Question

What is the equivalent capacitance between $\text{A}$ and $\text{B}$, if each capacitor is of $24\mu \text{F}$ ?

• A. $14\mu \text{F}$
• B. $21\mu \text{F}$
• C. $28\mu \text{F}$
• D. $35\mu \text{F}$

Answer 1

The correct option is B $21\mu \text{F}$

Let each capacitor have the capacitance $C$.

To simplify the circuit, assume the capacitor $1$ to be the equivalent of two capacitors of capacitance $2C$ connected in series as shown in the figure.


Notice how the circuit is symmetrical to the perpendicular line passing through the points $\text{P}$ and $\text{R}$ as shown.


This simply means that the potential of $\text{P}$ and $\text{R}$ are the same. So let's connect them with a conducting wire. The circuit is redrawn

So, equivalent resistance between $\text{A}$ and $\text{B}$ will be

$C_{\text{eq}}=\frac{\left(7C/4\right)}{2}=\frac{7C}{8}$

Given: $C=24\mu \text{F}$

$\Rightarrow C_{\text{eq}}=21\mu \text{F}$

Therefore, option $\left(b\right)$ is the correct choice.