Question

The equivalent capacitance between $A$ and $B$ is (in $pF$)

• A. $25$
• B. $\frac{84}{25}$
• C. $9$
• D. $\frac{25}{84}$
• E. $1$

Answer 1

Answer: (E)

Starting from the right end of the network, three $3\mu F$ capacitors are connected in series. The equivalent capacitance of these three capacitors is
$\frac{1}{C_S}=\frac{1}{3}+\frac{1}{3}+\frac{1}{3}$
$\Rightarrow C_S=1\mu F$
$C_S$ and $2\mu F$ are in parallel. The equivalent capacitance of these two capacitors is
$C_P=C_S+2\mu F=1\mu F+2\mu F=3\mu F$
Proceeding in this way, finally three 3 pF are in series. Therefore, the equivalent capacitance between A and B is
$\frac{1}{C_{AB}}=\frac{1}{3}+\frac{1}{3}+\frac{1}{3}$
$\Rightarrow C_{AB}=1\mu F$