Question

A wire of length L is bent to form a circle, then find a resistance between two points A and B which make an angle of 30?

Answer 1

Let

R=ρLA

If a wire of length L is bend to form a loop, then radius of the loop:

r=L2π

Length of the wire segment l=rθ

Resistance of the first wire segment:

R1=ρrθA

Resistance of the second wire segment:

R2=ρr(2π−θ)A

These two segments are in parallel. Therefore net resistance:

1Rnet=Aρrθ+Aρr(2π−θ)

On solving:

Rnet=(2π−θ)θρr2πA

Substitute r=L2π on the above equation:

Rnet=(2π−θ)θR4Π2