A and B are two points on a uniform ring of resistance R. The ∠ACB = θ, where C is the centre of the ring. The equivalent resistance between A and B is:

The correct option is Rθ(2π−θ)/4π²
Resistance per unit length = ρ = R/2πr
Lengths of section AP and AQ are rθ and r(2π−θ)
Resistance of sections AP and AQ are
R₁ = ρrθ = (R/2πr)rθ = Rθ/2π
and R₂ = (R/2πr)r(2π−θ) = R(2π−θ)/2π
As R₁ and R₂ are in parallel between A and B, their equivalent resistance is
Req = R₁R₂/(R₁+R₂) = (Rθ/2π)[R(2π−θ)/2π] / [(Rθ/2π) + R(2π−θ)/2π] = R²θ(2π−θ)/4π² / [R(θ + 2π−θ)/2π] = R²θ(2π−θ)/4π² / (2πR/2π) = Rθ(2π−θ)/4π².