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JEE Main 20249 AprilMorning Shift
Exam
JEE Main
Year
2024
Date
9 April
Shift
Morning Shift
Subject
Physics
Chapter
Capacitance

JEE Main 2024 · 9 April · Morning Shift · Physics · Capacitance

A capacitor is made of a flat plate of area A and a second plate...

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 A3\frac{A}{3} and the height is dd, the capacitance of the arrangement is : 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

Options

  1. A13ϵoA17d\frac{13 \epsilon_o A}{17 d}
  2. B11ϵoA18 d\frac{11 \epsilon_{\mathrm{o}} \mathrm{A}}{18 \mathrm{~d}}
  3. C18ϵoA11 d\frac{18 \epsilon_{\mathrm{o}} \mathrm{A}}{11 \mathrm{~d}}
  4. D11ϵoA20 d\frac{11 \epsilon_{\mathrm{o}} \mathrm{A}}{20 \mathrm{~d}}

Correct answer

B. 11ϵoA18 d\frac{11 \epsilon_{\mathrm{o}} \mathrm{A}}{18 \mathrm{~d}}

Step-by-step solution

All capacitor are in parallel combination. Also effective area is common area only ⇒Ceq =C1+C2+C3⇒Ceq =Aε03d+Aε03(2d)+Aε03(3d)⇒Ceq =Aε03(116d)⇒Ceq =11Aε018d\begin{aligned} & \Rightarrow C_{\text{eq }}=C_1+C_2+C_3 \\ & \Rightarrow C_{\text{eq }}=\frac{A \varepsilon_0}{3 d}+\frac{A \varepsilon_0}{3(2 d)}+\frac{A \varepsilon_0}{3(3 d)} \\ & \Rightarrow C_{\text{eq }}=\frac{A \varepsilon_0}{3}\left(\frac{11}{6 d}\right) \\ & \Rightarrow C_{\text{eq }}=\frac{11 A \varepsilon_0}{18 d}\end{aligned}
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