The equivalent capacitance of an infinite ladder of a circuit formed by the repetition of the same link consisting of identical capacitors, each with capacitance `C` , is
.

Options

A. `zero`
B. `(sqrt5-1)/2C`
C. `(sqrt5+1)/2C`
D. infinite

Answer

B

Explanation

Let capacitance between `A` and `B` be `x`. If we remove the first two capacitors. Then capacitance across `D` and `E` will also be `x` So the circuit can be redrawn as follows:
.
`x=(C(C+x))/(C+(C+x))`
Solve to get `x=(sqrt5-1)/2C`.