Question 1: Palette 1/15

JEE Advanced 2024 MCQ

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.

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) $2C_0$

A

$\mathrm{P} \rightarrow 3 ; \mathrm{Q} \rightarrow 2 ; \mathrm{R} \rightarrow 4 ; \mathrm{S} \rightarrow 5$

B

$\mathrm{P} \rightarrow 2 ; \mathrm{Q} \rightarrow 3 ; \mathrm{R} \rightarrow 2 ; \mathrm{S} \rightarrow 1$

C

$\mathrm{P} \rightarrow 3 ; \mathrm{Q} \rightarrow 2 ; \mathrm{R} \rightarrow 4 ; \mathrm{S} \rightarrow 1$

D

$\mathrm{P} \rightarrow 3 ; \mathrm{Q} \rightarrow 2 ; \mathrm{R} \rightarrow 2 ; \mathrm{S} \rightarrow 5$

Question 2: Palette 2/15

JEE Advanced 2023 MCQ

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]

A

$27 ~\mathrm{pF}$

B

$63 ~\mathrm{pF}$

C

$81 ~\mathrm{pF}$

D

$135 ~\mathrm{pF}$

Question 3: Palette 3/15

JEE Advanced 2023 MSQ

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

A

The value of the resistance $R$ is $3 \Omega$.

B

For $t < t_0 $, the value of current $I_1$ is $2 \mathrm{~A}$.

C

At $t=t_0+7.2 \mu \mathrm{s}$, the current in the capacitor is $0.6 \mathrm{~A}$.

D

For $t \rightarrow \infty$, the charge on the capacitor is $12 \mu \mathrm{C}$.

Question 4: Palette 4/15

JEE Advanced 2022 MCQ

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?

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.

Question 5: Palette 5/15

JEE Advanced 2017 MCQ

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 ln2

B

E_C = E_D

C

E_C = 2E_D

D

E_C = ${1 \over 2}$E_D

Question 6: Palette 6/15

JEE Advanced 2017 MCQ

In Process 2, total energy dissipated across the resistance E_D is

A

${E_D} = {1 \over 3}\left( {{1 \over 2}CV_0^2} \right)$

B

${E_D} = 3\left( {{1 \over 2}CV_0^2} \right)$

C

${E_D} = 3CV_0^2$

D

${E_D} = {1 \over 2}CV_0^2$

Question 7: Palette 7/15

JEE Advanced 2015 MCQ

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

A

${6 \over 5}$

B

${5 \over 3}$

C

${7 \over 5}$

D

${7 \over 3}$

Question 8: Palette 8/15

JEE Advanced 2014 MSQ

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

${{{E_1}} \over {{E_2}}} = 1$

B

${{{E_1}} \over {{E_2}}} = {1 \over K}$

C

${{{Q_1}} \over {{Q_2}}} = {3 \over K}$

D

${C \over {{C_1}}} = {{2 + K} \over K}$

Question 9: Palette 9/15

JEE Advanced 2013 MSQ

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 $2C{V_0}$

B

The charge on the upper plate of ${C_1}$ is $C{V_0}$

C

The charge on the upper plate of ${C_2}$ is $0$

D

The charge on the upper plate of ${C_2}$ is $ - C{V_0}$

Question 10: Palette 10/15

JEE Advanced 2012 MCQ

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

A

$ + \,32\,\mu C$

B

$ + \,40\,\mu C$

C

$ + \,48\,\mu C$

D

$ + \,80\,\mu C$

Question 11: Palette 11/15

JEE Advanced 2011 MCQ

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

A

$0\% $

B

$20\% $

C

$75\% $

D

$80\% $

Question 12: Palette 12/15

JEE Advanced 2007 MCQ

A circuit is connected as shown in the figure with the switch S open. When the switch is closed, the total amount of charge that flows from Y to X is

A

0

B

54 $\mu$C

C

27 $\mu$C

D

81 $\mu$C

Question 13: Palette 13/15

JEE Advanced 2007 MCQ

Column I gives certain situations in which a straight metallic wire of resistance R is used and Column II gives some resulting effects. Match the statements in Column I with the statements in Column II and indicate your answer by darkening appropriate bubbles in the 4 $\times$ 4 matrix given in the ORS.

	Column I		Column II
(A)	A charged capacitor is connected to the ends of the wire	(P)	A constant current flows through the wire
(B)	The wire is moved perpendicular to its length with a constant velocity in a uniform magnetic field perpendicular to the plane of motion	(Q)	Thermal energy is generated in the wire
(C)	The wire is placed in a constant electric field that has a direction along the length of the wire.	(R)	A constant potential difference develops between the ends of the wire
(D)	A battery of constant emf is connected to the ends of the wire	(S)	Charges of constant magnitude appear at the ends of the wire

A

A $\to$ (Q); B $\to$ (R); C $\to$ (R, S); D $\to$ (P, Q)

B

A $\to$ (Q); B $\to$ (R, S); C $\to$ (R, S); D $\to$ (P, Q, R)

C

A $\to$ (Q); B $\to$ (R, S); C $\to$ (R); D $\to$ (Q, R)

D

A $\to$ (Q, R); B $\to$ (R, S); C $\to$ (R); D $\to$ (P, Q, R)

Question 14: Palette 14/15

JEE Advanced 2006 MCQ

In the following circuits, it is given that $\mathrm{R}_1=1 \Omega, \mathrm{R}_2=2 \Omega, \mathrm{C}_1=2 \mu \mathrm{~F}$ and $\mathrm{C}_2=4 \mu \mathrm{~F}$.

The time constants (in $\mu \mathrm{s}$ ) for the circuits I, II, III are, rcspectively.

A

$18,8 / 9,4$

B

$18,4,8 / 9$

C

$4,8 / 9,18$

D

$8 / 9,18,4$

Question 15: Palette 15/15

JEE Advanced 2005 MCQ

In the given circuit, the switch S is closed at time $t=0$. The charge Q on the capacitor at any instant t is given by $Q(t)=Q_0(1-e^{-\alpha t})$. Find the value of Q$_0$ and $\alpha$ in terms of given parameters shown in the circuit.

A

$\mathrm{Q_0=\frac{2CVR_2}{R_1+R_2};\alpha=\frac{(R_1+R_2)}{CR_1R_2}}$

B

$\mathrm{Q_0=\frac{CVR_2}{R_1+R_2};\alpha=\frac{(R_1+R_2)}{3CR_1R_2}}$

C

$\mathrm{Q_0=\frac{CVR_2}{R_1+R_2};\alpha=\frac{(R_1+R_2)}{CR_1R_2}}$

D

$\mathrm{Q_0=\frac{2CVR_2}{R_1+R_2};\alpha=\frac{(R_1+R_2)}{3CR_1R_2}}$