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 A/3 and the height is d, the capacitance of the arrangement is: (a) (11ε₀ A)/(20d) (b) (13ε₀ A)/(17d) (c) (18ε₀ A)/(11d) (d) (11ε₀ A)/(18d)

Answer: (d). Each step faces the flat plate with area A/3 at gaps d, 2d, 3d; these act as three capacitors in parallel. C = (ε₀ A)/(3)(1/d + 1/2d + 1/3d) = (ε₀ A)/(3d)×11/6 C = (11ε₀ A)/(18d) So the answer is (d) (11ε₀ A)/(18d).

A capacitor is made of a flat plate of area A and a second plate… | JEE Main 2024 (9 Apr, Shift 1)

Q37JEE Main 2024 · 9 APR · SHIFT 1Difficult

Combination of Capacitors

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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Answer: (d)

Each step faces the flat plate with area $\frac{A}{3}$ at gaps $d$ , $2d$ , $3d$ ; these act as three capacitors in parallel.
$C = \frac{\epsilon_0 A}{3}\left(\frac{1}{d} + \frac{1}{2d} + \frac{1}{3d}\right) = \frac{\epsilon_0 A}{3d}\times\frac{11}{6}$
$C = \frac{11\epsilon_0 A}{18d}$
So the answer is (d) $\frac{11\epsilon_0 A}{18d}$ .

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