Two circuits are called circuit A and Circuit B. The equivalent resistance of Circuit A is x and that of Circuit B is y between 1 and 2.

Options

A. `y gt x`
B. `y=(sqrt3+1)R`
C. `xy=2R^2`
D. `y-x=2R`

Explanation

The two circuit can be re-drawn as
So, `x=(R(2R+x))/(3R+x) and Y=2R+(Ry)/(R+y)`
`implies 3Rx+x^2=2R^2+Rx implies. Ry+y^2=2R^2+2R+Ry`
`implies x^2+2Rx-2R^2=0 or y^2-2Ry-2R^2=0`
`x=(-2R+sqrt(4R^2+8R^2))/2 y=(2R+sqrt(4R^2+8R^2))/2`
`x=(sqrt3-1)R =R(1+sqrt3)`
`xy=R^2(sqrt3-1)(sqrt3+1)=2R^2, y-x=2R`