Find the equivalent capacitance of the infinite ladder shown in the figure (a) between the points A and B

Explanation

If we look at the infinite ladder between M and N the arrangement obtained is exactly same as we have between A and B .
Now suppose that the equivalent capacitance between A and B is x. Then the equivalent capacitance between M and N is also x . Hence

Thus `x=C + (2Cx)/(2C+x) =(2C^(2)+3Cx)/(2C+x)`

or `x^(2)-Cx-2C^(2)=0 "or" x=2 C `