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

Options

A. `(3)/(4)`
B. `(4)/(5)`
C. 2
D. `(1)/(2)`

Answer

A

Explanation

Let the equivalent resistance of one infinite ladder be x. Then the complete network reduces to
`therefore R_(AB)=(x xx 3x)/(x +3x)=(3)/(4)x`
and `R_(AC)=(2X xx 2x)=x`

Here `(R_(AB))/(R_(AC))=(3)/(4)`