Question

Find the equivalent capacitance of given circuit between the points $\text{A}$ and $\text{B}$?
$($Take the capacitance of each capacitor as $C=12\mu \text{F})$

• A. $15\mu \text{F}$
• B. $7\mu \text{F}$
• C. $14\mu \text{F}$
• D. $21\mu \text{F}$

Answer 1

The correct option is A $15\mu \text{F}$

Since, line $\text{AB}$ is the a parallel line of symmetry, then all points lying on perpendicular drawn to line $\text{AB}$ will be at the same potential.

Thus point $\text{D}$ is equipotential point, so we can remove the connection at equipotential points as follows.


If we simplify this we get,


Therefore, the equivalent capacitance across $\text{AB}$, we get

$C_{eq}=\frac{3C}{8}+\frac{C}{2}+\frac{3C}{8}=\frac{5C}{4}$

As, $C=12\mu \text{F}$

$\Rightarrow C_{eq}=\frac{5\left(12\right)}{4}=15\mu \text{F}$

Hence, option (a) is the correct answer.