How many questions from Capacitors and Dielectrics appear in JEE?

Capacitors and Dielectrics has appeared in 115 of the last 186 JEE Main and JEE Advanced papers — about 62% of them — contributing 134 questions in total across those papers.

Is Capacitors and Dielectrics an important chapter for JEE?

Judged by how often it is actually tested, it appears in roughly 62% of papers. Chapters above about 50% are effectively guaranteed to show up every session, so they repay thorough preparation; lower-frequency chapters are better treated as targeted revision.

Where do these Capacitors and Dielectrics questions come from?

Every question is from an official JEE Main or JEE Advanced paper, transcribed from the original paper and tagged to this chapter. Answers follow the official answer key.

Capacitors and Dielectrics JEE Previous Year Questions with Answers

Q1·PhysicsNumericalJEE Advanced 2026

Passage: A container of height 2 m, length 2 m and breadth 1 m is made of insulating vertical walls and two large area horizontal metal plates (

M_{1}

and

M_{2}

) which extend far beyond the vertical walls in all directions. The container is partitioned into two equal chambers with a thin insulating vertical wall. The partition wall contains a small hole of cross-sectional area

\sqrt{10}

cm

^{2}

near its bottom edge. Initially the hole is closed and the left chamber of the container is completely filled with a liquid of dielectric constant

\epsilon_{r} = 15

and the right chamber is empty (

\epsilon_{r} = 1

). At time

t = 0

, the hole is opened and the liquid flows from the left chamber to the right chamber. In both the chambers, the space above the liquid has

\epsilon_{r} = 1

and is maintained at atmospheric pressure. The schematic of the container at a time

t > 0

is shown in the figure. [Given: acceleration due to gravity is 10 ms

^{-2}

.] Question: The difference in the capacitance (in F) between the metal plates at

t = 0

and that at

t = 500

s is

(8 - n)\epsilon_{0}

, where

\epsilon_{0}

is the permittivity of free space. The value of

n

is:

Q2·PhysicsNumericalJEE Main 2026

A parallel plate capacitor is having separation between plates 0.885 mm. It has a capacitance of

1\,\mu

F when the space between the plates is filled with an insulating material of resistivity

1\times 10^{13}

\Omega

m and resistance

17.7\times 10^{14}

\Omega

. Relative permittivity of the insulating material is

\alpha \times 10^{7}

. The value of

\alpha

is ________. (Take permittivity of free space

= 8.85\times 10^{-12}

F/m)

Q3·PhysicsSingle correctJEE Main 2026

A sphere of capacitance 100 pF is charged to a potential of 100 V. Another identical uncharged metal sphere is brought in contact with the charged sphere, then the change in the total energy stored on these spheres, when they touch is

\alpha \times 10^{-7}

J. The value of

\alpha

is __________. (combined capacitance of spheres is 200 pF)

(A)5
(B) $\frac{5}{2}$
(C) $\frac{7}{2}$
(D) $\frac{9}{2}$

Q4·PhysicsSingle correctJEE Main 2026

A parallel plate air capacitor is connected to a battery. The plates are pulled apart at uniform speed

v

. If

x

is the separation between the plates at any instant, then the time rate of change of electrostatic energy of the capacitor is proportional to

x^{\alpha}

, where

\alpha

is ______.

(A) $-2$
(B) $1$
(C) $-1$
(D) $2$

Q5·PhysicsSingle correctJEE Main 2026

From the circuit given below, the capacitance between terminals

A

and

B

shown in the circuit is ______ μF. (take

C_{1} = C_{2} = C_{3} = 1

μF and

C_{4} = 2

μF.)

(A)2
(B)7/2
(C)7/3
(D)5/2

Q6·PhysicsSingle correctJEE Main 2026

A parallel plate air capacitor has a capacitance

C

. When it is half filled as show in figure with a dielectric constant

K = 5

, the percentage increase in the capacitance is ______.

(A)33.34
(B)66.67
(C)200
(D)400

Q7·PhysicsSingle correctJEE Main 2026

Identify the correct statements : A. Effective capacitance of a series combination of capacitors is always smaller than the smallest capacitance of the capacitor in the combination. B. When a dielectric medium is placed between the charged plates of a capacitor, displacement of charges cannot occur due to insulation property of dielectric. C. Increasing of area of capacitor plate or decreasing of thickness of dielectric is an alternate method to increase the capacitance. D. For a point charge, concentric spherical shells centered at the location of the charge are equipotential surfaces. Choose the correct answer from the options given below.

(A)A, B and C only
(B)C and D only
(C)A, C and D only
(D)B and D only

Q8·PhysicsSingle correctJEE Main 2026

Three parallel plate capacitors each with area A and separation d are filled with two dielectric (

k_1

and

k_2

) in the following fashion. Which of the following is true? (

k_1 > k_2

)

(A) $C_B > C_C > C_A$
(B) $C_C > C_B > C_A$
(C) $C_C > C_A > C_B$
(D) $C_A > C_C > C_B$

Q9·PhysicsSingle correctJEE Main 2026

A parallel plate capacitor with plate separation 5 mm is charged by a battery. On introducing a mica sheet of 2 mm and maintaining the connections of the plates with the terminals of the battery, it is found that it draws 25% more charge from the battery. The dielectric constant of mica is____.

(A)2.5
(B)2.0
(C)1.5
(D)1.0

Q10·PhysicsNumericalJEE Main 2026

The space between the plates of a parallel-plate capacitor of capacitance C (without any dielectric) is now filled with three dielectric slabs of dielectric constants

K_1 = 2

,

K_2 = 3

, and

K_3 = 5

(as shown in the figure). If new capacitance is

\frac{n}{3}C

then the value of n is ______.

Q11·PhysicsNumericalJEE Main 2026

A capacitor

P

with capacitance

10 \times 10^{-6}

F is fully charged with a potential difference of 6.0 V and disconnected from the battery. The charged capacitor

P

is connected across another capacitor

Q

with capacitance

20 \times 10^{-6}

F. The charge on capacitor

Q

when equilibrium is established will be

\alpha \times 10^{-5}

C (assume capacitor

Q

does not have any charge initially), the value of

\alpha

is ________ .

Q12·PhysicsSingle correctJEE Main 2026

A parallel plate capacitor has capacitance C, when there is vacuum within the parallel plates. A sheet having thickness

\left(\frac{1}{3}\right)^{\mathrm{rd}}

of the separation between the plates and relative permittivity K is introduced between the plates. The new capacitance of the system is :

(A) $\frac{3KC}{2K+1}$
(B) $\frac{CK}{2+K}$
(C) $\frac{3CK^{2}}{(2K+1)^{2}}$
(D) $\frac{4KC}{3K-1}$

Q13·PhysicsIntegerJEE Main 2025

Space between the plates of a parallel plate capacitor of plate area

4\ cm^2

and separation of (d) 1.77 mm, is filled with uniform dielectric materials with dielectric constants (3 and 5) as shown in figure. Another capacitor of capacitance 7.5 pF is connected in parallel with it. The effective capacitance of this combination is ___ pF. (Given

\varepsilon_0=8.85\times10^{-12}

F/m)

Q14·PhysicsIntegerJEE Main 2025

A parallel plate capacitor has charge

5\times10^{-8}

C. A dielectric slab is inserted between the plates and almost fills the space between the plates. If the induced charge on one face of the slab is

4\times10^{-8}

C then the dielectric constant of the slab is __________.

Q15·PhysicsIntegerJEE Main 2025

Four capacitor each of capacitance 16

\mu

F are connected as shown in the figure. The capacitance between points A and B is ______ (in

\mu

F).

