question_answer

Four metallic plates each with a surface area of one side A are placed at a distance d from each other. The plates are connected as shown in the circuit diagram. Then the capacitance of the system between \[a\] and \[b\] is

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

B)                    \[\frac{2{{\varepsilon }_{0}}A}{d}\]

C)                    \[\frac{2{{\varepsilon }_{0}}A}{3d}\]

D)                    \[\frac{3{{\varepsilon }_{0}}A}{2d}\]

Correct Answer: D

Solution :

                   The given circuit can be redrawn as follows Þ \[{{C}_{eq}}=\frac{3C}{2}=\frac{3{{\varepsilon }_{0}}A}{2d}\]