Well depending on the motor used and the size of the fan there can be considerable differences. A desktop fan
and this fan
will require considerably different circuitry to control it. In general a simple rheostat will have to dissipate all of the added power losses to control a fan all by itself. In contrast a modern motor control circuit can vary the motor speed with much less power wasted.
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"Don't disturb my circles." translation of Archimedes last words
Electronic regulators are not usually adjustable. The regulator s controlled through the ground side of the field circuit. An electronic regulator has no moving parts so it can cycle electronically between 10 and 7000 times per second. This quickness means that the regulator can control the output of the alternator more accurately. A zener diode is an electronic component in the voltage regulator that only conducts electricity when a certain voltage is reached. This capability allows an electronic regulator to keep battery voltage between two specified points. It is power losses is less. When we decrease its speed, it gives the needed power for that specific speed. In rheostatic control there is a resistance to increase or decrease step by step to get the desired control speed and the power usage is same for every speed and no power is saved.