Q16·PhysicsSingle correctJEE Main 2025

Three parallel plate capacitors

C_1

,

C_2

and

C_3

each of capacitance 5

\mu

F are connected as shown in the figure. The effective capacitance between points A and B, when the space between the parallel plates of

C_1

capacitor is filled with a dielectric medium having dielectric constant of 4, is:

(A) $22.5\ \mu F$
(B) $7.5\ \mu F$
(C) $9\ \mu F$
(D) $30\ \mu F$

Q17·PhysicsSingle correctJEE Main 2025

Using a battery, a 100 pF capacitor is charged to 60 V and then the battery is removed. After that, a second uncharged capacitor is connected to the first capacitor in parallel. If the final voltage across the second capacitor is 20 V, its capacitance is: (in pF)

(A)600
(B)200
(C)400
(D)100

Q18·PhysicsSingle correctJEE Main 2025

A parallel plate capacitor is filled equally (half) with two dielectrics of dielectric constant

\varepsilon_1

and

\varepsilon_2

, as shown in the figures. The distance between the plates is

d

and area of each plate is

A

. If the capacitances in the first configuration and the second configuration are

C_1

and

C_2

respectively, then

\dfrac{C_1}{C_2}

is:

(A) $\dfrac{\varepsilon_1\varepsilon_2^2}{(\varepsilon_1+\varepsilon_2)^2}$
(B) $\dfrac{4\varepsilon_1\varepsilon_2}{(\varepsilon_1+\varepsilon_2)^2}$
(C) $\dfrac{\varepsilon_1\varepsilon_2}{\varepsilon_1+\varepsilon_2}$
(D) $\dfrac{\varepsilon_0(\varepsilon_1+\varepsilon_2)}{2}$

Q19·PhysicsSingle correctJEE Main 2025

A capacitor,

C_1=6\ \mu F

is charged to a potential difference of

V_0=5

V using a 5 V battery. The battery is removed and another capacitor,

C_2=12\ \mu F

is inserted in place of the battery. When the switch ‘S’ is closed, the charge flows between the capacitors for some time until equilibrium condition is reached. What are the charges (

q_1

and

q_2

) on the capacitors

C_1

and

C_2

when equilibrium condition is reached.

(A) $q_1=15\ \mu C, q_2=30\ \mu C$
(B) $q_1=30\ \mu C, q_2=15\ \mu C$
(C) $q_1=10\ \mu C, q_2=20\ \mu C$
(D) $q_1=20\ \mu C, q_2=10\ \mu C$

Q20·PhysicsIntegerJEE Main 2025

A parallel plate capacitor consisting of two circular plates of radius 10 cm is being charged by a constant current of 0.15 A. If the rate of change of potential difference between the plates is

7\times 10^8

V/s then the integer value of the distance between the parallel plates is ______ μm. (Take

\varepsilon_0=9\times 10^{-12}

F/m,

\pi=\dfrac{22}{7}

.)

Q21·PhysicsSingle correctJEE Main 2025

A parallel plate capacitor of capacitance 1

\mu

F is charged to a potential difference of 20 V. The distance between plates is 1

\mu

m. The energy density between plates of capacitor is:

(A) $1.8\times10^3$ J/m $^3$
(B) $2\times10^{-4}$ J/m $^3$
(C) $2\times10^2$ J/m $^3$
(D) $1.8\times10^5$ J/m $^3$

Q22·PhysicsSingle correctJEE Main 2025

Two capacitors

C_1

and

C_2

are connected in parallel to a battery. Charge-time graph is shown below for the two capacitors. The energy stored with them are

U_1

and

U_2

, respectively. Which of the given statements is true?

(A) $C_1>C_2$ , $U_1>U_2$
(B) $C_2>C_1$ , $U_2<U_1$
(C) $C_1>C_2$ , $U_1<U_2$
(D) $C_2>C_1$ , $U_2>U_1$

Q23·PhysicsSingle correctJEE Main 2025

A parallel plate capacitor was made with two rectangular plates, each with a length of

l=3

cm and breadth of

b=1

cm. The distance between the plates is 3 μm. Out of the following, which are the ways to increase the capacitance by a factor of 10 ? A.

l=30

cm,

b=1

cm,

d=1

μm. B.

l=3

cm,

b=1

cm,

d=30

μm. C.

l=6

cm,

b=5

cm,

d=3

μm. D.

l=1

cm,

b=1

cm,

d=10

μm. E.

l=5

cm,

b=2

cm,

d=1

μm. Choose the correct answer from the options given below :

(A)C and E only
(B)B and D only
(C)A only
(D)C only

Q24·PhysicsSingle correctJEE Main 2025

Consider a parallel plate capacitor of area A (of each plate) and separation ‘d’ between the plates. If E is the electric field and

\varepsilon_0

is the permittivity of free space between the plates, then potential energy stored in the capacitor is :-

(A) $\dfrac{1}{2}\varepsilon_0 E^2 Ad$
(B) $\dfrac{3}{4}\varepsilon_0 E^2 Ad$
(C) $\dfrac{1}{4}\varepsilon_0 E^2 Ad$
(D) $\varepsilon_0 E^2 Ad$

Q25·PhysicsSingle correctJEE Main 2025

A parallel-plate capacitor of capacitance 40 μF is connected to a 100 V power supply. Now the intermediate space between the plates is filled with a dielectric material of dielectric constant K = 2. Due to the introduction of the dielectric, the extra charge and the change in the electrostatic energy of the capacitor, respectively, are:

(A)3 mC and 0.2 J
(B)8 mC and 2.0 J
(C)4 mC and 0.2 J
(D)2 mC and 0.2 J

Q26·PhysicsSingle correctJEE Advanced 2024

Four identical thin, square metal sheets,

S_{1}

,

S_{2}

,

S_{3}

and

S_{4}

, each of side

a

are kept parallel to each other with equal distance

d

(

\ll a

) between them, as shown in the figure. Let

C_{0} = \varepsilon_{0}a^{2}/d

, where

\varepsilon_{0}

is the permittivity of free space. Match the quantities mentioned in List-I with their values in List-II and choose the correct option.

List-I	List-II
P.The capacitance between $S_{1}$ and $S_{4}$ , with $S_{2}$ and $S_{3}$ not connected, is	1. $3C_{0}$
Q.The capacitance between $S_{1}$ and $S_{4}$ , with $S_{2}$ shorted to $S_{3}$ , is	2. $C_{0}/2$
R.The capacitance between $S_{1}$ and $S_{3}$ , with $S_{2}$ shorted to $S_{4}$ , is	3. $C_{0}/3$
S.The capacitance between $S_{1}$ and $S_{2}$ , with $S_{3}$ shorted to $S_{1}$ , and $S_{2}$ shorted to $S_{4}$ , is	4. $2C_{0}/3$
	5. $2C_{0}$

(A)P $\to$ 3; Q $\to$ 2; R $\to$ 4; S $\to$ 5
(B)P $\to$ 2; Q $\to$ 3; R $\to$ 2; S $\to$ 1
(C)P $\to$ 3; Q $\to$ 2; R $\to$ 4; S $\to$ 1
(D)P $\to$ 3; Q $\to$ 2; R $\to$ 2; S $\to$ 5

Q27·PhysicsSingle correctJEE Main 2024

A capacitor is made of a flat plate of area A and a second plate having a stair-like structure as shown in figure. If the area of each stair is

\dfrac{A}{3}

and the height is d, the capacitance of the arrangement is:

(A) $\dfrac{11\varepsilon_0 A}{18 d}$
(B) $\dfrac{13\varepsilon_0 A}{17 d}$
(C) $\dfrac{11\varepsilon_0 A}{20 d}$
(D) $\dfrac{18\varepsilon_0 A}{11 d}$

Q28·PhysicsSingle correctJEE Main 2024

A capacitor has air as dielectric medium and two conducting plates of area 12 cm

^2

and they are 0.6 cm apart. When a slab of dielectric having area 12 cm

^2

and 0.6 cm thickness is inserted between the plates, one of the conducting plates has to be moved by 0.2 cm to keep the capacitance same as in previous case. The dielectric constant of the slab is: (Given

\varepsilon=8.834\times10^{-12}

F/m)

(A)1.50
(B)1.33
(C)0.66
(D)1

Q29·PhysicsNumericalJEE Main 2024

A capacitor of

10\,\mu

F capacitance whose plates are separated by 10 mm through air and each plate has area 4 cm

^{2}

is now filled equally with two dielectric media of

K_{1} = 2

,

K_{2} = 3

respectively as shown in figure. If new force between the plates is 8 N. The supply voltage is ______ V.

