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 $C′$ is given by

$\frac{1}{C'}=\frac{1}{C_{1}} + \frac{1}{C_{2}}$
$\frac{1}{C'} =\frac{1}{20}+\frac{1}{20}$
$ \Rightarrow \:\: C' = 10 \mu F $
Similarly, $\frac{1}{C''} = \frac{1}{C_3} + \frac{1}{C_4}$
$ \frac{1}{C''} = \frac{1}{10} + \frac{1}{10} \Rightarrow C'' = 5 \, \mu F$
Here C′ and C″ are in parallel. Hence, the equivalent capacitance between points A and B is
$C_{AB} = C' + C'' = 10 + 5 = 15 \, \mu F$