Question

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

• A. $\frac{7C}{8}$
• B. $\frac{7C}{4}$
• C. $\frac{9C}{2}$
• D. $\frac{9C}{4}$

Answer 1

The correct option is A $\frac{7C}{8}$

Circuit diagram can be redrawn asThis circuit is symmetrical about perpendicular bisector of $AB.$ Hence, point $X$ and point $Y$are at same potential.
Between $1and(X,Y)2CandC$are parallel.
So, their equivalent $=2C+C=3C$

Similar case in the right part of the circuit,

$Cand3C$ are in series, so their equivalent = $\frac{C\times 3C}{C+3C}$= $\frac{3C}{4}$
Now,
Now, $\frac{3C}{4}$ and $C$ are in parallel. So, their equivalent capacitance
$=\frac{3C}{4}+C=\frac{7C}{4}$


Both are in series.
So equivalent capacitance,
$C_{eq}=\frac{\frac{7C}{4}\times \frac{7C}{4}}{\frac{7C}{4}+\frac{7C}{4}}=\frac{7C}{8}$