Question

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

• A. $7\mu \text{F}$
• B. $14\mu \text{F}$
• C. $21\mu \text{F}$
• D. $12\mu \text{F}$

Answer 1

The correct option is B $14\mu \text{F}$

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

Thus point $\text{D}$ is equipotential point, we can remove the connection at equipotential point, as follow



On simplifying the above circuit we get,


Therfore, the equivalent capacitance across $\text{AB}$,

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

$\Rightarrow C_{eq}=\frac{7C}{6}$

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

$\Rightarrow C_{eq}=14\mu \text{F}$

Hence, option (b) is the correct answer.

Why this question : Since points $\text{A}$ and $\text{B}$ are connected to a battery and it is also line of symmetry for the given circuit, thus all points lying on perpendicular drawn to line $\text{AB}$ are at its same potential.