A wire of resistance 8R is bent in the form of a circle. What is the effective resistance between the ends of a diameter AB?

The resistance of the wire is = 8 Ω.

So, resistance per unit length of the wire, if its length is L, will be (8/L) Ω.

When the wire is bent in circular form of radius ‘r’, the circumference of the circle is, L = 2πr

=> r = L/2π

A and B are two opposite points on the wire when bent in circular form. So, the wire is divided into two equal parts each of length equal to the half of the circumference of the circle.

Resistance of one part between A and B is = (8/L)(πr) = (8/L)[π(L/2π)] = 8/2 = 4 Ω

Similarly, resistance of the other part is also 4 Ω.

These two 4 Ω are connected in parallel across A and B.

So, equivalent resistance will be, 1/R = ¼ + ¼

=> R = 2 Ω

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Reffective=R/4

Proof:

1/R=1/R1+1/R2

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