}_{\mathrm{C}}={\mathrm{V}}_B={\mathrm{V}}_A$

A parallel plate air capacitor has a capacity of \(C\), the distance of separation between plates is \(d\) and potential difference \(V\) is applied between the plates. The force of attraction between the plates of the parallel plate air capacitor is:

The electrostatic force between the metal plates of an isolated parallel plate capacitor C having a charge Q and area A, is

1. Independent of the distance between the plates

2. linearly proportional to the distance between the plates

3. proportional to the sqaure root of the distance between the plates

4. inversely proportional to the distance between the plates

Charges +q and –q are placed at points A and B, respectively; which are at a distance 2L apart, C is the midpoint between A and B. The work done in moving a charge +Q along the semicircle CRD is : 
`

1. $\frac{qQ}{4{\mathrm{\pi \epsilon }}_0\mathrm{L}}$

2. $\frac{qQ}{2{\mathrm{\pi \epsilon }}_0\mathrm{L}}$

3. $\frac{qQ}{6{\mathrm{\pi \epsilon }}_0\mathrm{L}}$

4. $-\frac{qQ}{6{\mathrm{\pi \epsilon }}_0\mathrm{L}}$

A parallel-plate capacitor of area A, plate separation d and capacitance C is filled with four dielectric materials having dielectric constants k₁, k₂, k₃ and k₄ as shown in the figure below. If a single dielectric material is to be used to have the same capacitance C in this capacitor, then its dielectric constant k is given by 

1.  $\mathrm{K}={\mathrm{k}}_1+{\mathrm{k}}_2+{\mathrm{k}}_3+3{\mathrm{k}}_4$

2.  $\mathrm{k}=\frac{2}{3}{\mathrm{k}}_4\left(\frac{{\mathrm{k}}_1}{{\mathrm{k}}_1+{\mathrm{K}}_4}+\frac{{\mathrm{k}}_2}{{\mathrm{k}}_2+{\mathrm{k}}_4}+\frac{{\mathrm{k}}_3}{{\mathrm{k}}_3+{\mathrm{k}}_4}\right)$

3.  $\frac{2}{\mathrm{k}}=\frac{3}{{\mathrm{k}}_1+{\mathrm{k}}_2+{\mathrm{k}}_3}+\frac{1}{{\mathrm{k}}_4}$

4.  $\frac{1}{\mathrm{k}}=\frac{1}{{\mathrm{k}}_1}+\frac{1}{{\mathrm{k}}_2}+\frac{1}{{\mathrm{k}}_3}+\frac{3}{2{\mathrm{k}}_4}$