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JEE MAIN 2024
09-04-24 S1
Question
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:
Select the correct option:
A
$\frac{11 \varepsilon_0 \mathrm{~A}}{18 \mathrm{~d}}$
B
$\frac{13 \varepsilon_0 \mathrm{~A}}{17 d}$
C
$\frac{11 \varepsilon_0 \mathrm{~A}}{20 \mathrm{~d}}$
D
$\frac{18 \varepsilon_0 \mathrm{~A}}{11 \mathrm{~d}}$
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
Solution
All capacitor are in parallel combination. Also effective area is common area only $$ \begin{aligned} & \Rightarrow C_{e q}=C_1+C_2+C_3 \\ & \Rightarrow C_{e q}=\frac{A \varepsilon_0}{3 d}+\frac{A \varepsilon_0}{3(2 d)}+\frac{A \varepsilon_0}{3(3 d)} \\ & \Rightarrow C_{e q}=\frac{A \varepsilon_0}{3}\left(\frac{11}{6 d}\right) \\ & \Rightarrow C_{e q}=\frac{11 A \varepsilon_0}{18 d} \end{aligned} $$
Question Tags
JEE Main
Physics
Medium
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