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Jack of some trades
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Long story short, on single-phase capacitor motors, large values of capacitance are used for starting and much smaller values are used for running. Yet it would seem that the amount of electrical phase shift needed is dictated and fixed by the physical relationship between the main and auxiliary windings around the stator core. (E.g. on a small four-pole fan motor, the auxiliary winding is 45 degrees off from the main one.) Does the rotation of the rotor change the value of capacitance needed for a given degree of electrical phase shift, or is something else going on here?