The equivalent resistance of the following infinite network of resistance is

Options

A. Less than `4 Omega`
B. `4 Omega`
C. more than `4 Omega` but less than `12 Omega`
D. `12 Omega`

Answer

C

Explanation

(c ) `R = 2 + 2 + (2 xx R)/(2 + R)`
`implies 2R + R^(2) = 8 + 4 R + 2 R`
`implies R_(2) - 4R - 8 = 0`
`implies R = (4 +- sqrt(16 + 32))/(2) = 2 +- 2 sqrt3`
`R` cannot be negative, hence
`R = 2 + 2 sqrt3 = 5.46 Omega`