The equivalent capacitance of the combination shown in the figure is: 

1. C/2

2. 3C/2 

3. 3C 

4. 2C

A parallel plate capacitor has a uniform electric field \(\vec{E}\) in the space between the plates. If the distance between the plates is \(d\) and the area of each plate is \(A\) the energy stored in the capacitor is: 
\(\left ( \epsilon_{0} = \text{permittivity of free space} \right )\)

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

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

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

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

Two charged spherical conductors of radii R₁ and R₂ are connected by a wire. The ratio of surface charge densities of spheres \(\left ( \frac{\sigma _{1}}{\sigma _{2}}\right )\) is:
1. $\sqrt{\left(\frac{{\mathrm{R}}_1}{{\mathrm{R}}_2}\right)}$

2. $\frac{{\mathrm{R}}_1^2}{{\mathrm{R}}_2^2}$

3. $\frac{{\mathrm{R}}_1}{{\mathrm{R}}_2}$

4. $\frac{{\mathrm{R}}_2}{{\mathrm{R}}_1}$

Twenty seven drops of same size are charged at 220 V each. They combine to form a bigger drop. Calculate the potential of the bigger drop.

1. 1520 V

2. 1980 V

3. 660 V

4. 1320 V

In a certain region of space with volume 0.2 m³, the electric potential is found to be 5 V throughout. The magnitude of electric field in this region is:

1. 0.5 N/C

2. 1 N/C

3. 5 N/C

4. zero

A short electric dipole has a dipole moment of $16\times {10}^{-9} \mathrm{C-}\mathrm{m}$. The electric potential due to the dipole at a point at a distance of 0.6 m from the centre of the dipole situated on a line making an angle of $60°$ with the dipole axis is:

$(\frac{1}{4{\mathrm{\pi \epsilon }}_0}=9\times {10}^9 \mathrm{N-}{\mathrm{m}}^2/{\mathrm{C}}^2)$

1. 200 V

2. 400 V

3. zero

4. 50 V

The capacitance of a parallel plate capacitor with air as medium is $\mathrm{6 }\mathrm{\mu F}$. With the introduction of a dielectric medium, the capacitance becomes 30 $\mathrm{\mu F}$. The permittivity of the medium is: ( ${\mathrm{\epsilon }}_{\mathrm{o}} = 8.85\times {10}^{-12} {\mathrm{C}}^2{\mathrm{N}}^{-1}{\mathrm{m}}^{-\mathrm{2\; )}}$

1. $1.77\times {10}^{-12} {\mathrm{C}}^2{\mathrm{N}}^{-1}{\mathrm{m}}^{-2}$

2. $0.44\times {10}^{-10} {\mathrm{C}}^2{\mathrm{N}}^{-1}{\mathrm{m}}^{-2}$

3. $5.00 {\mathrm{C}}^2{\mathrm{N}}^{-1}{\mathrm{m}}^{-2}$

4. $0.44\times {10}^{-13} {\mathrm{C}}^2{\mathrm{N}}^{-1}{\mathrm{m}}^{-2}$

The variation of electrostatic potential with radial distance r from the centre of a positively charged metallic thin shell of radius R is given by the graph:

1.		2.
3.		4.

A parallel plate capacitor with cross-sectional area A and separation d has air between the plates. An insulating slab of the same area but the thickness of d/2 is inserted between the plates as shown in the figure having a dielectric constant, K=4. The ratio of new capacitance to its original capacitance will be:

1.  2: 1

2.  8: 5

3.  6: 5

4.  4: 1