Question

A wire has resistance 12 ohms. It is bent, and its two ends are connected to form a circle. The effective resistance between the two points on any diameter of the circle is:

(a) 3 ohms
(b) 6 ohms
(c) 12 ohms
(d) 24 ohms

Answer 1

The effective resistance between the two points on any diameter of the circle formed by the bent wire is 6 ohms.

Step-by-step explanation:

To find the effective resistance between the two points on any diameter of the circle formed by the bent wire, we can use the concept of parallel resistance.

When the wire is bent into a circle, the two ends form the two points on any diameter. Since the two ends are connected, the resistances at these points are in parallel.

The formula for calculating the total resistance in a parallel circuit is:

1/Reff = 1/R1 + 1/R2 + ... + 1/Rn

Since the resistance of the wire is 12 ohms, the effective resistance between the two points on any diameter of the circle is:

1/Reff = 1/12 + 1/12 = 2/12 = 1/6

Therefore, the effective resistance between the two points on any diameter of the circle is 6 ohms.