Question

Figure shows four plates each of area S separated from one another by a distance d. What is the capacitance between A and B?

• A. $\frac{4{\epsilon }_{0}A}{d}$
• B. $\frac{3{\epsilon }_{0}A}{d}$
• C. $\frac{2{\epsilon }_{0}A}{d}$
• D. $\frac{{\epsilon }_{0}A}{d}$

Answer 1

Answer: (C)

$\frac{2{\epsilon }_{0}A}{d}$

Two plates of B are joined together and therefore cannot form a capacitor. Thus, there are only two capacitors in parallel-one between the upper most plate and the next one can second between the lower most plate and the one above it.
Hence, $C=C_1+C_2=\frac{{\epsilon }_{0}A}{d}+\frac{{\epsilon }_{0}A}{d}=\frac{2{\epsilon }_{0}A}{d}$.