# Average Equivalent Ring Resistance

There are two colored points (purely abstract entities) situated on a conducting circular ring.

The ring has a total electrical resistance $$R$$, which is uniformly distributed over its circumference.

The green point is fixed at a particular location on the ring (the particular location doesn't matter).

The red point traverses over the ring's circumference at a constant angular speed $$\omega$$, and its location coincides with that of the green point at time $$t = 0$$.

The time-averaged (over an integer number of rotational periods beginning at $$t = 0$$) equivalent resistance between the two points can be expressed as $$\large{\frac{R}{\alpha}}$$.

Determine the value of $$\alpha$$.

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