Question

Find the equivalent capacitance between $\text{A}$ and $\text{B}$.

• A. $\frac{C}{2}$
• B. $\frac{3C}{2}$
• C. $2C$
• D. $\frac{5C}{2}$

Answer 1

The correct option is B $\frac{3C}{2}$

The given circuit is symmetrical about line $\text{ED}$.

We can see that due to symmetry, whatever charge is flowing through branch $\text{AE}$ will enter branch $\text{EB}$.

Similarly, charge going into branch $\text{AD}$ will enter branch $\text{DB}$.

$\therefore$ No charge will enter branch $\text{ED}$ or potential of point $\text{E}$ & $\text{D}$ are equal.

This neglecting the capacitors in $\text{ED}$ branch.


In each branch, the set of two capacitors are in series.

$\therefore C_{eq}=\frac{C\times C}{C+C}=\frac{C}{2}$


Now the net capacitance of the circuit between $\text{A}$ & $\text{B}$:

$C_{net}=\frac{C}{2}+\frac{C}{2}+\frac{C}{2}=\frac{3C}{2}$

Hence, option $\left(b\right)$ is correct.