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

Answer

A, B, C, D

Explanation

Circuit A: `x = (R(2R+x))/(3R+x) or 3Rx + x^(2) = 2R^(2)+Rx`
or `x^(2) +2Rx - 2R^(2) = 0 or x = (-2R+sqrt(4R^(2)+8R^(2)))/(2)`
or `x = - (2R+2sqrt(3R))/(2) = (sqrt3-1)R`
,
Circuit B: `y = (yR)/(y +R) +2R or y^(2) + Ry = yR +2Ry +2R^(2)`
or `y^(2) - 2YR - 2R^(2) = 0 or y = (sqrt3+1)R`