An infinite ladder is constructed with `1(Omega)`and `2(Omega)`resistor as shown in figure.(a)Find the effective resistance between the point A and B. (b) Find the current that passes through the `(2 Omega)` resistor nearest to the battery.

Explanation

Let the effective resistance between points C and D be R,
the the circuit can be redrawn as hown in fig.

the effective resistance between A and B is
`R_eq = 1+(2xxR)/(R+2)`
this resistance `R_eq` can be taken as R beacues if we add one
identical item in infinite item, then the result will be the same. Therefore, `1+(2xxR)/(R+2) R or R+2+2R = R^2 +2R`
`R^2-R-R-2 = 0 or (R+1) (R_2) = 0 or R - 2omega`
`6 =1 i +2 (i//2) = 0 or i = 3 A.`
current in `2omega" is" I//2 = 1.5A`