Capacitors

JEE Main level, single correct, medium

30 of 180

Question 30 of 180

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 :

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Answer: (B) 11ϵoA18 d\frac{11 \epsilon_{\mathrm{o}} \mathrm{A}}{18 \mathrm{~d}}

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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