A run capacitor uses the charge in the dielectric to boost the current which provides power to the motor. It is used to maintain a charge.
In AC units, there are dual run capacitors. One capacitor provides power to the fan motor. The other sends power to the compressor. Run capacitors measure in at approximately 7-9 micro-Farads.
The value or rating of the run capacitor must be accurate. If the value is too high, the phase shift will be less than perfect and the winding current will be too high. If the capacitor value/rating is too low, the phase shift will be higher and the winding current will be too low. If run capacitors are not ideal, then the motor could overheat and the true torque will not be enough to drive current.