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

1. C/2

2. 3C/2

3. 3C

4. 2C

Subtopic:  Combination of Capacitors |
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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. ${\mathrm{\epsilon }}_{0}\mathrm{EAd}$

Subtopic:  Energy stored in Capacitor |
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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. $\frac{{\mathrm{R}}_{2}}{{\mathrm{R}}_{1}}$

Subtopic:  Electric Potential |
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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

Subtopic:  Electric Potential |
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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

Subtopic:  Relation between Field & Potential |
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A short electric dipole has a dipole moment of . 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:

1. 200 V

2. 400 V

3. zero

4. 50 V

Subtopic:  Energy of Dipole in an External Field |
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The capacitance of a parallel plate capacitor with air as medium is . With the introduction of a dielectric medium, the capacitance becomes 30 $\mathrm{\mu F}$. The permittivity of the medium is: (

1.

2.

3.

4.

Subtopic:  Dielectrics in Capacitors |
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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
Subtopic:  Electric Potential |
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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

Subtopic:  Dielectrics in Capacitors |
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Two metal spheres, one of radius $$R$$ and the other of radius $$2R$$ respectively have the same surface charge density $$\sigma.$$ They are brought in contact and separated.  What will be the new surface charge densities on them?
1. $$\sigma_{1}=\frac{5}{6}\sigma ,~\sigma_{2}=\frac{5}{6}\sigma$$
2. $$\sigma_{1}=\frac{5}{2}\sigma ,~\sigma_{2}=\frac{5}{6}\sigma$$
3. $$\sigma_{1}=\frac{5}{2}\sigma ,~\sigma_{2}=\frac{5}{3}\sigma$$
4. $$\sigma_{1}=\frac{5}{3}\sigma ,~\sigma_{2}=\frac{5}{6}\sigma$$
Subtopic:  Electric Potential |
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