The easiest way to regulate the speed of an electric motor, is to decrease / increase the supplied voltage. This can be done by putting an adjustable serial resistor in series with the motor.

This is exactly how my first 'Scalectric' speed control worked. It had a high-resistance wire wrapped around a core and when you pressed the accelerate button the contact moved from the point of highest resistance (longest piece of wire) to the point of lowest resistance (shortest piece of wire.)

This method has a big drawback - energy wasted as heat.

A quick example:
We have a 12V battery connected to a speed control with a resistance of 10 Ohms and an electric motor with a resistance of 2 Ohms (we will ignore the inductance of the motor to make the calculations easier. )

The total current:
I = V / R
=12V / 12R
=1A

The voltage across R1:
V = I x R
=1A x 10R
=10V

The voltage across the electric motor:
V = I x R
=1A x 2R
=2V

The power used by the motor:
P = V x I
=2V x 1A
=2Watt

The power wasted on R1:
P = V x I
=10V x 1A
= 10 Watt

Thus most of the energy goes to the speed control (R1) and not to the motor! Not only will resistor R1 get very hot, but the battery will also drain quickly. There must be a better way! Fortunately, there is.

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