Question

For given combination of capacitor where each capacitance is C

Equivalent capacitance of the system is

• A. $\frac{38}{33}$
• B. $\frac{35}{32}$
• C. $\frac{38}{35}$
• D. $\frac{33}{38}$

Answer 1

The correct option is A $\frac{38}{33}$

By folding lower side over upper side we get. The circuit is symmetric along the vertical line going through the centre of the circuit. Therefore, the following alteration can be made.
Now by, comibing the resistors in series and parallel, the circuit gets converted to,

The potential difference across 'C' is assumed to be y and, the potential difference across the vertical '2C' is x.

By applying KCL at the node on the top right corner and at node P, the following equations can be obtained.

3c(100-2x)+2c(y-x) = 2cx
$\Rightarrow$ 5x - y = 150 --(1)
2c(y-x)+cy = 2c(100 - 2y)
$\Rightarrow$ 7y - 2x = 200 --(2)
Solving (1) and (2)
x = $\frac{1250}{33}$ and $y=\frac{1300}{33}$

The charge suppied by the battery is 2cx + cy. Say, the equivalent capacitance is $C_{eq}$. Then,
$2cx+cy=100C_{eq}$
$C_{eq}=\frac{38}{33}$