Question

a wire of resistance 5 ohm is bent in the the form of a circle . what is the effective resistance between the two ends of any diameter of the circle?

Answer 1

Resistance of the wire, R = 5 ohm
Both the resistance are in parallel.

So the equivalent resistance of the wire along the points AB is

1/R= 1/(R/2) + 1/(R/2)

1/R= 1/ 2.5 + 1/ 2.5 = 4/5

R = 1.25 ohms

Answer 2

Answer:

Explanation:

Solution :-

The length of the wire between two points at the ends of a diameter of a circle is half of the whole wire The resistance of a conductor is directly proportional to its length.

Then,

Resistance of a wire between two points at the ends of any diameter

= 5  Ω/2 = 2.5  Ω

These two sections of the wire from a parallel combination of two resistances.

If R is the effective resistance between the two points,

Then

1/R = 1/2.5  Ω + 1/2.5  Ω = 2/2.5  Ω

This gives , R = 2.5/2  Ω = 1.25  Ω

Hence,  the effective resistance between the two ends of any diameter of the circle is 1.25  Ω.