1
JEE Advanced 2023 Paper 1 Online
MCQ (More than One Correct Answer)
+4
-2
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 $12 \mu \mathrm{C}$.
2
JEE Advanced 2022 Paper 1 Online
MCQ (More than One Correct Answer)
+4
-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).

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.
3
JEE Advanced 2015 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2
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
$${7 \over 3}$$
4
JEE Advanced 2014 Paper 1 Offline
MCQ (More than One Correct Answer)
+3
-0
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
$${C \over {{C_1}}} = {{2 + K} \over K}$$
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