Question

Find the equivalent capacitance of the combination between points $\text{P}$ and $\text{Q}$.

• A. $5\mu \text{F}$
• B. $12\mu \text{F}$
• C. $10\mu \text{F}$
• D. $16\mu \text{F}$

Answer 1

The correct option is C $10\mu \text{F}$

The loop $\text{ABCDA}$ is a balanced wheat stone's bridge.

Equivalent capacitance of balanced wheatstone bridge is,

$C^{\prime }=\frac{C_1{C}_4}{C_1+C_4}+\frac{C_2{C}_5}{C_2+C_5}$

$\Rightarrow C^{\prime }=\frac{10\left(8\right)}{10+8}+\frac{5\left(4\right)}{5+4}=\frac{20}{3}\mu \text{F}$

$C_6$ and $C_7$ are in series their effective capacitance $C^{\prime \prime }$ is

$C^{\prime \prime }=\frac{C_6{C}_7}{C_6+C_7}=\frac{10\left(5\right)}{10+5}=\frac{10}{3}\mu \text{F}$

Since $C^{\prime }$ and $C^{\prime \prime }$ are in parallel. So, the equivalent capacitance between points $\text{P}$ and $\text{Q}$ is

$C_{eqv}=C^{\prime }+C^{\prime \prime }=\frac{20}{3}+\frac{10}{3}=10\mu \text{F}$

Hence, option (c) is the correct answer.