An infinite sequence of resistance is shown in the figure. The resultant between `A` and `B` will be, when `R_(1) = 1 ohm` and `R_(2) = 2 ohm`

Options

A. `"Infinity"`
B. `1 Omega`
C. `2 Omega`
D. `1.5 Omega`

Answer

C

Explanation

(c ) Let the resultant be `R`. If we add one more branch, then the resultant resistance would be the same because this is an infinite sequence
`:. (R R_(2))/(R + R_(2)) + R_(1) = R implies 2R + R + 2 = R^(2) + 2R`
`implies R^(2) - R - 2 = 0 implies R = - 1R = 2 ohm`