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

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}+\ldots \ldots \ldots \ldots \ldots C_{n} $
$C_{\text {eq }} =1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\ldots \ldots \ldots \ldots $
$=\frac{1}{1-\frac{1}{2}}=2 \,\mu F$