A capacitor is made of a flat plate of area A and a second plate having a stair-like structure as shown in the diagram. The capacitance of the arrangement is-

Question

A capacitor is made of a flat plate of area A and a second plate having a stair-like structure as shown in the diagram. The capacitance of the arrangement is- <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-zy586f6if7ibsfso.jpg" /> (A) (ϵ 0 A/d) (B) ( 18/11)(ϵ 0 A/d) (C) ( 11/18)(ϵ 0 A/d) (D) (ϵ 0 A/3 d)

Tardigrade Admin · Accepted Answer

All the steps of stair makes three parellel capacitors. Ce q=C1+C2+C3 =(ϵ 0 A/3 d)+(ϵ 0 A/3 × 2 d)+(ϵ 0 A/3 × 3 d)=(11 ϵ 0 A/18 d)

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 diagram. The capacitance of the arrangement is-

$\frac{ϵ _{0} A}{d}$

$\frac{18}{11} \frac{ϵ _{0} A}{d}$

$\frac{11}{18} \frac{ϵ _{0} A}{d}$

$\frac{ϵ _{0} A}{3 d}$

All the steps of stair makes three parellel capacitors.
$C_{e q} = C_{1} + C_{2} + C_{3}$
$= \frac{ϵ _{0} A}{3 d} + \frac{ϵ _{0} A}{3 \times 2 d} + \frac{ϵ _{0} A}{3 \times 3 d} = \frac{11 ϵ _{0} A}{18 d}$

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 diagram. The capacitance of the arrangement is-

dϵ0​A​

1118​dϵ0​A​

1811​dϵ0​A​

3dϵ0​A​