The equivalent resistance of the following infinite network of resistances 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

`R = 4 + (2 xx R)/(R + 2)`
`rArr R^(2) + 2R = 4R + 8 + 2R`
`rArr R^(2) - 4R-8=0`

`R = (4+- sqrt(16 + 32))/2`
`= 2 +- 2sqrt(3)`
`R = 2 + 2sqrt(3) = 5.4 Omega`