Q30·PhysicsNumericalJEE Main 2024

Three capacitors of capacitances

25\ \mu\text{F}

,

30\ \mu\text{F}

and

45\ \mu\text{F}

are connected in parallel to a supply of 100 V. The energy stored in this combination is E. When these capacitors are connected in series to the same supply, the stored energy is

\dfrac{9}{x}E

. The value of

x

is ___.

Q31·PhysicsNumericalJEE Main 2024

The electric field between the two parallel plates of a capacitor of

1.5\ \mu\text{F}

capacitance drops to one third of its initial value in

6.6\ \mu\text{s}

when the plates are connected by a thin wire. The resistance of this wire is ___

\Omega

. (Given

\log 3 = 1.1

.)

Q32·PhysicsNumericalJEE Main 2024

A parallel plate capacitor of capacitance 12.5 pF is charged by a battery connected between its plates to potential difference of 12.0 V. The battery is now disconnected and a dielectric slab

(\varepsilon_r=6)

is inserted between the plates. The change in its potential energy after inserting the dielectric slab is ______

\times10^{-12}

J.

Q33·PhysicsNumericalJEE Main 2024

Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle

\theta

with each other. When suspended in water the angle remains the same. If density of the material of the sphere is

1.5\,g/cc

, the dielectric constant of water will be ___. (Take density of water

=1\,g/cc

)

Q34·PhysicsSingle correctJEE Main 2024

Two identical capacitors have same capacitance

C

. One of them is charged to the potential

V

and other to the potential

2V

. The negative ends of both are connected together. When the positive ends are also joined together, the decrease in energy of the combined system is:

(A) $\dfrac14 CV^2$
(B) $2CV^2$
(C) $\dfrac12 CV^2$
(D) $\dfrac34 CV^2$

Q35·PhysicsSingle correctJEE Main 2024

Force between two point charges

q_1

and

q_2

placed in vacuum at '

r

' cm apart is F. Force between them when placed in a medium having dielectric

K=5

at '

r/5

' cm apart will be:

(A) $\dfrac{F}{25}$
(B)5F
(C) $\dfrac{F}{5}$
(D)25F

Q36·PhysicsNumericalJEE Main 2024

A parallel plate capacitor with plate separation 5 mm is charged up by a battery. It is found that on introducing a dielectric sheet of thickness 2 mm, while keeping the battery connections intact, the capacitor draws 25% more charge from the battery than before. The dielectric constant of the sheet is ______.

Q37·PhysicsNumericalJEE Main 2024

Two identical charged spheres are suspended by string of equal lengths. The string make an angle of

37^\circ

with each other. When suspended in a liquid of density 0.7 g/cm

^3

, the angle remains same. If density of material of the sphere is 1.4 g/cm

^3

, the dielectric constant of the liquid is ______.

\left(\tan 37^\circ=\dfrac{3}{4}\right)

Q38·PhysicsNumericalJEE Main 2024

A capacitor of capacitance

C

and potential

V

has energy

E

. It is connected to another capacitor of capacitance

2C

and potential

2V

. Then the loss of energy is

\dfrac{x}{3}E

, where

x

is ___

Q39·PhysicsNumericalJEE Main 2024

In the given figure, the charge stored in 6

\mu

F capacitor, when points A and B are joined by a connecting wire is ___

\mu

C.

Q40·PhysicsSingle correctJEE Advanced 2023

A container has a base of 50 cm

\times

5 cm and height 50 cm, as shown in the figure. It has two parallel electrically conducting walls each of area 50 cm

\times

50 cm. The remaining walls of the container are thin and non-conducting. The container is being filled with a liquid of dielectric constant 3 at a uniform rate of 250

cm^3\ s^{-1}

. What is the value of the capacitance of the container after 10 seconds? [Given: Permittivity of free space

\varepsilon_0 = 9 \times 10^{-12}\ C^2N^{-1}m^{-2}

, the effects of the non-conducting walls on the capacitance are negligible

(A)27 pF
(B)63 pF
(C)81 pF
(D)135 pF

Q41·PhysicsNumericalJEE Main 2023

In the given figure the total charge stored in the combination of capacitors is

100\ \mu

C. The value of 'x' is __________.

Q42·PhysicsNumericalJEE Main 2023

In the circuit shown, the energy stored in the capacitor is

n

\mu

J. The value of n is ____.

Q43·PhysicsSingle correctJEE Main 2023

In the network shown below, the charge accumulated in the capacitor in steady state will be:

(A)7.2 $\mu$ C
(B)4.8 $\mu$ C
(C)10.3 $\mu$ C
(D)12 $\mu$ C

Q44·PhysicsNumericalJEE Main 2023

In the given circuit,

C_1=2\ \mu

F,

C_2=0.2\ \mu

F,

C_3=2\ \mu

F,

C_4=4\ \mu

F,

C_5=2\ \mu

F,

C_6=2\ \mu

F. The charge stored on capacitor

C_4

is ____

\mu

C.

Q45·PhysicsSingle correctJEE Main 2023

A parallel plate capacitor of capacitance 2 F is charged to a potential V. The energy stored in the capacitor is

E_1

. The capacitor is now connected to another uncharged identical capacitor in parallel combination. The energy stored in the combination is

E_2

. The ratio

E_2/E_1

is :

(A) $2 : 1$
(B) $1 : 2$
(C) $1 : 4$
(D) $2 : 3$

Q46·PhysicsSingle correctJEE Main 2023

A capacitor of capacitance C is charged to a potential V. The flux of the electric field through a closed surface enclosing the positive plate of the capacitor is:

(A) $\dfrac{CV}{2\varepsilon_0}$
(B) $\dfrac{2CV}{\varepsilon_0}$
(C) $\dfrac{CV}{\varepsilon_0}$
(D)Zero

Q47·PhysicsSingle correctJEE Main 2023

The equivalent capacitance of the combination shown is:

(A) $\dfrac{C}{2}$
(B)4C
(C)3C
(D) $\dfrac53 C$

Q48·PhysicsSingle correctJEE Main 2023

The distance between two plates of a capacitor is

d

and its capacitance is

C_1

when air is the medium between the plates. If a metal sheet of thickness

\tfrac{2d}{3}

and of the same area as the plates is introduced between the plates, the capacitance of the capacitor becomes

C_2

. The ratio

\tfrac{C_2}{C_1}

is:

(A) $2:1$
(B) $4:1$
(C) $3:1$
(D) $1:1$

Q49·PhysicsNumericalJEE Main 2023

A 600 pF capacitor is charged by a 200 V supply. It is then disconnected from the supply and is connected to another uncharged 600 pF capacitor. The electrostatic energy lost in the process is ____

\mu

J.

Q50·PhysicsNumericalJEE Main 2023

A parallel plate capacitor with plate area

A

and plate separation

d

is filled with a dielectric material of dielectric constant

K=4

. The thickness of the dielectric material is

x

, where

x<d

. Let

C_1

and

C_2

be the capacitance of the system for

x=\dfrac{1}{3}d

and

x=\dfrac{2}{3}d

, respectively. If

C_1=2\,\mu F

then the value of

C_2

is _____

\mu F

.

Q51·PhysicsNumericalJEE Main 2023

As shown in the figure, two parallel plate capacitors having equal plate area of 200 cm

^2

are joined together. The equivalent capacitance of the combination is

x\,\varepsilon_0

F. The value of

x

is

Q52·PhysicsSingle correctJEE Main 2023

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R. Assertion A: Two metallic spheres are charged to the same potential. One of them is hollow and another is solid, and both have the same radii. Solid sphere will have lower charge than the hollow one. Reason R: Capacitance of metallic spheres depend on the radii of spheres. In the light of the above statements, choose the correct answer from the options given below.

