1
JEE Advanced 2024 Paper 1 Online
+3
-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.

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
$\mathrm{P} \rightarrow 3 ; \mathrm{Q} \rightarrow 2 ; \mathrm{R} \rightarrow 2 ; \mathrm{S} \rightarrow 5$
2
JEE Advanced 2023 Paper 1 Online
+3
-1
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
$135 ~\mathrm{pF}$
3
JEE Advanced 2017 Paper 2 Offline
+3
-0
Consider a simple RC circuit as shown in Figure 1.

Process 1 : In the circuit the switch S is closed at t = 0 and the capacitor is fully charged to voltage V0 (i.e. charging continues for time T >> RC). In the process some dissipation (ED) occurs across the resistance R. The amount of energy finally stored in the fully charged capacitor is EC.

Process 2 : In a different process the voltage is first set to $${{{V_0}} \over 3}$$ and maintained for a charging time T >> RC. Then, the voltage is raised to $${{2{V_0}} \over 3}$$ without discharging the capacitor and again maintained for a time T >> RC. The process is repeated one more time by raising the voltage to V0 and the capacitor is charged to the same final voltage V0 as in Process 1.

These two processes are depicted in Figure 2.
In Process 1, the energy stored in the capacitor EC and heat dissipated across resistance ED are related by
A
EC = ED ln2
B
EC = ED
C
EC = 2ED
D
EC = $${1 \over 2}$$ED
4
JEE Advanced 2017 Paper 2 Offline
+3
-0
Consider a simple RC circuit as shown in Figure 1.

Process 1 : In the circuit the switch S is closed at t = 0 and the capacitor is fully charged to voltage V0 (i.e. charging continues for time T >> RC). In the process some dissipation (ED) occurs across the resistance R. The amount of energy finally stored in the fully charged capacitor is EC.

Process 2 : In a different process the voltage is first set to $${{{V_0}} \over 3}$$ and maintained for a charging time T >> RC. Then, the voltage is raised to $${{2{V_0}} \over 3}$$ without discharging the capacitor and again maintained for a time T >> RC. The process is repeated one more time by raising the voltage to V0 and the capacitor is charged to the same final voltage V0 as in Process 1.

These two processes are depicted in Figure 2.

In Process 2, total energy dissipated across the resistance ED 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
$${E_D} = {1 \over 2}CV_0^2$$
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