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

Resistance of section PSQ
`R_(1)=(R)/(2pir).rtheta=(Rtheta)/(2pi)`, resitance of section `PTQ`
`R_(2)=(Rr(2pi-theta))/(2pir),R_(2)=(R(2pi-theta))/(2pi)`
As `R_(1)` and `R_(2)` are in parallel
So, `R_(eq)=(R_(1)R_(2))/(R_(1)+R_(2))=(Rtheta)/(4pi^(2))(2pi-theta)`