Question

Each capacitor in the given circuit has capacitance C. Find $V_{AB}$.

• A. $\frac{65}{60}V$
• B. $\frac{60}{65}V$
• C. $\frac{30}{35}V$
• D. none of these

Answer 1

The correct option is B $\frac{60}{65}V$

The equivalent circuit is shown in figure below.
here, $C_{eq1}=C+\frac{CC}{C+C}=\left(3/2\right)C$ and

$C_{eq2}=C+\frac{C{C}_{eq1}}{C+C_{eq1}}=C+\frac{C.\left(3/2\right)C}{C+\left(3/2\right)C}=\left(8/5\right)C$
now , $V_{xy}=\frac{C{V}_0}{C+C_{eq2}}=\frac{C\times 12}{C+\left(8/5\right)C}=\frac{60}{13}V$
$V_{pq}=\frac{C{V}_{xy}}{C+C_{eq1}}=\frac{C\times \left(60/13\right)}{C+\left(3/2\right)C}=\frac{120}{65}V$
thus, $V_{AB}=\frac{C{V}_{pq}}{C+C}=\frac{C\times \left(120/65\right)}{2}=\frac{60}{65}V$