(A)Both A and R are true and R is the correct explanation of A
(B)Both A and R are true but R is not the correct explanation of A
(C)A is true but R is false
(D)A is false but R is true

Q53·PhysicsNumericalJEE Main 2023

Two parallel plate capacitors

C_1

and

C_2

each having capacitance of

10\,\mu F

are individually charged by a

100

V D.C. source. Capacitor

C_1

is kept connected to the source and a dielectric slab is inserted between it plates. Capacitor

C_2

is disconnected from the source and then a dielectric slab is inserted in it. Afterwards the capacitor

C_1

is also disconnected from the source and the two capacitors are finally connected in parallel combination. The common potential of the combination will be _________ V. (Assuming Dielectric constant

=10

)

Q54·PhysicsNumericalJEE Main 2023

A capacitor of capacitance

900\,\mu F

is charged by a

100

V battery. The capacitor is disconnected from the battery and connected to another uncharged identical capacitor such that one plate of uncharged capacitor connected to positive plate and another plate of uncharged capacitor connected to negative plate of the charged capacitor. The loss of energy in this process is measured as

x\times10^{-2}

J. The value of

x

is

Q55·PhysicsNumericalJEE Main 2023

A capacitor has capacitance

5\,\mu F

when its parallel plates are separated by air medium of thickness

d

. A slab of material of dielectric constant 1.5 having area equal to that of plates but thickness

\frac{d}{2}

is inserted between the plates. Capacitance of the capacitor in the presence of slab will be ______

\mu F

.

Q56·PhysicsSingle correctJEE Main 2023

A parallel plate capacitor has plate area 40 cm

^2

and plates separation 2 mm. The space between the plates is filled with a dielectric medium of thickness 1 mm and dielectric constant 5. The capacitance of the system is:

(A) $24\varepsilon_0$ F
(B) $\dfrac{10}{3}\varepsilon_0$ F
(C) $\dfrac{3}{10}\varepsilon_0$ F
(D) $10\varepsilon_0$ F

Q57·PhysicsNumericalJEE Main 2023

A parallel plate capacitor with air between the plate has a capacitance of

15

pF. The separation between the plate becomes twice and the space between them is filled with a medium of dielectric constant

3.5

. Then the capacitance becomes

\dfrac{x}{4}

pF. The value of

x

is _________

Q58·PhysicsNumericalJEE Advanced 2022

In the following circuit

C_1 = 12\ \mu F

,

C_2 = C_3 = 4\ \mu F

and

C_4 = C_5 = 2\ \mu F

. The charge stored in

C_3

is ________

\mu C

.

Q59·PhysicsMultiple correctJEE Advanced 2022

A medium having dielectric constant

K > 1

fills the space between the plates of a parallel plate capacitor. The plates have large area, and the distance between them is

d

. The capacitor is connected to a battery of voltage

V

, as shown in Figure (a). Now, both the plates are moved by a distance d/2 of from their original positions, as shown in Figure (b). In the process of going from the configuration depicted in Figure (a) to that in Figure (b), which of the following statement(s) is(are) correct?

(A)The electric field inside the dielectric material is reduced by a factor of 2K.
(B)The capacitance is decreased by a factor of $\frac{1}{K+1}$ .
(C)The voltage between the capacitor plates is increased by a factor of (K+1).
(D)The work done in the process DOES NOT depend on the presence of the dielectric material.

Q60·PhysicsSingle correctJEE Main 2022

Two identical thin metal plates has charge

q_1

and

q_2

respectively such that

q_1 > q_2

. The plates were brought close to each other to form a parallel plate capacitor of capacitance C. The potential difference between them is :

(A) $\frac{(q_1 + q_2)}{C}$
(B) $\frac{(q_1 - q_2)}{C}$
(C) $\frac{(q_1 - q_2)}{2C}$
(D) $\frac{2(q_1 - q_2)}{C}$

Q61·PhysicsSingle correctJEE Main 2022

Two capacitors, each having capacitance 40 μF are connected in series. The space between one of the capacitors is filled with dielectric material of dielectric constant K such that the equivalence capacitance of the system became 24 μF. The value of K will be :

(A)1.5
(B)2.5
(C)1.2
(D)3

Q62·PhysicsSingle correctJEE Main 2022

A slab of dielectric constant K has the same cross-sectional area as the plates of a parallel plate capacitor and thickness

\dfrac{3}{4}d

, where d is the separation of the plates. The capacitance of the capacitor when the slab is inserted between the plates will be : (Given

C_o

= capacitance of capacitor with air as medium between plates.)

(A) $\dfrac{4KC_0}{3+K}$
(B) $\dfrac{3KC_0}{3+K}$
(C) $\dfrac{3+K}{4KC_0}$
(D) $\dfrac{K}{4+K}$

Q63·PhysicsNumericalJEE Main 2022

A parallel plate capacitor with width 4 cm, length 8 cm and separation between the plates of 4mm is connected to a battery of 20 V. A dielectric slab of dielectric constant 5 having length 1cm, width 4 cm and thickness 4 mm is inserted between the plates of parallel plate capacitor. The electrostatic energy of this system will be………∈

_0

J. (Where ∈

_0

is the permittivity of free space)

Q64·PhysicsSingle correctJEE Main 2022

The total charge on the system of capacitance C

_{1}

= 1μF, C

_{2}

= 2μF, C

_{3}

= 4μF and C

_{4}

= 3μF connected in parallel is (Assume a battery of 20V is connected to the combination)

(A)200μC
(B)200C
(C)10μC
(D)10C

Q65·PhysicsNumericalJEE Main 2022

A composite parallel plate capacitor is made up of two different dielectric materials with different thickness (t

_{1}

and t

_{2}

) as shown in figure. The two different dielectric material are separated by a conducting foil F. The voltage of the conducting foil is _____V.

Q66·PhysicsSingle correctJEE Main 2022

A source of potential difference V is connected to the combination of two identical capacitors as shown in the figure. When key 'K' is closed, the total energy stored across the combination is

E_1

. Now key 'K' is opened and dielectric of dielectric constant 5 is introduced between the plates of the capacitors. The total energy stored across the combination is now

E_2

. The ratio

E_1/E_2

will be :

(A) $\frac{1}{10}$
(B) $\frac{2}{5}$
(C) $\frac{5}{13}$
(D) $\frac{5}{26}$

Q67·PhysicsSingle correctJEE Main 2022

A condenser of 2

\mu

F capacitance is charged steadily from 0 to 5C. Which of the following graph represents correctly the variation of potential difference (V) across it's plates with respect to the charge (Q) on the condenser ?

(A)(A)
(B)(B)
(C)(C)
(D)(D)

Q68·PhysicsSingle correctJEE Main 2022

A parallel plate capacitor filled with a medium of dielectric constant 10, is connected across a battery and is charged. The dielectric slab is replaced by another slab of dielectric constant 15. Then the energy of capacitor will :

(A)increase by 50%
(B)decrease by 15%
(C)increase by 25%
(D)increase by 33%

Q69·PhysicsSingle correctJEE Main 2022

A capacitor is discharging through a resistor R. Consider in time

t_1

, the energy stored in the capacitor reduces to half of its initial value and in time

t_2

, the charge stored reduces to one eighth of its initial value. The ratio

t_1/t_2

will be :

(A)1/2
(B)1/3
(C)1/4
(D)1/6

Q70·PhysicsNumericalJEE Main 2022

A capacitor C

_1

of capacitance 5μF is charged to a potential of 30 V using a battery. The battery is then removed and the charged capacitor is connected to an uncharged capacitor C

_2

of capacitance 10μF as shown in figure. When the switch is closed charge flows between the capacitors. At equilibrium, the charge on the capacitor C

_2

is ________ μC .

Q71·PhysicsSingle correctJEE Main 2022

A force of 10N acts on a charged particle placed between two plates of a charged capacitor. If one plate of capacitor is removed, then the force acting on that particle will be :

(A)5 N
(B)10 N
(C)20 N
(D)Zero

Q72·PhysicsNumericalJEE Main 2022

A capacitor of capacitance 50 pF is charged by 100 V source. It is then connected to another uncharged identical capacitor. Electrostatic energy loss in the process is ____ nJ.

