Single phase electric motors need a capacitor to energize a second-phase winding. If the wrong run capacitor is installed, the motor will not have an even magnetic field, and this will cause the rotor to hesitate at those spots that are uneven. This hesitation can cause the motor to become noisy, increase energy consumption, cause performance to drop, and cause the motor to overheat and fail. Additionally, the motor may not run at the correct speed or have the proper horsepower to move the right quantity of air through the coils. The capacitor itself can become overheated and prematurely fail.
The motor should have a rating tag on the housing indicating horsepower and capacitor requirement.