A uniform wire of resistance 36 is bent in the form of a complete circle. The equivalent resistance between two points on the circumference of the circle, which subtend an angle of 60^ at the centre, is _____ .

Step-by-step solution

Total resistance of the wire, R = 36 . When bent into a circle, the two points subtending 60^ at the centre divide the wire into two arcs. The resistance of the minor arc is R₁ = 60^ 360^ 36 = 6 . The resistance of the major arc is R₂ = 360^ - 60^ 360^ 36 = 30 . These two parts are connected in parallel across the two points. The equivalent resistance R_ eq is given by: R_ eq = R₁R₂ R₁ + R₂ R_ eq = 6 30 6 + 30 = 180 36 = 5 . Answer: 5