Resistance per unit length
=ρ=2πrR
Lengths of sections A P B
andAQB are
rθ and
r(2π−θ)
Resistances of sections A P B
andAQB are
R1=ρrθ=2πrRrθ=2πRθ and R2=2πrRr(2π−θ)=2πR(2π−θ)
As
R1andR2 are in parallel between A and B
,theirequivalentresistanceisReq=R1+R2R1R2=2πRθ+2πR(2π−θ)2πRθ⋅2πR(2π−θ)=2πR[θ+2π−θ]4π2R2θ(2π−θ)=4π2R(2π−θ)θ$$