Physics · Capacitors and R-C Circuits

JEE Main 2024 — 9 April, Shift 1 — Question 37

A capacitor is made of a flat plate of area A and a second plate having a stair-like structure as shown in figure. If the area of each stair is $\frac{\mathrm{A}}{3}$ and the height is d, the capacitance of the arrangement is:

Option A:
$\frac{11 \varepsilon_{0} \mathrm{~A}}{18 \mathrm{~d}}$
Correct
Option B:
$\frac{13 \varepsilon_{0} A}{17 d}$
Option C:
$\frac{11 \varepsilon_{0} \mathrm{~A}}{20 \mathrm{~d}}$
Option D:
$\frac{18 \varepsilon_{0} \mathrm{~A}}{11 \mathrm{~d}}$

Answer: A

Step-by-step solution

All capacitor are in parallel combination. Also effective area is common area only $\Rightarrow \mathrm{C}_{\mathrm{eq}}=\mathrm{C}_{1}+\mathrm{C}_{2}+\mathrm{C}_{3}$

$\Rightarrow \mathrm{C}_{\mathrm{eq}}=\frac{\mathrm{A} \varepsilon_{0}}{3 \mathrm{~d}}+\frac{\mathrm{A} \varepsilon_{0}}{3(2 \mathrm{~d})}+\frac{\mathrm{A} \varepsilon_{0}}{3(3 \mathrm{~d})}$

$\Rightarrow \mathrm{C}_{\mathrm{eq}}=\frac{\mathrm{A} \varepsilon_{0}}{3}\left(\frac{11}{6 \mathrm{~d}}\right)$

$\Rightarrow \mathrm{C}_{\mathrm{eq}}=\frac{11 \mathrm{~A} \varepsilon_{0}}{18 \mathrm{~d}}$

Answer key and solution verified before publishing.

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Exam: JEE Main 2024
Paper: 9 April, Shift 1
Subject: Physics
Chapter: Capacitors and R-C Circuits
Topic: Combination of Capacitors and Circuit Analysis

A bulb and a capacitor are connected in series across an ac supply. A dielectric is then placed between the plates of the capacitor. The…

Answer: A

Step-by-step solution

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