# A parallel-plate capacitor of area $$A$$, plate separation $$d$$ and capacitance $$C$$ is filled with four dielectric materials having dielectric constants $$k_1, k_2,k_3$$ and $$k_4$$ 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. $${k}={k}_1+{k}_2+{k}_3+3 {k}_4$$ 2. $${k}=\frac{2}{3}\left({k}_1+{k}_2+{k}_3\right)+2 {k}_4$$ 3. $${k}=\frac{2}{3} {k}_4\left(\frac{{k}_1}{{k}_1+{K}_4}+\frac{{k}_2}{{k}_2+{k}_4}+\frac{{k}_3}{{k}_3+{k}_4}\right)$$ 4. $$\frac{1}{{k}}=\frac{1}{{k}_1}+\frac{1}{{k}_2}+\frac{1}{{k}_3}+\frac{3}{2 {k}_4}$$

Subtopic:  Dielectrics in Capacitors |
62%
From NCERT
NEET - 2016
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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 square root of the distance between the plates 4 inversely proportional to the distance between the plates
Subtopic:  Capacitance |
60%
From NCERT
NEET - 2018
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A capacitor of $$2~\mu\text{F}$$ is charged as shown in the figure. When the switch $${S}$$ is turned to position $$2,$$, the percentage of its stored energy dissipated is:

1. $$20\%$$
2. $$75\%$$
3. $$80\%$$
4. $$0\%$$
Subtopic:  Energy stored in Capacitor |
72%
From NCERT
NEET - 2016
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A parallel plate air capacitor has capacitance $$C,$$ 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:

 1 $$\frac{C^2V^2}{2d}$$ 2 $$\frac{CV^2}{2d}$$ 3 $$\frac{CV^2}{d}$$ 4 $$\frac{C^2V^2}{2d^2}$$
Subtopic:  Capacitance |
69%
From NCERT
NEET - 2015
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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?

 1 the potential difference between the plates decreases $$K$$ times. 2 the energy stored in the capacitor decreases $$K$$ times. 3 the change in energy stored is $$\frac{1}{2}CV^{2}\left ( \frac{1}{K} -1\right )$$ 4 the charge on the capacitor is not conserved.

Subtopic:  Energy stored in Capacitor |
71%
From NCERT
NEET - 2015
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Two thin dielectric slabs of dielectric constants $$K_1$$ and $$K_2$$ $$(K_1<K_2)$$ are inserted between plates of a parallel plate capacitor, as shown in the figure. The variation of electric field $$'E'$$ between the plates with distance $$'d'$$ as measured from the plate $$P$$ is correctly shown by:

 1 2 3 4
Subtopic:  Dielectrics in Capacitors |
77%
From NCERT
AIPMT - 2014
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A conducting sphere of the radius $$R$$ is given a charge $$Q.$$ The electric potential and the electric field at the centre of the sphere respectively are:

 1 zero and $$\frac{Q}{4 \pi \varepsilon_0 {R}^2}$$ 2 $$\frac{Q}{4 \pi \varepsilon_0 R}$$ and zero 3 $$\frac{Q}{4 \pi \varepsilon_0 R}$$ and $$\frac{Q}{4 \pi \varepsilon_0{R}^2}$$ 4 both are zero
Subtopic:  Electric Potential |
83%
From NCERT
AIPMT - 2014
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$$A$$, $$B$$ and $$C$$ are three points in a uniform electric field. The electric potential is:

 1 maximum at $$B$$ 2 maximum at $$C$$ 3 same at all the three points $$A, B$$ and $$C$$ 4 maximum at $$A$$
Subtopic:  Relation between Field & Potential |
84%
From NCERT
AIPMT - 2013
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An electric dipole of moment $$p$$ is placed in an electric field of intensity $$E.$$ The dipole acquires a position such that the axis of the dipole makes an angle $$\theta$$ with the direction of the field. Assuming that the potential energy of the dipole to be zero when $$\theta = 90^{\circ}$$, the torque and the potential energy of the dipole will respectively be:
1. $$pE\text{sin}\theta, ~-pE\text{cos}\theta$$
2. $$pE\text{sin}\theta, ~-2pE\text{cos}\theta$$
3. $$pE\text{sin}\theta, ~2pE\text{cos}\theta$$
4. $$pE\text{cos}\theta, ~-pE\text{sin}\theta$$

Subtopic:  Energy of Dipole in an External Field |
81%
From NCERT
AIPMT - 2012
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Four-point charges $$-Q, -q, 2q~\text{and}~2Q$$ are placed, one at each corner of the square. The relation between $$Q$$ and $$q$$ for which the potential at the center of the square is zero is:

 1 $$Q= -q$$ 2 $$Q= -2q$$ 3 $$Q= q$$ 4 $$Q= 2q$$
Subtopic:  Electric Potential |
75%
From NCERT
AIPMT - 2012
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