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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 $\frac{A}{3}$ and the height is $d$, the capacitance of the arrangement is :
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The correct answer is:
$\frac{11 \epsilon_{\mathrm{o}} \mathrm{A}}{18 \mathrm{~d}}$
All capacitor are in parallel combination.
Also effective area is common area only
$\begin{aligned} & \Rightarrow C_{\text {eq }}=C_1+C_2+C_3 \\ & \Rightarrow C_{\text {eq }}=\frac{A \varepsilon_0}{3 d}+\frac{A \varepsilon_0}{3(2 d)}+\frac{A \varepsilon_0}{3(3 d)} \\ & \Rightarrow C_{\text {eq }}=\frac{A \varepsilon_0}{3}\left(\frac{11}{6 d}\right) \\ & \Rightarrow C_{\text {eq }}=\frac{11 A \varepsilon_0}{18 d}\end{aligned}$
Also effective area is common area only
$\begin{aligned} & \Rightarrow C_{\text {eq }}=C_1+C_2+C_3 \\ & \Rightarrow C_{\text {eq }}=\frac{A \varepsilon_0}{3 d}+\frac{A \varepsilon_0}{3(2 d)}+\frac{A \varepsilon_0}{3(3 d)} \\ & \Rightarrow C_{\text {eq }}=\frac{A \varepsilon_0}{3}\left(\frac{11}{6 d}\right) \\ & \Rightarrow C_{\text {eq }}=\frac{11 A \varepsilon_0}{18 d}\end{aligned}$
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