Question

Find the equivalent capacitance of the system between points $\text{A}$ and $\text{B}$. All the capacitors have equal capacitance $C$.

• A. $\frac{4C}{3}$
• B. $\frac{4C}{9}$
• C. $\frac{7C}{6}$
• D. $\frac{7C}{9}$

Answer 1

The correct option is A $\frac{4C}{3}$

This circuit is symmetrical about the perpendicular bisector of $\text{AB}$. Hence, points $\text{X,Y}$ and $\text{Z}$ are equipotential points.


We can see clearly from above circuit, capacitors $\text{AX}$ and $\text{AY}$ are in parallel combination, and similarly capacitors $\text{1Z}$ and $\text{1Y}$ are also in parallel combination.

So, their equivalent capacitance will be $C+C=2C$.


Since, $2C$ and $C$ are in series, so their equivalent will be

$\frac{2C\times C}{2C+C}=\frac{2C}{3}$


Again, $\frac{2C}{3}$ and $2C$ are in parallel, so, their equivalent capacitance will be $\frac{2C}{3}+2C=\frac{8C}{3}$


Both are in series, so, the equivalent capacitance of the circuit will be

$C_{eq}=\frac{8C}{6}=\frac{4C}{3}$

Therefore, option $\left(A\right)$ is the correct answer.