Capacitance and Capacitors

Interactive Feed

JEE Advanced 1991

A parallel plate capacitor of plate area $A$ and plate separation $d$ is charged to potential difference $V$ and then the battery is disconnected. A slab of dielectric constant $K$ is then inserted between the plates of the capacitor so as to fill the space between the plates. If $Q$ , $E$ and $W$ denote respectively, the magnitude of charge on each plate, the electric field between the plates (after the slab is inserted), and work done on the system, in question, in the process of inserting the slab, then

Q = \frac{ε _{0} A V}{d}

(B)

Q = \frac{ε _{0} K A V}{d}

(C)

E = \frac{V}{K d}

(D)

W = \frac{ε _{0} A V ^{2}}{2 d} [1 - \frac{1}{K}]

JEE Advanced 1996

LEVELJEE Advanced

The capacitance of a parallel plate capacitor with plate area $A$ and separation $d$ , is $C$ . The space between the plates is filled with two wedges of dielectric constants $K_{1}$ and $K_{2}$ respectively (figure). Find the capacitance of the resulting capacitor.

LEVELJEE Main

For the circuit shown, which of the following statements is true ?

(A)

With

S_{1}

closed,

V_{1} = 15 V, V_{2} = 20 V

(B)

With

S_{3}

closed,

V_{1} = V_{2} = 25 V

(C)

With

S_{1}

and

S_{2}

closed,

V_{1} = V_{2} = 0

(D)

With

S_{3}

closed,

V_{1} = 30 V, V_{2} = 20 V

LEVELJEE Main

Two identical metal plates are given positive charges $Q_{1}$ and $Q_{2}$ ( $< Q_{1}$ ) respectively. If they are now brought close together to form a parallel plate capacitor with capacitance $C$ , the potential difference between them is

(A)

(Q_{1} + Q_{2}) /2 C

(B)

(Q_{1} + Q_{2}) / C

(C)

(Q_{1} - Q_{2}) / C

(D)

(Q_{1} - Q_{2}) /2 C

JEE Advanced 1985

LEVELJEE Main

A parallel plate air capacitor is connected to a battery. The quantities charge, voltage, electric field and energy associated with this capacitor are given by $Q_{0}$ , $V_{0}$ , $E_{0}$ and $U_{0}$ respectively. A dielectric slab is now introduced to fill the space between the plates with the battery still in connection. The corresponding quantities now given by $Q$ , $V$ , $E$ and $U$ are related to the previous one as

* Multiple Correct Options

(A)

Q > Q_{0}

(B)

V > V_{0}

(C)

E > E_{0}

(D)

U > U_{0}

LEVELJEE Main

A dielectric slab of thickness $d$ is inserted in a parallel plate capacitor whose negative plate is at $x = 0$ and positive plate is at $x = 3 d$ . The slab is equidistant from the plates. The capacitor is given some charge. As $x$ goes from $0$ to $3 d$

* Multiple Correct Options

(A)

the magnitude of the electric field remains the same.

(B)

the direction of the electric field remains the same.

(C)

the electric potential increases continuously.

(D)

the electric potential increases at first, then decreases and again increases.

LEVELJEE Main

A parallel plate capacitor is charged and the charging battery is then disconnected. If the plates of the capacitor are moved farther apart by means of insulating handles

* Multiple Correct Options

(A)

the charge on the capacitor increases

(B)

the voltage across the plates increases

(C)

the capacitance increases

(D)

the electrostatic energy stored in the capacitor increases

JEE Advanced 2014

LEVELJEE Advanced

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.

* Multiple Correct Options

(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}

JEE Advanced 1983

LEVELJEE Advanced

The figure shows two identical parallel plate capacitors $A$ and $B$ connected to a battery with the switch $S$ closed. The switch is now opened and the free space between the plates of the capacitors is filled with a dielectric of dielectric constant (or relative permittivity) 3. Find the ratio of the total electrostatic energy stored in both capacitors before and after the introduction of the dielectric.

