Question

Find equivalent capacitance across $\text{A}$ and $\text{B}$

• A. $15\mu \text{F}$
• B. $\frac{28}{3}\mu \text{F}$
• C. $\frac{15}{2}\mu \text{F}$
• D. $\frac{28}{5}\mu \text{F}$

Answer 1

The correct option is C $\frac{15}{2}\mu \text{F}$

Rearrange the circuit into wheatstone bridge as shown in fgure. Also $23\mu \text{F}$ and $12\mu \text{F}$ are in parallel and also $1\mu \text{F}$ and $1\mu \text{F}$ are in parallel.


$\frac{C_1}{C_2}=\frac{35}{7}=5$

$\frac{C_3}{C_4}=\frac{10}{2}=5$

The ratio of $\frac{C_1}{C_2}$ and $\frac{C_3}{C_4}$ proves that, it is a balanced wheatstone. Hence the capacitor $13\mu \text{F}$ is inactive.



$C_{12}=\frac{35\times 7}{35+7}=\frac{35}{6}$

$C_{34}=\frac{10\times 2}{10+2}=\frac{10\times 2}{12}=\frac{5}{3}$

$C_{eff}=C_{12}+C_{34}=\frac{35}{6}+\frac{5}{3}=\frac{45}{6}=\frac{15}{2}$

$C_{eff}=\frac{15}{2}\mu \text{F}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, (c) is the correct answer.