A motor run capacitor is an electrical component used in single-phase AC motors to provide continuous energy to the auxiliary winding, creating a rotating magnetic field for smooth, efficient operation. Unlike a start capacitor, the run capacitor is designed for continuous duty, remaining connected to the motor during the entire run cycle to maintain phase shift and a good power factor. It is essential for the motor's performance, and using an incorrect value can lead to noise, poor performance, and overheating.