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 RR, 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 ω\omega, and its location coincides with that of the green point at time t=0t = 0.

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

Determine the value of α\alpha.


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