Q73·PhysicsNumericalJEE Main 2022

A paralle plate capacitor is made up of stair like structure with a palte area A of each stair and that is connected with a wire of length b, as shown in the figure. The capacitance of the arrangement is

\dfrac{x}{15}\dfrac{\varepsilon_0 A}{b}

. The value of x is ________ .

Q74·PhysicsSingle correctJEE Main 2022

Assertion (A) : Non-polar amterials do not have my permanent dipole moment. Reason (R) : When an non-polar material is placed in a electric field. the centre of the positive charge distribution of it's individual atom or molecule coinsides with the centre of the negative charge distribution. In the light of above statements, choose the most appropriate answer from the options given below.

(A)Both (A) and (R) are correct and (R) is the correct explanation of (A).
(B)Both (A) and (R) are correct and (R) is not the correct explanation of (A).
(C)(A) is correct but (R) is not correct.
(D)(A) is not correct but (R) is correct.

Q75·PhysicsSingle correctJEE Main 2022

A parallel plate capacitor with plate area A and plate separation d=2 m has a capacitance of 4 μF. The new capacitance of the system if half of the space between them is filled with a dielectric material of dielectric constant K=3 (as shown in figure) will be :

(A)2μF
(B)32μF
(C)6μF
(D)8μF

Q76·PhysicsSingle correctJEE Main 2022

The charge on capacitor of capacitance 15μF in the figure given below is :

(A)60μc
(B)130μc
(C)260 μc
(D)585 μc

Q77·PhysicsSingle correctJEE Main 2022

Two capacitors having capacitance

C_{1}

and

C_{2}

respectively are connected as shown in figure. Initially, capacitor

C_{1}

is charged to a potential difference V volt by a battery. The battery is then removed and the charged capacitor

C_{1}

is now connected to uncharged capacitor

C_{2}

by closing the switch S. The amount of charge on the capacitor

C_{2}

, after equilibrium is :

(A) $\frac{C_{1}C_{2}}{\left(C_{1}+C_{2}\right)}V$
(B) $\frac{\left(C_{1}+C_{2}\right)}{C_{1}C_{2}}V$
(C) $(C_{1}+C_{2})V$
(D) $(C_{1}-C_{2})V$

Q78·PhysicsSingle correctJEE Main 2022

Two metallic plates form a parallel plate capacitor. The distance between the plates is 'd'. A metal sheet of thickness

\frac{d}{2}

and of area equal to area of each plate is introduced between the plates. What will be the ratio of the new capacitance to the original capacitance of the capacitor ?

(A)2:1
(B)1:2
(C)1:4
(D)4:1

Q79·PhysicsNumericalJEE Main 2022

The equivalent capacitance between points A and B in below shown figure will be _____ μF.

Q80·PhysicsSingle correctJEE Main 2022

A parallel plate capacitor is formed by two plates each of area

30\pi

cm

^{2}

separated by 1 mm. A material of dielectric strength

3.6\times10^{7}

Vm

^{-1}

is filled between the plates. If the maximum charge that can be stored on the capacitor without causing any dielectric breakdown is

7\times10^{-6}

C, the value of dielectric constant of the material is :

\left\{\text{Use}:\dfrac{1}{4\pi\varepsilon_{0}}=9\times10^{9}\ \text{Nm}^{2}\text{C}^{-2}\right\}

(A)1.66
(B)1.75
(C)2.25
(D)2.33

Q81·PhysicsSingle correctJEE Main 2022

If the charge on a capacitor is increased by 2 C, the energy stored in it increases by 44%. The original charge on the capacitor is (in C) :

(A)10
(B)20
(C)30
(D)40

Q82·PhysicsSingle correctJEE Main 2021

A capacitor is connected to a 20 V battery through a resistance of 10Ω. It is found that the potential difference across the capacitor rises to 2 V in 1 μs. The capacitance of the capacitor is ....................μF. Given :

\ln\left(\frac{10}{9}\right) = 0.105

(A)9.52
(B)0.95
(C)0.105
(D)1.85

Q83·PhysicsNumericalJEE Main 2021

A capacitor of 50

\mu

F is connected in a circuit as shown in figure. The charge on the upper plate of the capacitor is ______

\mu

C.

Q84·PhysicsNumericalJEE Main 2021

A parallel plate capacitor of capacitance 200

\mu

F is connected to a battery of 200 V. A dielectric slab of dielectric constant 2 is now inserted into the space between plates of capacitor while the battery remain connected. The change in the electrostatic energy in the capacitor will be______J.

Q85·PhysicsSingle correctJEE Main 2021

Three capacitors

C_{1}

= 2μF,

C_{2}

= 6 μF and

C_{3}

= 12 μF are connected as shown in figure. Find the ratio of the charges on capacitors

C_{1}

,

C_{2}

and

C_{3}

respectively :

(A)2 : 1 : 1
(B)2 : 3 : 3
(C)1 : 2 : 2
(D)3 : 4 : 4

Q86·PhysicsSingle correctJEE Main 2021

The material filled between the plates of a parallel plate capacitor has resistivity 200

\Omega

m. The value of capacitance of the capacitor is 2 pF. If a potential difference of 40 V is applied across the plates of the capacitor, then the value of leakage current flowing out of the capacitor is : (given the value of relative permitivity of material is 50)

(A)9.0 $\mu$ A
(B)9.0 mA
(C)0.9 mA
(D)0.9 $\mu$ A

Q87·PhysicsSingle correctJEE Main 2021

A parallel - plate capacitor with plate area A has separation d between the plates. Two dielectric slabs of dielectric constant

K_{1}

and

K_{2}

of same area A/2 and thickness d/2 are inserted in the space between the plates. The capacitance of the capacitor will be given by :

(A) $\frac{\varepsilon_{0}A}{d}\left(\frac{1}{2} + \frac{K_{1}K_{2}}{K_{1} + K_{2}}\right)$
(B) $\frac{\varepsilon_{0}A}{d}\left(\frac{1}{2} + \frac{K_{1}K_{2}}{2\left(K_{1} + K_{2}\right)}\right)$
(C) $\frac{\varepsilon_{0}A}{d}\left(\frac{1}{2} + \frac{K_{1} + K_{2}}{K_{1}K_{2}}\right)$
(D) $\frac{\varepsilon_{0}A}{d}\left(\frac{1}{2} + \frac{2\left(K_{1} + K_{2}\right)}{K_{1}K_{2}}\right)$

Q88·PhysicsSingle correctJEE Main 2021

Two capacitors of capacities 2C and C are joined in parallel and charge up to potential V. The battery is removed and the capacitor of capacity C is filled completely with a medium of dielectric constant K. The potential difference across the capacitors will now be :

(A) $\frac{3V}{K}$
(B) $\frac{V}{K}$
(C) $\frac{V}{K + 2}$
(D) $\frac{3V}{K + 2}$

Q89·PhysicsSingle correctJEE Main 2021

A capacitor of capacitance C = 1μF is suddenly connected to a battery of 100 volt through a resistance R = 100Ω. The time taken for the capacitor to be charged to get 50 V is : [Take ln 2 = 0.69 ]

(A) $3.33 \times 10^{-4}$ s
(B) $1.44 \times 10^{-4}$ s
(C) $0.30 \times 10^{-4}$ s
(D) $0.69 \times 10^{-4}$ s

Q90·PhysicsSingle correctJEE Main 2021

A simple pendulum of mass 'm', length '

\ell

' and charge '+q' suspended in the electric field produced by two conducting parallel plates as shown. The value of deflection of pendulum in equilibrium position will be :

(A) $\tan^{-1}\left[\frac{q}{mg} \times \frac{C_2(V_2 - V_1)}{(C_1 + C_2)(d - t)}\right]$
(B) $\tan^{-1}\left[\frac{q}{mg} \times \frac{C_1(V_1 + V_2)}{(C_1 + C_2)(d - 1)}\right]$
(C) $\tan^{-1}\left[\frac{q}{mg} \times \frac{C_1(V_2 - V_1)}{(C_1 + C_2)(d - t)}\right]$
(D) $\tan^{-1}\left[\frac{q}{mg} \times \frac{C_2(V_1 + V_2)}{(C_1 + C_2)(d - t)}\right]$

