Question

A wire of resistance 2 ohms per meter is bent to form a circle of radius 1 m. The equivalent resistance between its two diametrically opposite points, A and B as shown in the figure is

(a)  π Ω

(b)\(\frac{π}{2}\) Ω

(c)2πΩ

(d)\(\frac{π}{4}\) Ω

Answer 1

length of a half circuit that is the half circumference of the circle = πr

Resistance is given as 2 ohm per meter

Resistance in 1 m wire=2ohm

Resistance in πr m wire= 2 πr

So as per the given diagram we can compare the given circuit to a parallel connection simple circuit.

Equivalent Resistance=

1/R=1/2π + 1/2π

1/R= 2/2π

R=π ohm