question_answer

Three dielectric slabs of thickness d/4, d/7 and d/2 having dielectric constants 2, 8/7 and 4 respectively are inserted between the plates of a parallel plate capacitor having plate separation d and plate area A. The remaining space is filled with a conducting medium. Find the capacitance of the system.

A)  \[\frac{8{{\varepsilon }_{0}}A}{d}\]                       

B)  \[\frac{8{{\varepsilon }_{0}}A}{3d}\]

C)  \[\frac{26{{\varepsilon }_{0}}A}{35d}\]                

D)  \[\frac{12{{\varepsilon }_{0}}A}{35d}\]

Correct Answer: B

Solution :

Here, three slabs are in series, \[{{C}_{eq}}=\frac{{{\varepsilon }_{0}}A}{\left( \frac{d/A}{2}+\frac{d/7}{8/7}+\frac{d/2}{4} \right)}\] \[=\frac{{{\varepsilon }_{0}}A}{\left( \frac{d}{8}+\frac{d}{8}+\frac{d}{8} \right)}=\frac{8{{\varepsilon }_{0}}}{3d}\]