Question

Find out the effective capacitance between points A and B as shown in the figure. Here $C_1=C_2=20\mu F$ and $C_3=C_4=10\mu F$

• A. $10\mu F$
• B. $15\mu F$
• C. $20\mu F$
• D. $25\mu F$

Answer 1

Answer: (B)

Here, $C_1$ and $C_2$ are in series. Hence, their effective capacitance $C\prime$ is given by

$\frac{1}{C^{\prime }}=\frac{1}{C_1}+\frac{1}{C_2}$
$\frac{1}{C^{\prime }}=\frac{1}{20}+\frac{1}{20}$
$\Rightarrow C^{\prime }=10\mu F$
Similarly, $\frac{1}{C^{\prime \prime }}=\frac{1}{C_3}+\frac{1}{C_4}$
$\frac{1}{C^{\prime \prime }}=\frac{1}{10}+\frac{1}{10}\Rightarrow C^{\prime \prime }=5\mu F$
Here C′ and C″ are in parallel. Hence, the equivalent capacitance between points A and B is
$C_{AB}=C^{\prime }+C^{\prime \prime }=10+5=15\mu F$