Question

Find the capacitance of an infinite circuit formed by the repetition of the same link consisting of two identical capacitors, each with capacitance $C$ (Fig.).

Answer 1

The infinite circuit, may be reduced to the circuit, shown in the Fig. where, $C_0$ is the net capacitance of the combination.

So, $\frac{1}{C+C_0}+\frac{1}{C}=\frac{1}{C_0}$

Solving the quadratic,

$C{C}_0+C_0^2-C^2=0$,

We get,

$C_0=\frac{(\sqrt{5}-1)}{2}C$, taking only $+ve$ value as $C_0$ can not be negative.