Find the capacitance of the infinite ladder between points X and Y, Fig.

Answer

`2 muF`

Explanation

Let `C` be the equivalent capacitance of the infinite network. It consists of repeating unit of two capacitors of `1 muF` and `2 muF`. Let equivalent capacitance of that unit be `C`. The network wll appear as shown in Fig.

Eqivalent capacitance of new arrangment must be equal to `C`.
`C =1 + (2 xx C)/(2 + C)`
`C^(2) - C - 2 = 0 :. C = 2 muF` or `-1 muF`
As capacitance cannot be negative, so equivalent capacitance is `2 muF`