# 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:  $$\left ( \varepsilon_{0} = \text{permittivity of free space} \right )$$ 1. $$\frac{1}{2}\varepsilon_0 E^2 Ad$$ 2. $$\frac{E^2 Ad}{\varepsilon_0}$$ 3. $$\frac{1}{2}\varepsilon_0 E^2$$ 4. $$\varepsilon_0 EAd$$

Subtopic:  Energy stored in Capacitor |
71%
From NCERT
NEET - 2021
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Two charged spherical conductors of radii $$R_1$$ and $$R_2$$ are connected by a wire. The ratio of surface charge densities of spheres $$\left ( \frac{\sigma _{1}}{\sigma _{2}}\right )$$ is:

 1 $$\sqrt{\dfrac{R_1}{R_2}}$$ 2 $$\dfrac{R^2_1}{R^2_2}$$ 3 $$\dfrac{R_1}{R_2}$$ 4 $$\dfrac{R_2}{R_1}$$
Subtopic:  Electric Potential |
64%
From NCERT
NEET - 2021
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Twenty seven drops of same size are charged at $$220~\text{V}$$ each. They combine to form a bigger drop. Calculate the potential of the bigger drop:
1. $$1520~\text{V}$$
2. $$1980~\text{V}$$
3. $$660~\text{V}$$
4. $$1320~\text{V}$$

Subtopic:  Electric Potential |
67%
From NCERT
NEET - 2021
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The equivalent capacitance of the combination shown in the figure is:

 1 $$\dfrac{C}{2}$$ 2 $$\dfrac{3C}{2}$$ 3 $$3C$$ 4 $$2C$$
Subtopic:  Combination of Capacitors |
54%
From NCERT
NEET - 2021
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Three capacitors each of capacity $$4$$ µF are to be connected in such a way that the effective capacitance is $$6$$ µF. This can be done by:

 1 connecting all of them in a series. 2 connecting them in parallel. 3 connecting two in series and one in parallel. 4 connecting two in parallel and one in series.

Subtopic:  Combination of Capacitors |
89%
From NCERT
AIPMT - 2003
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Energy per unit volume for a capacitor having area $$A$$ and separation $$d$$ kept at a potential difference $$V$$ is given by:
1. $$\frac{1}{2}\varepsilon_0\frac{V^2}{d^2}$$
2. $$\frac{1}{2}\frac{V^2}{\varepsilon_0d^2}$$
3. $$\frac{1}{2}CV^2$$
4. $$\frac{Q^2}{2C}$$

Subtopic:  Energy stored in Capacitor |
81%
From NCERT
AIPMT - 2001
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If identical charges $$(-q)$$ are placed at each corner of a cube of side $$b$$ then the electrical potential energy of charge $$(+q)$$ which is placed at centre of the cube will be:

 1 $$\dfrac{- 4 \sqrt{2} q^{2}}{\pi\varepsilon_{0} b}$$ 2 $$\dfrac{- 8 \sqrt{2} q^{2}}{\pi\varepsilon_{0} b}$$ 3 $$\dfrac{- 4 q^{2}}{\sqrt{3} \pi\varepsilon_{0} b}$$ 4 $$\dfrac{8 \sqrt{2} q^{2}}{4 \pi\varepsilon_{0} b}$$
Subtopic:  Electric Potential Energy |
62%
From NCERT
AIPMT - 2002
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A capacitor of capacity $$C_1$$ is charged up to $$V$$ volt and then connected to an uncharged capacitor $$C_2$$. Then final P.D. across each will be:
1. $$\frac{C_{2} V}{C_{1} + C_{2}}$$
2. $$\frac{C_{1} V}{C_{1} + C_{2}}$$
3. $$\left(1 + \frac{C_{2}}{C_{1}}\right)$$
4. $$\left(1 - \frac{C_{2}}{C_{1}} \right) V$$

Subtopic:  Combination of Capacitors |
79%
From NCERT
AIPMT - 2002
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Some charge is being given to a conductor. Then it's potential:

 1 is maximum at the surface. 2 is maximum at the centre. 3 remains the same throughout the conductor. 4 is maximum somewhere between the surface and the centre.

Subtopic:  Electrostatic Shielding |
74%
From NCERT
AIPMT - 2002
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The energy and capacity of a charged parallel plate capacitor are $$E$$ and $$C$$ respectively. If a dielectric slab of ${}_{}$$$E_r=6$$ is inserted in it, then the energy and capacity become:
(Assuming the charge on plates remains constant)
 1 $$6 E,6 C$$ 2 $$E,C$$ 3 $$\frac{E}{6},6C$$ 4 $$E,6C$$
Subtopic:  Energy stored in Capacitor |
75%
From NCERT
AIPMT - 1999
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