A metal wire of resistance 3 Ω is elongated to make a uniform wire of double its previous length. This new wire is now bent and the ends joined to make a circle. If two points on this circle make an angle 60 o at the center, the equivalent resistance between these two points will be:

Step-by-step solution

We know, R = ρ l A = ρ l 2 A l = ρ l 2 V o l u m e R ∝ l 2 , if the volume is constant. ∴   New resistance = 4 R R 1 = 4 R 360 × 300 = 10 R 3 R 2 = 4 R 360 × 60 = 2 R 3 ∴ Equivalent resistance R e q = R 1 R 2 R 1 + R 2 = 10 R 3 × 2 R 3 10 R 3 + 2 R 3 = 5 R 9 = 5 3   Ω