Q91·PhysicsSingle correctJEE Main 2021

In the reported figure, a capacitor is formed by placing a compound dielectric between the plates of parallel plate capacitor. The expression for the capacity of the said capacitor will be : (Given area of plate = A)

(A) $\frac{15}{34} \ \frac{K \varepsilon_0 A}{d}$
(B) $\frac{15}{6} \ \frac{K \varepsilon_0 A}{d}$
(C) $\frac{25}{6} \ \frac{K \varepsilon_0 A}{d}$
(D) $\frac{9}{6} \ \frac{K \varepsilon_0 A}{d}$

Q92·PhysicsSingle correctJEE Main 2021

A parallel plate capacitor with plate area 'A' and distance of separation 'd' is filled with a dielectric. What is the capacity of the capacitor when permittivity of the dielectric varies as:

\varepsilon\left(x\right) = \varepsilon_0 + kx

, for

\left(0 < x \leq \frac{d}{2}\right)

\varepsilon\left(x\right) = \varepsilon_0 + k\left(d - x\right)

, for

\left(\frac{d}{2} \leq x \leq d\right)

(A)0
(B) $\frac{kA}{2}\ \ell n\left(\frac{2\varepsilon_0}{2\varepsilon_0 - kd}\right)$
(C) $\frac{kA}{2\ \ell n\left(\frac{2\varepsilon_0 + kd}{2\varepsilon_0}\right)}$
(D) $\left(\varepsilon_0 + \frac{kd}{2}\right)^{2/kA}$

Q93·PhysicsSingle correctJEE Main 2021

If

q_f

is the free charge on the capacitor plates and

q_b

is the bound charge on the dielectric slab of dielectric constant k placed between the capacitor plates, then bound charge

q_b

can be expressed as :

(A) $q_b = q_f\left(1 + \frac{1}{\sqrt{k}}\right)$
(B) $q_b = q_f\left(1 - \frac{1}{\sqrt{k}}\right)$
(C) $q_b = q_f\left(1 - \frac{1}{k}\right)$
(D) $q_b = q_f\left(1 + \frac{1}{k}\right)$

Q94·PhysicsNumericalJEE Main 2021

The circuit shown in the figure consists of a charged capacitor of capacity 3 µF and a charge of 30 µC. At time t = 0, when the key is closed, the value of current flowing through the 5 MΩ resistor is 'x' µ-A. The value of 'x to the nearest integer is _______.

Q95·PhysicsNumericalJEE Main 2021

A parallel plate capacitor has plate area 100 m

^{2}

and plate separation of 10 m. The space between the plates is filled up to a thickness 5 m with a material of dielectric constant of 10. The resultant capacitance of the system is 'x' pF. The value of ε

_{0}

= 8.85 × 10

^{-12}

F.m

^{-1}

. The value of 'x' to the nearest integer is_____.

Q96·PhysicsNumericalJEE Main 2021

A 2 μF capacitor C

_{1}

is first charged to a potential difference of 10 V using a battery.Then the battery is removed and the capacitor is connected to an uncharged capacitor C

_{2}

of 8μF. The charge in C

_{2}

on equilibrium condition is_______μC. (Round off to the Nearest Integer)

Q97·PhysicsNumericalJEE Main 2021

Four identical rectangular plates with length,

l

= 2 cm and breadth, b =

\frac{3}{2}

cm are arranged as shown in figure. The equivalent capacitance between A and C is

\frac{\mathrm{x}\,\varepsilon_0}{\mathrm{d}}

. The value of x is ___. (Round off to the Nearest Integer)

Q98·PhysicsNumericalJEE Main 2021

A parallel plate capacitor whose capacitance C is 14 pF is charged by a battery to a potential difference V = 12V between its plates. The charging battery is now disconnected and a porcelin plate with k = 7 is inserted between the plates, then the plate would oscillate back and forth between the plates with a constant mechanical energy of ______ pJ. (Assume no friction)

Q99·PhysicsSingle correctJEE Main 2021

For changing the capacitance of a given parallel plate capacitor, a dielectric material of dielectric constant K is used, which has the same area as the plates of the capacitor. The thickness of the dielectric slab is

\frac{3}{4}

d, where 'd' is the separation between the plates of parallel plate capacitor. The new capacitance (C') in terms of original capacitance (C

_0

) is given by the following relation :

(A) $C' = \frac{3+K}{4K}C_0$
(B) $C' = \frac{4+K}{3}C_0$
(C) $C' = \frac{4K}{K+3}C_0$
(D) $C' = \frac{4}{3+K}C_0$

Q100·PhysicsNumericalJEE Main 2021

In a parallel plate capacitor set up, the plate area of capacitor is 2 m

^{2}

and the plates are separated by 1m. If the space between the plates are filled with a dielectric material of thickness 0.5 m and area 2m

^{2}

(see fig.) the capacitance of the set-up will be _______ ε

_{0}

. (Dielectric constant of the material = 3.2) (Round off to the Nearest Integer)

Q101·PhysicsSingle correctJEE Main 2021

Two equal capacitors are first connected in series and then in parallel. The ratio of the equivalent capacities capacities in the two cases will be -

(A)2 : 1
(B)1 : 4
(C)4 : 1
(D)1 : 2

Q102·PhysicsSingle correctJEE Main 2020

A parallel plate capacitor has plate of length '\ell', width 'w' and separation of plates is 'd'. It is connected to a battery of emf V. A dielectric slap of the same thickness 'd' and of dielectric constant k = 4 is being, inserted between the plates of the capacitor. At what length of the slab inside plates, will be energy stored in the capacitor be two times the initial energy stored?

(A) $2\ell/3$
(B) $\ell/2$
(C) $\ell/4$
(D) $\ell/3$

Q103·PhysicsSingle correctJEE Main 2020

Two capacitors of capacitances C and 2C are charged to potential differences V and 2V, respectively. These are then connected in parallel in such a manner that the positive terminal of one is connected to the negative terminal of the other. The final energy of this configuration is:

(A) $\dfrac{3}{2}CV^2$
(B) $\dfrac{9}{2}CV^2$
(C) $\dfrac{25}{6}CV^2$
(D)zero

Q104·PhysicsSingle correctJEE Main 2020

In the circuit shown, charge on the 5

\mu

F capacitor is:

(A)16.36 $\mu$ C
(B)5.45 $\mu$ C
(C)10.90 $\mu$ C
(D)18.00 $\mu$ C

Q105·PhysicsSingle correctJEE Main 2020

A capacitor C is fully charged with voltage

V_0

. After disconnecting the voltage source, it is connected in parallel with another uncharged capacitor of capacitance.

\frac{C}{2}

. The energy loss in the process after the charge is distributed between the two capacitor is:

(A) $\frac{1}{6}CV_0^{2}$
(B) $\frac{1}{2}CV_0^{2}$
(C) $\frac{1}{4}CV_0^{2}$
(D) $\frac{1}{3}CV_0^{2}$

Q106·PhysicsSingle correctJEE Main 2020

In the circuit shown in the figure, the total charge is 750 μC and the voltage across capacitor C

_{2}

is 20 V. Then the charge on capacitor C

_{2}

is

(A)160 μC
(B)650 μC
(C)590 μC
(D)450 μC

Q107·PhysicsSingle correctJEE Main 2020

A capacitor is made of two square plats each of side 'a' making a very small angle a between them, as shown in figure. The capacitance will be close to:

(A) $\dfrac{\epsilon_{0} a^{2}}{d}\left(1+\dfrac{\alpha a}{d}\right)$
(B) $\dfrac{\epsilon_{0} a^{2}}{d}\left(1-\dfrac{\alpha a}{4d}\right)$
(C) $\dfrac{\epsilon_{0} a^{2}}{d}\left(1-\dfrac{3\alpha a}{2d}\right)$
(D) $\dfrac{\epsilon_{0} a^{2}}{d}\left(1-\dfrac{\alpha a}{2d}\right)$

