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-

• A. $\frac{\epsilon _{0} A}{d}$
• B. $\frac{ \, 18}{11}\frac{\epsilon _{0} A}{d}$
• C. $\frac{ \, 11}{18}\frac{\epsilon _{0} A}{d}$
• D. $\frac{\epsilon _{0} A}{3 d}$

Answer 1

Answer: (C)

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