JEE Advanced 2015

LEVELJEE Advanced

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 ( $ε_{1} = 2$ and $ε_{2} = 4$ ) are introduced between the two plates as shown in the figure, the capacitance becomes $C_{2}$ . The ratio $\frac{C _{2}}{C _{1}}$ is

(A)

\frac{6}{5}

(B)

\frac{5}{3}

(C)

\frac{7}{5}

(D)

\frac{7}{3}

LEVELJEE Main

Consider the situation shown in the figure. The capacitor $A$ has a charge $q$ on it whereas $B$ is uncharged. The charge appearing on the capacitor $B$ a long time after the switch is closed is

(A)

zero

(B)

q /2

(C)

q

(D)

2 q

LEVELJEE Advanced

Two square metal plates of side $1 m$ are kept $0.01 m$ apart like a parallel plate capacitor in air in such a way that one of their edges is perpendicular to an oil surface in a tank filled with an insulating oil. The plates are connected to a battery of emf $500 V$ . The plates are then lowered vertically into the oil at a speed of $0.001 ms^{- 1}$ . Calculate the current drawn from the battery during the process. (Dielectric constant of oil $= 11$ , $ε_{0} = 8.85 \times 1 0^{- 12} C^{2} N^{- 1} m^{- 2}$ ).

JEE Main 2008

LEVELJEE Advanced

A parallel plate capacitor $C$ with plates of unit area and separation $d$ is filled with a liquid of dielectric constant $K = 2$ . The level of liquid is $d /3$ initially. Suppose the liquid level decreases at a constant speed $v$ , the time constant as a function of time $t$ is

(A)

\frac{6 ε _{0} R}{5 d + 3 v t}

(B)

\frac{( 15 d + 9 v t ) ε _{0} R}{2 d ^{2} - 3 d v t - 9 v ^{2} t ^{2}}

(C)

\frac{6 ε _{0} R}{5 d - 3 v t}

(D)

\frac{( 15 d - 9 v t ) ε _{0} R}{2 d ^{2} + 3 d v t - 9 v ^{2} t ^{2}}

JEE Advanced 2016

LEVELJEE Advanced

Comprehension Passage

Consider an evacuated cylindrical chamber of height

h

having rigid conducting plates at the ends and an insulating curved surface as shown in the figure. A number of spherical balls made of a light weight and soft material and coated with a conducting material are placed on the bottom plate. The balls have a radius

r ≪ h

. Now, a high voltage source (HV) connected across the conducting plates such that the bottom plate is at

+ V_{0}

and the top plate at

- V_{0}

. Due to their conducting surface, the balls will get charge, will become equipotential with the plate and are repelled by it. The balls will eventually collide with the top plate, where the coefficient of restitution can be taken to be zero due to te soft nature of the material of the balls. The electric field in the chamber can be considered to be that of a parallel plate capacitor. Assume that there are no collisions between the balls and the interaction between them is negligible. (Ignore gravity)

Question 1:

Which one of the following statement is correct?

(A)

The balls will execute simple harmonic motion between the two plates.

(B)

The balls will bounce back to the bottom plate carrying the same charge they went up with.

(C)

The balls will stick to the top plate and remain there.

(D)

The balls will bounce back to the bottom plate carrying the opposite charge they went up with.

Question 2:

The average current in the steady state registered by the ammeter in the circuit will be

(A)

proportional to

V_{0}^{2}

(B)

proportional to the potential

V_{0}

V_{0}^{1/2}

JEE Advanced 2022

LEVELJEE Main

In the following circuit $C_{1} = 12 μ F$ , $C_{2} = C_{3} = 4 μ F$ and $C_{4} = C_{5} = 2 μ F$ . The Charge stored in $C_{3}$ is _______ $μ C$ .

JEE Advanced 2022

LEVELJEE Advanced

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 of $\frac{d}{2}$ 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?

* Multiple Correct Options

(A)

The electric field inside the dielectric material is reduced by a factor of

2 K

(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.

JEE Advanced 2019

LEVELJEE Advanced

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 $δ = \frac{d}{N}$ . The dielectric constant of the $m^{th}$ layer is $K_{m} = K (1 + \frac{m}{N})$ . For a very large N ( $> 1 0^{3}$ ), the capacitance C is $α (\frac{K ϵ _{0} A}{d l n 2})$ . The value of $α$ will be _____.

