Single-phase motors do not produce strong starting torque on their own. A start capacitor in series with the start winding shifts the current's timing, creating a stronger rotating field at start-up. The compressor turns over quickly, spends less time at high current, and copes better with marginal voltage. Some compressors also have a run capacitor that stays connected to improve running efficiency.
Capacitors age. Heat in the machine compartment, frequent starts and voltage spikes gradually reduce their capacity. A weak capacitor makes the compressor slow to start or causes it to trip on overload, especially on hot days or in the evening when voltage sags. A bulging, leaking or cracked capacitor should be replaced with one of the same rating.
Capacitors can hold a charge after power is removed, so testing and replacement is a job for a trained technician. When starting problems appear, a technician will typically test the capacitor and relay before condemning the compressor.