Question

Four metal plates numbered $1,2,3$ and $4$ are arranged as shown below. The area of each plate is $A$ and separation between adjacent plates is $d$. The capacitance of the arrangement is

• A. $\frac{{\epsilon }_{o}A}{d}$
• B. $\frac{3{\epsilon }_{o}A}{d}$
• C. $\frac{4{\epsilon }_{o}A}{d}$
• D. $\frac{2{\epsilon }_{o}A}{d}$

Answer 1

The correct option is B $\frac{3{\epsilon }_{o}A}{d}$

Connecting the point A and B to a battery having emf $V$

Plate 1 is connected to plate 3 and plate 2 is connected to plate 4.


Thus, there are three capacitors in parallel, each of capacitance, $C=\frac{{\epsilon }_{o}A}{d}$ as shown

$C_{eq}=3C$

$C_{eq}=\frac{3{\epsilon }_{\circ }A}{d}$