Question

Find equivalent capacitance between points A and B :
[Assume each conducting plate is having same dimensions and neglect the thickness of the plate, $\frac{{\epsilon }_{0}A}{d}=7\mu F$, where A is area of plates]

• A. $7\mu F$
• B. $11\mu F$
• C. $12\mu F$
• D. $15\mu F$

Answer 1

Answer: (B)

$11\mu F$

Here, $C=\frac{A{ϵ}_0}{d}=7\mu F$. The equivalent circuits are shown in the figure.
Now, $C_{eq}=C+\frac{C\left(C/2\right)}{C+\left(C/2\right)}=C+\left(1/3\right)C=\left(4/3\right)C$
and $C_{AB}=C+\frac{C_{eq}C}{C_{eq}+C}=C+\frac{\left(4/3\right)CC}{\left(4/3\right)C+C}=C+\left(4/7\right)C=\left(11/7\right)C=\left(11/7\right)\left(7\right)=11\mu F$