JEE Advanced 2023

LEVELJEE Advanced

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 $ϵ_{0} = 9 \times 1 0^{- 12} C^{2} N^{- 1} m^{- 2}$ , the effects of the non-conducting walls on the capacitance are negligible]

A parallel plate capacitor has plate area $100 m^{2}$ and plate separation of 10 m. The space between the plates is filled upto a thickness 5 m with a material of dielectric constant of 10. The resultant capacitance of the system is $x pF$ . The value of $ε_{0} = 8.85 \times 1 0^{- 12} F m^{- 1}$ . The value of $x$ to the nearest integer is …… .

JEE Main 2020

LEVELJEE Advanced

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

(A)

\frac{ε _{0} a ^{2}}{d} (1 - \frac{α a}{4 d})

(B)

\frac{ε _{0} a ^{2}}{d} (1 + \frac{α a}{d})

(C)

\frac{ε _{0} a ^{2}}{d} (1 - \frac{α a}{2 d})

(D)

\frac{ε _{0} a ^{2}}{d} (1 - \frac{3 α a}{2 d})

JEE Main 2021

LEVELJEE Advanced

A simple pendulum of mass $m$ , length $l$ 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} [\frac{q}{m g} \times \frac{C _{1} ( V _{2} - V _{1} )}{( C _{1} + C _{2} ) ( d - t )}]

(B)

tan^{- 1} [\frac{q}{m g} \times \frac{C _{2} ( V _{2} - V _{1} )}{( C _{1} + C _{2} ) ( d - t )}]

(C)

tan^{- 1} [\frac{q}{m g} \times \frac{C _{2} ( V _{1} + V _{2} )}{( C _{1} + C _{2} ) ( d - t )}]

(D)

tan^{- 1} [\frac{q}{m g} \times \frac{C _{1} ( V _{1} + V _{2} )}{( C _{1} + C _{2} ) ( d - t )}]

LEVELJEE Main

The work done in placing a charge of $8 \times 1 0^{- 18} C$ on a condenser of capacity $100 μ F$ is

(A)

16 \times 1 0^{- 32} J

(B)

3.1 \times 1 0^{- 26} J

(C)

4 \times 1 0^{- 10} J

(D)

32 \times 1 0^{- 32} J

JEE Main 2019

LEVELJEE Main

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 give same capacitance when fully inserted in above capacitor, would be

The charge on a capacitor plate in a circuit as a function of time is shown in the figure. What is the value of current at $t = 4 s$ ?

(A)

2 μ A

(B)

1.5 μ A

(C)

Zero

(D)

3 μ A

JEE Main 2016

LEVELJEE Advanced

A combination of capacitors is set-up as shown in the figure. The magnitude of the electric field, due to a point charge $Q$ (having a charge equal to the sum of the charges on the $4 μ F$ and $9 μ F$ capacitors), at a point distance $30 m$ from it, would equal to

(A)

240 N/C

(B)

360 N/C

(C)

420 N/C

(D)

480 N/C

For the circuit shown, which of the following statements is true ?

A parallel plate capacitor is charged and the charging battery is then disconnected. If the plates of the capacitor are moved farther apart by means of insulating handles

Comprehension Passage

Which one of the following statement is correct?

The average current in the steady state registered by the ammeter in the circuit will be

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } In the following circuit C1​=12μF, C2​=C3​=4μF and C4​=C5​=2μF. The Charge stored in C3​ is _______ μC.

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.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The work done in placing a charge of 8×10−18 C on a condenser of capacity 100μF is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The charge on a capacitor plate in a circuit as a function of time is shown in the figure. What is the value of current at t=4 s?

In the following circuit $C_{1} = 12 μ F$ , $C_{2} = C_{3} = 4 μ F$ and $C_{4} = C_{5} = 2 μ F$ . The Charge stored in $C_{3}$ is _______ $μ C$ .

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

The work done in placing a charge of $8 \times 1 0^{- 18} C$ on a condenser of capacity $100 μ F$ is

The charge on a capacitor plate in a circuit as a function of time is shown in the figure. What is the value of current at $t = 4 s$ ?