Find the capacitance of an infinite circuit formed by the repetitioin of the same link consisting of two indentical capacitors, each with capacitors `C` (fig).

Explanation

The infnite circuit, may be reduced to the circuit, shown in Fig, where, `C_(0)` is the net capacitance of the combination.
So, `(1)/(C + C_(0)) + (1)/(C) = (1)/(C_(0))`
Solving the quadratic,
`C C_(0) + C_(0)^(2) - C^(2) = 0`,
We get,
`C_(0) = ((sqrt(5) - 1))/(2) C`. taking only `+ve` value as `C_(0)` can not be negative.