A capacitor is made of a flat plate of area A and a second plate having a stair-like structure as shown in the figure. If the area of each stair is and the height is ddd, the capacitance of the arrangement is:

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Q.
A capacitor is made of a flat plate of area A and a second plate having a stair-like structure as shown in the figure. If the area of each stair is $\frac{A}{3}$ and the height is d, the capacitance of the arrangement is: [2024]

1 $\frac{11 ϵ_{0} A}{18 d}$

2 $\frac{13 ϵ_{0} A}{17 d}$

3 $\frac{11 ϵ_{0} A}{20 d}$

4 $\frac{18 ϵ_{0} A}{11 d}$

Ans.
(1)

All capacitors are in parallel combination.

Also, effective area is common area only

$C_{e q} = C_{1} + C_{2} + C_{3}$

$= \frac{ϵ_{0} A}{3 \times d} + \frac{ϵ_{0} A}{3 \times 2 d} + \frac{ϵ_{0} A}{3 \times 3 d}$

$= \frac{6 ϵ_{0} A + 3 ϵ_{0} A + 2 ϵ_{0} A}{18 d} = \frac{11 ϵ_{0} A}{18 d}$

Solution

Q.
A capacitor is made of a flat plate of area A and a second plate having a stair-like structure as shown in the figure. If the area of each stair is $\frac{A}{3}$ and the height is d, the capacitance of the arrangement is: [2024]

1 $\frac{11 ϵ_{0} A}{18 d}$

2 $\frac{13 ϵ_{0} A}{17 d}$

3 $\frac{11 ϵ_{0} A}{20 d}$

4 $\frac{18 ϵ_{0} A}{11 d}$

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Solution

Q. A capacitor is made of a flat plate of area A and a second plate having a stair-like structure as shown in the figure. If the area of each stair is A3 and the height is d, the capacitance of the arrangement is: [2024]

1 11ϵ0A18d

2 13ϵ0A17d

3 11ϵ0A20d

4 18ϵ0A11d

Ans. (1) All capacitors are in parallel combination. Also, effective area is common area only Ceq=C1+C2+C3 =ϵ0A3×d+ϵ0A3×2d+ϵ0A3×3d =6ϵ0A+3ϵ0A+2ϵ0A18d=11ϵ0A18d

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Q.
A capacitor is made of a flat plate of area A and a second plate having a stair-like structure as shown in the figure. If the area of each stair is $\frac{A}{3}$ and the height is d, the capacitance of the arrangement is: [2024]

1 $\frac{11 ϵ_{0} A}{18 d}$

2 $\frac{13 ϵ_{0} A}{17 d}$

3 $\frac{11 ϵ_{0} A}{20 d}$

4 $\frac{18 ϵ_{0} A}{11 d}$