The equivalent resistance between point A and B of an infinite net work of resistances each of `1 Omega` connected

Options

A. infinite
B. `2 Omega`
C. `(1 + sqrt(3))/(2)`
D. zero

Answer

c

Explanation

Let `x` be the total resistance of infinite net work of adding connected to point `A` and `B`. Therefore adding of one step of resistance in the total resistance `x` of the network. Therefore equivalent circuit will be total resistance `A'` and `B'` is `x` given by

`x = 1+ (1xx x)/(1 + x) = (1+ 2x)/(1 + x)`
or `x+x^(2) = 1+ 2x or x^(2) - x- 1 = 0`
`x = (1 +- sqrt(5))/(2) = (1+ sqrt(3))/(2)`
Since since negtive value of `R` is not possible.