Question

A uniform wire of resistance 20 ohm is bent in the form of a circle. If the resistance between points A and B is 2 ohm then, what is the length of the shorter one?

Answer 1

Resistance given here is 20 ohm

As it is bend into wire so, L = 2πr

so, Ri = Rho×2πr/A = 20 ohm

Now, resistance between two point at the end of diameter can be given by

1/R = (1/Ri/2)+(1/Ri/2) {as half of the wire is attached to the other half so it may be considered as parallel connection}

1/R = 1/10+1/10 { Ri = 20ohm so Ri/2 = 10 ohm }
or 1/R = 2/10
so, R = 5 ohm ,(across ends of diameter)