Find the equivalent resistance between thepoints a and b of the infinite ladder shown in figure.

Explanation

Let the equivalent resistance between a and b be R.As the ladder is inifinite, R is also the equivalent resistence of the ladder ro the right of the points c and d. Thus,we can replace the part to the right of cd by a resistances R and redraw the circuit as in figure.
`R=r+(rR)/(r+R)`
`or, rR+R^(2)=r^(2)+2rR`
or,`R^(2)-rR-r^(2)=0`
or,`R=r+sqrt(r^(2)+4r^(2))/2=(1+sqrt5)/2r.