Question

How Regulator controls the speed of Motor in the fan?

Answer 1

The regulator has spools of wire with different amounts of resistance. When you set the knob at a particular position, you include a certain resistance in series with the fan. A series connection implies the resistance is in line with the fan. This reduces the voltage drop across the fan and its speed to your desired level. The greater the resistance, higher is the voltage drop across it and that lowers the speed of the fan.