Q108·PhysicsSingle correctJEE Main 2020

Effective capacitance of parallel combination of two capacitors

C_{1}

and

C_{2}

is 10

\mu

F. When these capacitor are individually connected to a voltage source of 1 V, the energy stored in the capacitor

C_{2}

is 4 times that of

C_{1}

. If these capacitors are connected in series, their effective capacitance will be

(A)3.2 $\mu$ F
(B)8.4 $\mu$ F
(C)1.6 $\mu$ F
(D)4.2 $\mu$ F

Q109·PhysicsSingle correctJEE Main 2020

A parallel plate capacitor has plates of area A separated by distance 'd' between them. It is filled with a dielectric which has a dielectric constant that varies as k(n) = k(1 + \alpha n) where 'x' is he distance measured from one of the plates. If (

\alpha

d) << 1, the total capacitance of the system is best given by the expression:

(A) $\dfrac{AK\varepsilon_0}{d}\left(1+\dfrac{\alpha d}{2}\right)$
(B) $\dfrac{A\varepsilon_0 K}{d}\left(1+\dfrac{\alpha^2 d^2}{2}\right)$
(C) $\dfrac{AK\varepsilon_0}{d}(1+\alpha d)$
(D) $\dfrac{A\varepsilon_0 K}{d}\left[1+\left(\dfrac{\alpha d}{2}\right)^2\right]$

Q110·PhysicsNumericalJEE Main 2020

A 60 pF capacitor is fully charged by a 20 V supply. It is then disconnected from the supply and is connected to another uncharged 60 pF capacitor in parallel. The electrostatic energy that is lost in this process by the time the charge is redistributed between them is (in nJ) __________.

Q111·PhysicsMultiple correctJEE Advanced 2019

In the circuit shown, initially there is no charge on capacitors and keys

S_1

and

S_2

are open. The values of the capacitors are

C_1

= 10 μF,

C_2

= 30 μF and

C_3

=

C_4

= 80 μF. Which of the statement(s) is/are correct?

(A)The key $S_1$ is kept closed for long time such that capacitors are fully charged. Now key $S_2$ is closed, at this time, the instantaneous current across 30Ω resistor (between points P and Q) will be 0.2 A (round off to $1^{st}$ decimal place).
(B)If key $S_1$ is kept closed for long time such that capacitors are fully charged, the voltage across the capacitor $C_1$ will be 4V.
(C)At time t = 0, the key $S_1$ is closed, the instantaneous current in the closed circuit will be 25 mA
(D)If key $S_1$ is kept closed for long time such that capacitors are fully charged, the voltage difference between points P and Q will be 10 V.

Q112·PhysicsNumericalJEE Advanced 2019

A parallel plate capacitor of capacitance C has spacing d between two plates having area A. The region between the plates is filled with N dielectric layers, parallel to its plates, each with thickness

\delta = \frac{d}{N}

. The dielectric constant of the

m^{th}

layer is

K_m = K\left(1+\frac{m}{N}\right)

. For a very large

N\left(>10^3\right)

, the capacitance C is

\alpha\left(\frac{K\varepsilon_0 A}{d \ln 2}\right)

. The value of α will be ______. [

\varepsilon_0

is the permittivity of free space]

Q113·PhysicsSingle correctJEE Main 2019

Two identical parallel plate capacitors, of capacitance C each, have plates of area A, separated by a distance d. The space between the plates of the two capacitors, is filled with three dielectrics, of equal thickness and dielectric constants

K_1

,

K_2

and

K_3

. The first capacitor is filled as shown in fig. I, and the second one is filled as shown in fig. II. If these two modified capacitors are charged by the same potential V, the ratio of the energy stored in the two, would be (

E_1

refers to capacitor (I) and

E_2

to capacitor (II)) :

(A) $\dfrac{E_1}{E_2}=\dfrac{K_1K_2K_3}{(K_1+K_2+K_3)(K_2K_3+K_3K_1+K_1K_2)}$
(B) $\dfrac{E_1}{E_2}=\dfrac{9K_1K_2K_3}{(K_1+K_2+K_3)(K_2K_3+K_3K_1+K_1K_2)}$
(C) $\dfrac{E_1}{E_2}=\dfrac{(K_1+K_2+K_3)(K_2K_3+K_3K_1+K_1K_2)}{9K_1K_2K_3}$
(D) $\dfrac{E_1}{E_2}=\dfrac{(K_1+K_2+K_3)(K_2K_3+K_3K_1+K_1K_2)}{K_1K_2K_3}$

Q114·PhysicsSingle correctJEE Main 2019

In the given circuit, the charge on 4 μF capacitor will be :

(A)13.4 μC
(B)24 μC
(C)9.6 μC
(D)5.4 μC

Q115·PhysicsSingle correctJEE Main 2019

Figure shows charge (q) versus voltage (V) graph for series and parallel combination of to given capacitors. The capacitances are:

(A)40 µF and 10 µF
(B)50 µF and 30 µF
(C)60 µF and 40 µF
(D)20 µF and 30 µF

Q116·PhysicsSingle correctJEE Main 2019

The parallel combination of two air filled parallel plate capacitors of capacitance C and nC is connected to a battery of voltage, V. When the capacitor are fully charged, the battery is removed and after that a dielectric material of dielectric constant K is placed between the two plates of the first capacitor. The new potential difference of the combined system is:

(A) $\dfrac{V}{K + n}$
(B)V
(C) $\dfrac{(n + 1)V}{(K + n)}$
(D) $\dfrac{nV}{K + n}$

Q117·PhysicsSingle correctJEE Main 2019

A capacitor with capacitance 5 μF is charged to 5 μC. If the plates are pulled apart to reduce the capacitance to 2 μF, how much work is done?

(A) $3.75\times10^{-6}$ J
(B) $2.55\times10^{-6}$ J
(C) $6.25\times10^{-6}$ J
(D) $2.16\times10^{-6}$ J

Q118·PhysicsSingle correctJEE Main 2019

Voltage rating of a parallel plate capacitor is 500V. Its dielectric can withstand a maximum electric field of

10^{6}\,\dfrac{V}{m}

. The plate area is

10^{-4}

m

^{2}

. What is the dielectric constant if the capacitance is 15 pF? (given

\epsilon_{0} = 8.86 \times 10^{-12}

C

^{2}

/N m

^{2}

)

(A)3.8
(B)6.2
(C)4.5
(D)8.5

Q119·PhysicsSingle correctJEE Main 2019

A parallel plate capacitor has 1

\mu

F capacitance. One of its two plates is given +2

\mu

C charge and the other plate, +4

\mu

C charge. The potential difference developed across the capacitor is:

(A)3V
(B)1V
(C)5V
(D)2V

Q120·PhysicsSingle correctJEE Main 2019

In the circuit shown, find C if the effective capacitance of the whole circuit is to be 0.5 μF. All values in the circuit are in μF.

(A) $\frac{7}{11}$ μF
(B) $\frac{6}{5}$ μF
(C)4 μF
(D) $\frac{7}{10}$ μF

Q121·PhysicsSingle correctJEE Main 2019

In the figure shown, after the switch 'S' is turned from position 'A' to position 'B', the energy dissipated in the circuit in terms of capacitance 'C' and total charge 'Q' is:

(A) $\dfrac{1}{8}\dfrac{Q^2}{C}$
(B) $\dfrac{3}{8}\dfrac{Q^2}{C}$
(C) $\dfrac{5}{8}\dfrac{Q^2}{C}$
(D) $\dfrac{3}{4}\dfrac{Q^2}{C}$

Q122·PhysicsSingle correctJEE Main 2019

A parallel plate capacitor with plates of area 1 m

^{2}

each, are at a separation of 0.1 m. If the electric field between the plates is 100 N/C, the magnitude of charge on each plate is:

(A) $7.85 \times 10^{-10}$ C
(B) $6.85 \times 10^{-10}$ C
(C) $8.85 \times 10^{-10}$ C
(D) $9.85 \times 10^{-10}$ C

Q123·PhysicsSingle correctJEE Main 2019

In the figure shown below, the charge on the left plate of the

\mu

F capacitor is

-30\mu

C. The charge on the right place of the 6

\mu

F capacitor is:

(A) $-12\mu$ C
(B) $+12\mu$ C
(C) $-18\mu$ C
(D) $+18\mu$ C

Q124·PhysicsSingle correctJEE Main 2019

Seven capacitors, each of the capacitance 2μF, are to be connected in a configuration to obtain an effective capacitance of

\left(\frac{6}{13}\right)

μF. Which of the combinations, shown in figures below, will achieve the desired value?

