Question

$5$ Conducting plates each are placed face to face & at equi-spaced at distance d. Area of each plate is half the previous plate. If area of first plate is A . Then the equivalent capacitance of the system shown is :-

• A. $\frac{{ϵ}_{0}A}{d}$
• B. $\frac{{ϵ}_{0}A}{10d}$
• C. $\frac{{ϵ}_{0}A}{20d}$
• D. $\frac{{ϵ}_{0}A}{30d}$

Answer 1

The correct option is D $\frac{{ϵ}_{0}A}{30d}$

$\begin{array}{c}Equivalentcapaci\tan ce=\frac{1}{\frac{A{\epsilon }_o}{2d}+\frac{A{\epsilon }_o}{4d}+\frac{A{\epsilon }_o}{8d}+\frac{A{\epsilon }_o}{16d}}\\ =\frac{1}{\frac{30d}{A{\epsilon }_o}}=\frac{A{\epsilon }_o}{30d}\\ Hence,theoptionDisthecorrectanswer.\end{array}$