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 equivalent resistance of the
combination be R .
So, (2R/(r+2)+1 = R
` 3R + 2 = R^2 + 2R `
` rArr R^2 - R - 2 = 0 `
` rArr R = (+1+(sqrt(1+4.12))/2.1)`
` = (+1+(sqrt(9))/2.1) = 2 Omega`
(b) Total current send by battery
` = -6/R_eff = 6/2 = 3 `
Potential difference between A and B
` 3.1 + 2i = 6 `
` rArr 2i = 3 `
` rArr i = 3/2 = 1.5A ` .