In the infinite gride. If the value of `r = 2 (sqrt(5 - 1)) Omega`. Find the Equivalent resistance between the point `a` and `c`.

Options

A. `6 (sqrt(5 - 1)) Omega`
B. `4 (sqrt(5 - 1)) Omega`
C. `4 Omega`
D. none of these

Answer

C

Explanation

(c ) Due to symmetry, the line of resistors passing through `b` will be useless
`r_(eq) = 2r + (r r_(eq))/(2 r + r_(eq)) implies r_(eq) = (1 + sqrt5) r`
`= (sqrt( 5 + 1)) 2 (sqrt(5 - 1)) = 4 Omega`