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.

Answer

`1.5A`

Explanation

Let `x` be the equivalent resistance of uniform network .Since the network is uniform its total resistance `x` will not charge with the addition of one more unit of two resistance. Then the equivalent circuit of network will be as .Here the total resistance of network is `x = 1 + (2 xx s)/(2 + s) = (2 + 3s)/(2+ s)`
or `2 s + x^(2) = 2 + 3 x or x^(2) - x- 2 = 0`
On solving we get `x = 2 Omega`

Current in the circuit, `I = (epsilon)/(x) = (6)/(2) = 3A`
voltage drop across `1 Omega = 3 xx 1 = 3V`
`:.` Voltage drop across C and `D = 6 - 3 = 3V`
Hence drop in arm `CD = 3//2 = 1.5 A`