For infinite ladder network containing identical resistance of `R Omega` each, are combined as shown in figure. The equivalent resistance between `A` and `B` is `R_(AB)` and between `A` and `C` is `R_(AC)`. Then the value `(R_(AB))/(R_(AC))` is :

Options

A. `(3)/(4)`
B. `(4)/(3)`
C. `2`
D. `(1)/(2)`

Answer

A

Explanation

Let the equivalent resistance of one infinite ladder be x. Then the complete network reduces to

`:. R_(AB) = (x xx 3x)/(x + 3x) = (3)/(4) x`
and `R_(AC) = (2x xx 2x)/(2x + 2x) = x`
Hence `(R_(AB))/(R_(AC))= (3)/(4)`