Question

a uniform wire of resistance 36 ohm is bent in tne form of a circle .calculate the effective resistance across the points A and B.

Answer 1

a uniform wire of resistance 36 ohm is bent in tne form of a circle . then we have to find effective resistance across the point A and point B.

because wire is bent into circle and then points A and B divide the circle into two half semicircle as shown in figure.

so, length of upper semicircle wire = length of lower semicircle wire = half of length of wire.

and we know, resistance of wire is directly proportional to length of it.

so, resistance of each semicircular wire is R/2 = 36/2 = 18 ohm.

now, it is clear that two wires of resistance 18ohm are joined in parallel, then effective resistance across the points A and B will be , Req = 18 × 18/(18 + 18) = 9 ohm.

hence, effective resistance across the points A and B will be 9ohm.