Question

In the figure shown, the equivalent capacitance between ${}^{\prime }{A}^{\prime }$ and ${}^{\prime }{B}^{\prime }$ is:

• A. $3.75F$
• B. $2F$
• C. $21F$
• D. $16F$

Answer 1

The correct option is B $2F$


As $3F$ and $6F$ are in series, effective capacitance between C and B is $\frac{3\times 6}{3+6}=2F$.

Circuit can be simplified as



It is a balanced wheatstone bridge. So, $5F$ can be removed.

From circuit we can observe that, series setup of $1F$ and $2F$ is connected in parallel with series setup of $2F$ and $4F$. So, effective capacitance between A and B is

$C_{AB}=\frac{1\times 2}{1+2}+\frac{2\times 4}{2+4}$
$C_{AB}=\frac{2}{3}+\frac{4}{3}$
$C_{AB}=2F$