Question

An infinite number of identical capacitors each of capacitance $1\mu F$ are connected as in the figure. The equivalent capacitance between $A$ and $B$ (in $\mu F)$ is______

Answer 1

Answer: 2

For capacitors in series $C_{eq}=\frac{C_1{C}_2}{C_1+C_2}$
As $C_1=C_2\cdots$
$C_{\text{oq }}=\frac{C}{n}$
For capacitors in parallel
$C_{eq}=C_1+C_2+C_3+\dots \dots \dots \dots \dots C_n$
$C_{\text{eq }}=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\dots \dots \dots \dots$
$=\frac{1}{1-\frac{1}{2}}=2\mu F$