How do fans control speed?
Regarding this, how does a capacitor control fan speed?
The idea behind a capacitor regulator remains the same, which is to adjust the voltage across the motor of the fan. Now, when you increase the capacitance, the voltage across the capacitor decreases but that across the fan motor increases. Accordingly, the speed of the fan increases.
In this regard, how do I control the speed of a 3 wire fan?
A 3-wire fan can be controlled using the same kind of drive as for 2-wire fans—variable dc or low-frequency PWM. The difference between 2-wire fans and 3-wire fans is the availability of feedback from the fan for closed-loop speed control. The tach signal indicates whether the fan is running and its rate of speed.
You can change the capacitor and restore the rated speed of fan. However, that will not make it go any faster than its rated speed. The only case it might make the fan faster is if the capacitor used were smaller than ideal to begin with.