(A)(A)
(B)(B)
(C)(C)
(D)(D)

Q125·PhysicsSingle correctJEE Main 2019

A parallel plate capacitor is of area 6 cm

^{2}

and a separation 3 mm. The gap is filled with three dielectric materials of equal thickness (see figure) with dielectric constants K

_{1}

= 10, K

_{2}

= 12 and K

_{3}

= 14. The dielectric constant of a material which when fully inserted in above capacitor, gives same capacitance would be:

(A)4
(B)14
(C)12
(D)36

Q126·PhysicsSingle correctJEE Main 2019

A parallel plate capacitor is made of two square plates of side 'a', separated by a distance d(d <<a). The lower triangular portion is filled with a dielectric of dielectric constant K, as shown in the figure. Capacitance of this capacitor is

(A) $\frac{K\varepsilon_0 a^2}{2d(K+1)}$
(B) $\frac{K\varepsilon_0 a^2}{d(K-1)}\ln K$
(C) $\frac{K\varepsilon_0 a^2}{d}\ln K$
(D) $\frac{1}{2}\frac{K\varepsilon_0 a^2}{d}$

Q127·PhysicsSingle correctJEE Main 2019

A parallel palate capacitor with square plates is filled with four dielectrics of dielectric constants K

_1

, K

_2

, K

_3

, K

_4

arranged as shown in the figure. The effective dielectric constant K will be:

(A)K = $\dfrac{(K_1+K_3)(K_2+K_4)}{K_1+K_2+K_3+K_4}$
(B)K = $\dfrac{(K_1+K_2)(K_3+K_4)}{2(K_1+K_2+K_3+K_4)}$
(C)K = $\dfrac{(K_1+K_2)(K_3+K_4)}{K_1+K_2+K_3+K_4}$
(D)K = $\dfrac{(K_1+K_4)(K_2+K_3)}{2(K_1+K_2+K_3+K_4)}$

Q128·PhysicsNumericalJEE Advanced 2018

Three identical capacitors

C_{1}

,

C_{2}

and

C_{3}

have a capacitance of

1.0\ \mu F

each and they are uncharged initially. They are connected in a circuit as shown in the figure and

C_{1}

is then filled completely with a dielectric material of relative permittivity

\in_{r}

. The cell electromotive force (emf)

V_{0} = 8V

. First the switch

S_{1}

is closed while the switch

S_{2}

is kept open. When the capacitor

C_{3}

is fully charged,

S_{1}

is opened and

S_{2}

is closed simultaneously. When all the capacitors reach equilibrium, the charge on

C_{3}

is found to be

5\mu C

. The value of

\in_{r} =

__________.

Q129·PhysicsSingle correctJEE Advanced 2017

PARAGRAPH 1 Consider a simple RC circuit as shown in Figure 1. Process 1: In the circuit the switch S is closed at

t = 0

and the capacitor is fully charged to voltage

V_{0}

(i.e. charging continues for time

T \gg RC

). In the process some dissipation

(E_{D})

occurs across the resistance R. The amount of energy finally stored in the fully charged capacitor is

E_{C}

. Process 2: In a different process the voltage is first set to

\dfrac{V_{0}}{3}

and maintained for a charging time

T \gg RC

. Then the voltage is raised to

\dfrac{2V_{0}}{3}

without discharging the capacitor and again maintained for time

T \gg RC

. The process is repeated one more time by raising the voltage to

V_{0}

and the capacitor is charged to the same final voltage

V_{0}

as in Process 1. These two processes are depicted in Figure 2. In Process 2, total energy dissipated across the resistance

E_{D}

is:

(A) $E_{D} = \dfrac{1}{2}CV_{0}^{2}$
(B) $E_{D} = 3\left(\dfrac{1}{2}CV_{0}^{2}\right)$
(C) $E_{D} = \dfrac{1}{3}\left(\dfrac{1}{2}CV_{0}^{2}\right)$
(D) $E_{D} = 3CV_{0}^{2}$

Q130·PhysicsSingle correctJEE Advanced 2017

PARAGRAPH 1 Consider a simple RC circuit as shown in Figure 1. Process 1: In the circuit the switch S is closed at

t = 0

and the capacitor is fully charged to voltage

V_{0}

(i.e. charging continues for time

T \gg RC

). In the process some dissipation

(E_{D})

occurs across the resistance R. The amount of energy finally stored in the fully charged capacitor is

E_{C}

. Process 2: In a different process the voltage is first set to

\dfrac{V_{0}}{3}

and maintained for a charging time

T \gg RC

. Then the voltage is raised to

\dfrac{2V_{0}}{3}

without discharging the capacitor and again maintained for time

T \gg RC

. The process is repeated one more time by raising the voltage to

V_{0}

and the capacitor is charged to the same final voltage

V_{0}

as in Process 1. These two processes are depicted in Figure 2. In Process 1, the energy stored in the capacitor

E_{C}

and heat dissipated across resistance

E_{D}

are related by:

(A) $E_{C} = E_{D}$
(B) $E_{C} = E_{D}\ln 2$
(C) $E_{C} = \dfrac{1}{2}E_{D}$
(D) $E_{C} = 2E_{D}$

Q131·PhysicsMultiple correctJEE Advanced 2016

In the circuit shown below, the key is pressed at time t = 0. Which of the following statement(s) is (are) true?

(A)The voltmeter displays – 5 V as soon as the key is pressed, and displays +5 V after a long time
(B)The voltmeter will display 0 V at time $t = \ln 2$ seconds
(C)The current in the ammeter becomes $1/e$ of the initial value after 1 second
(D)The current in the ammeter becomes zero after a long time

Q132·PhysicsMultiple correctJEE Advanced 2015

A parallel plate capacitor having plates of area S and plate separation d, has capacitance

C_{1}

in air. When two dielectrics of different relative permittivities (

\varepsilon_{1} = 2

and

\varepsilon_{2} = 4

) are introduced between the two plates as shown in the figure, the capacitance becomes

C_{2}

. The ratio

\dfrac{C_{2}}{C_{1}}

is

(A)6/5
(B)5/3
(C)7/5
(D)7/3

Q133·PhysicsMultiple correctJEE Advanced 2014

A parallel plate capacitor has a dielectric slab of dielectric constant

K

between its plates that covers

1/3

of the area of its plates, as shown in the figure. The total capacitance of the capacitor is

C

while that of the portion with dielectric in between is

C_1

. When the capacitor is charged, the plate area covered by the dielectric gets charge

Q_1

and the rest of the area gets charge

Q_2

. The electric field in the dielectric is

E_1

and that in the other portion is

E_2

. Choose the correct option/options, ignoring edge effects.

(A) $\frac{E_1}{E_2} = 1$
(B) $\frac{E_1}{E_2} = \frac{1}{K}$
(C) $\frac{Q_1}{Q_2} = \frac{3}{K}$
(D) $\frac{C}{C_1} = \frac{2+K}{K}$

Q134·PhysicsMultiple correctJEE Advanced 2013

In the circuit shown in the figure, there are two parallel plate capacitors each of capacitance C. The switch

S_{1}

is pressed first to fully charge the capacitor

C_{1}

and then released. The switch

S_{2}

is then pressed to charge the capacitor

C_{2}

. After some time,

S_{2}

is released and then

S_{3}

is pressed. After some time,

(A)the charge on the upper plate of $C_{1}$ is $2CV_{0}$ .
(B)the charge on the upper plate of $C_{1}$ is $CV_{0}$ .
(C)the charge on the upper plate of $C_{1}$ is 0.
(D)the charge on the upper plate of $C_{2}$ is $-CV_{0}$ .

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