Physics · Capacitors and R-C Circuits

JEE Advanced 2023 — Paper 1 — Question 21

A container has a base of $50 \mathrm{~cm} \times 5 \mathrm{~cm}$ and height 50 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

$\varepsilon_{0}=9 \times 10^{-12} \mathrm{C}^{2} \mathrm{~N}^{-1} \mathrm{~m}^{-2}$ , the effects of the non-conducting walls on the capacitance are negligible

Option A:
27 pF
Option B:
63 pF
Correct
Option C:
81 pF
Option D:
135 pF

Answer: B

Step-by-step solution

Let container is filled upto height x in 10 sec

$250 \times 10=50 \times 5 \times x$

$\mathrm{X}=10 \mathrm{~cm}$

$\mathrm{C}=\mathrm{C}_{1}+\mathrm{C}_{2}$

$C=\frac{A_{1} \in_{0}}{d}+\frac{K A_{2} \in_{0}}{d}$

$\mathrm{C}=\frac{\epsilon_{0}}{\mathrm{~d}}\left[\mathrm{~A}_{1}+\mathrm{KA}_{2}\right]$ $\mathrm{C}=\frac{9 \times 10^{-12}}{5 \times 10^{-2}}\left[40 \times 50 \times 10^{-4}+3 \times 50 \times 10 \times 10^{-4}\right]$

$=63 \times 10^{-12} \mathrm{~F}$

$\mathrm{C}=63 \mathrm{pF}$

Answer key and solution verified before publishing.

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Exam: JEE Advanced 2023
Paper: Paper 1
Subject: Physics
Chapter: Capacitors and R-C Circuits
Topic: Effect of Dielectrics

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 A flows…

Answer: B

Step-by-step solution

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