Question

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?

Answer 1

When it is bent to form circle.......the ends of diameter seperates the circle into semicircles in such a way that the two semicircles make a parallel connection in the circuit.Also both the semicircles have equal circumference therefore they have equal resistance.We get 4R as the resistances of the semi circles {8R=4R+4R}.

Therefore 1/effective resistence =1/4 + 1/4 =1/2 ===Effective resistance=2R

Answer 2

Since resistance is directly proportional to the length,

When we divide the length of the wire in the form of two semi circular halves, the resistance also gets divided into half. Now, both the resistances are connected in parallel combination.

Therefore,

Total resistance= (r*R)/(r+R)

Total resistance= (4*4)/(4+4)

So,

Total resistance= 2ohms