Question

Find the equivalent resistance between the points a and b of infinite ladder shown in figure (32 - W20a).

Answer 1

Refer image.

Assume $R_{ab}=R.JF$ one more network is added or subtracted resistance remains unchanged. Then the equivalent circuit is

$\Rightarrow \frac{R_r}{R+r}+R=R\Rightarrow 2R_r+r^2=R^2+R_r$

$\Rightarrow R^2-R_r-r^2=0$

$\Rightarrow R=\frac{r\pm \sqrt{r^2+4r^2}}{2}\Rightarrow R=\frac{e+\sqrt{5}r}{2}$