Question

Suppose you need to control the speed of a motor that takes 1200W at full power. This is typical
of a big domestic vacuum-cleaner or a washing-machine motor, and is a little more power than a
single-bar electric fire uses. First, you try the obvious method: a variable resistor in series, and no
other complications. If you adjust the resistor to have a very high value so little current passes,
this will make the motor run very slowly or stop. At the other extreme, if you adjust the resistor to
have a very low or zero resistance, then the motor will run at full power. So far, so good. But,
suppose I tell you to run the motor at one-quarter of its full power? To do this, you adjust the
series variable resistor so its resistance is exactly the same as the motor’s resistance. Then, the
supply voltage splits equally between the motor and resistor, and also the current is halved
because the total resistance is double that of the motor alone. Therefore, the power in the motor
(= current  voltage) is now 1200/(2  2) = 300W as required.
(a) Under these conditions, what power is now wasted as heat in the variable resistor? Is this a
lot? (e.g., how does it compare with the maximum power allowed in the variable resistors
supplied in your parts kit?)
While pondering what to do about this, you remember this experiment and PWM, and you think
about discarding the variable resistor and instead connecting an active semiconductor device such
as a transistor in series with the motor.

(b) What current passes through the transistor when it is switched OFF? So, since power is the
product of voltage and current, what power is wasted in the transistor when it is switched OFF?
(c) What voltage appears across the transistor when it is switched ON? (Careful – I didn’t ask,
this time anyway, what voltage appears across the motor! Assume for simplicity that if the
transistor were switched ON continuously, the motor would run at exactly full power just as it
would if connected directly to the supply.) So, since power is voltage multiplied by current, what
power is
wasted in the transistor when it is switched ON?
(d) So, using PWM, and from your answers to parts (b) and (c) of this question, what average
power is wasted in the transistor? How does this depend upon the duty cycle value? Is this an
improvement over using a series variable resistor?

Answer 1