Q: How does a capacitor work in a fan?

A: 

Fan usually operates with a single-phase induction motor. It is non-self-starting. Single-phase supply on the stator of this motor gives alternating magnetic field but we need a rotating magnetic field such as in case of three-phase induction motor to make it self starting.

Methods like

1. Usage of auxiliary winding

2. Usage of capacitors,

are used to split the phase and make it operate like a multi-phase motor, so that the rotating magnetic field is developed and the motor becomes self-starting.

Hence capacitor start capacitor run motors are used in fans

The above information was conveyed in my Electrical Machines 2 subject. Practically when the fan doesn't function up to its maximum speed, A  condenser ( that's how our electrician calls capacitor ) is added to it by the electrician, after that, it tends to operate faster.

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