In a uniform ring of resistance `R` there are two points `A` and `B` such that `/_ ACB = theta`, where `C` is the centre of the ring. The equivalent resistance between `A` and `B` is

Explanation

Length of radius `ADB` and `AEB` are ` r theta and r (2 pi - theta)`
resistance of series `ADB` is `R_(1) = p r theta = (R )/(2 pi r) r theta = (R theta)/(2pi) `
resistance of series `AEB` is `R_(2)= (R )/(2 pi r) r (2 pi theta) = (R(2pi theta))/(2pi) `
Here `R_(1) and R_(2)` are in parrelel between A and B their equivalent resistance
`R_(eq)= (R_(1)R_(2))/(R_(1) + R_(2)) = ((R theta)/(2pi) xx (R(2pi - theta))/(2pi))/((R theta )/(2 pi) + (R(2pi - theta))/(2pi)) = (R theta (2pi - theta))/(4pi^(2))`