Capacitor · Physics · JEE Advanced
MCQ (Single Correct Answer)
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) $2C_0$ |
[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]



MCQ (More than One Correct Answer)
[Given: $e^{-1}=0.36$ ]

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?



Numerical

The magnitude of q1 is ________________.

The magnitude of q2 is ________________.
The value of $$\alpha $$ will be ..................
[$$ \in $$0 is the permittivity of free space.]

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)