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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