MCQ (Single Correct Answer)

1

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 $${C_0} = {{{\varepsilon _0}{a^2}} \over d}$$, where $\varepsilon_0$ is the permittivity of free space.

JEE Advanced 2024 Paper 1 Online Physics - Capacitor Question 1 English

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) $\frac{C_0}{2}$
(R) The capacitance between $S_1$ and $S_3$, with $S_2$ shorted to $S_4$, is (3) $\frac{C_0}{3}$
(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) $\frac{2C_0}{3}$
(5) $2C_0$
JEE Advanced 2024 Paper 1 Online
2
A container has a base of $50 \mathrm{~cm} \times 5 \mathrm{~cm}$ and height $50 \mathrm{~cm}$, as shown in the figure. It has two parallel electrically conducting walls each of area $50 \mathrm{~cm} \times 50 \mathrm{~cm}$. 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 $250 \mathrm{~cm}^3 \mathrm{~s}^{-1}$. What is the value of the capacitance of the container after 10 seconds?

[Given: Permittivity of free space $\epsilon_0=9 \times 10^{-12} \mathrm{C}^2 \mathrm{~N}^{-1} \mathrm{~m}^{-2}$, the effects of the non-conducting walls on the capacitance are negligible]

JEE Advanced 2023 Paper 1 Online Physics - Capacitor Question 2 English
JEE Advanced 2023 Paper 1 Online
3
In Process 1, the energy stored in the capacitor EC and heat dissipated across resistance ED are related by
JEE Advanced 2017 Paper 2 Offline
4
In Process 2, total energy dissipated across the resistance ED is
JEE Advanced 2017 Paper 2 Offline
5
In the given circuit, a charge of $$+80$$ $$\mu C$$ is given to the upper plate of the $$4$$ $$\mu F$$ capacitor. Then in the steady state, the charge on the upper plate of the $$3$$ $$\mu F$$ capacitor is
IIT-JEE 2012 Paper 2 Offline Physics - Capacitor Question 16 English
IIT-JEE 2012 Paper 2 Offline
6
A $$2$$ $$\mu F$$ capacitor is charged as shown in the figure. The percentage of its stored energy dissipated after the switch $$S$$ is turned to position $$2$$ is
IIT-JEE 2011 Paper 1 Offline Physics - Capacitor Question 17 English
IIT-JEE 2011 Paper 1 Offline

MCQ (More than One Correct Answer)

1
In a circuit shown in the figure, the capacitor $C$ is initially uncharged and the key $K$ is open. In this condition, a current of $1 \mathrm{~A}$ flows through the $1 \Omega$ resistor. The key is closed at time $t=t_0$. Which of the following statement(s) is(are) correct?

[Given: $e^{-1}=0.36$ ]

JEE Advanced 2023 Paper 1 Online Physics - Capacitor Question 3 English
JEE Advanced 2023 Paper 1 Online
2

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).

JEE Advanced 2022 Paper 1 Online Physics - Capacitor Question 4 English

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?

JEE Advanced 2022 Paper 1 Online
3
A parallel plate capacitor having plates of area S and plate separation d, has capacitance C1 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 C2. The ratio $${{{C_2}} \over {{C_1}}}$$ is

JEE Advanced 2015 Paper 2 Offline Physics - Capacitor Question 10 English
JEE Advanced 2015 Paper 2 Offline
4
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.

JEE Advanced 2014 Paper 1 Offline Physics - Capacitor Question 14 English
JEE Advanced 2014 Paper 1 Offline
5
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
JEE Advanced 2013 Paper 1 Offline Physics - Capacitor Question 15 English
JEE Advanced 2013 Paper 1 Offline

Numerical

1
In the circuit shown below, the switch S is connected to position P for a long time so that the charge on the capacitor becomes q1 $$\mu$$C. Then S is switched to position Q. After a long time, the charge on the capacitor is q2 $$\mu$$C.

JEE Advanced 2021 Paper 1 Online Physics - Capacitor Question 9 English

The magnitude of q1 is ________________.
JEE Advanced 2021 Paper 1 Online
2
In the circuit shown below, the switch S is connected to position P for a long time so that the charge on the capacitor becomes q1 $$\mu$$C. Then S is switched to position Q. After a long time, the charge on the capacitor is q2 $$\mu$$C.

JEE Advanced 2021 Paper 1 Online Physics - Capacitor Question 8 English

The magnitude of q2 is ________________.
JEE Advanced 2021 Paper 1 Online
3
Two capacitors with capacitance values C1 = 2000 $$ \pm $$ 10 pF and C2 = 3000 $$ \pm $$ 15 pF are connected in series. The voltage applied across this combination is V = 5.00 $$ \pm $$ 0.02 V. The percentage error in the calculation of the energy stored in this combination of capacitors is ________.
JEE Advanced 2020 Paper 2 Offline
4
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, $$\delta = {d \over N}$$. The dielectric constant of the mth layer is $${K_m} = K\left( {1 + {m \over N}} \right)$$. For a very large N(>103), the capacitance C is $$\alpha \left( {{{K{\varepsilon _0}A} \over {d\ln 2}}} \right)$$

The value of $$\alpha $$ will be ..................

[$$ \in $$0 is the permittivity of free space.]
JEE Advanced 2019 Paper 1 Offline
5
Three identical capacitors $${C_1},{C_2}$$ and $${C_3}$$ have a capacitance of $$1.0\,\mu F$$ each and they are unchanged 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 $${\varepsilon _r}.$$ The cell electromotive force $$\left( {emf} \right)\,\,{V_0} = 8V.$$ 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 $${\varepsilon _r} = $$ _________________.

JEE Advanced 2018 Paper 1 Offline Physics - Capacitor Question 13 English
JEE Advanced 2018 Paper 1 Offline
6

At time t = 0, a battery of 10 V is connected across points A and B in the given circuit. If the capacitors have no charge initially, at what time (in seconds) does the voltage across them becomes 4 V? (Take ln5 = 1.6, ln3 = 1.1)

IIT-JEE 2010 Paper 2 Offline Physics - Capacitor Question 5 English

IIT-JEE 2010 Paper 2 Offline
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