Rubin Batfino Illinois Institute
of
Technology Chicago
Using Variable Voltage Transformers to Control Heaters
The most frequent laboratory application of variable voltage transformers is in controlling heaters, although most students will admit that this is usually done in the most unthinking way. If one wishes to double the heat output, he usually doubles the voltage; this actually quadruples the heat output. This note is meant as a reminder, with a graph for ready reference. The wattage or heat output is given by W
=
P R = IV = Va/R
(1)
where I is the current, V is the applied voltage (either rms for ac or straight for dc), and R is the resistance of the heating element. When I is in amperes, F' in volts, and R in ohms, then W is in watts or joules per second. The heat output is directly proportional to the square of the voltage (if R is constant). As a rough approximation, if the heater is not used over too wide a range, the resistance of the heating element can be considered to be constant. Heating elements are commonly made from nichrome wire which has a temperature coefficient of 4 X ohm/ohm degree. This is an increase in resistance of 0.04%/ degree (i.e., a 25'C increase is neceeaary to change the resistance by 1%). The effectis small and is such that the wattage calculated hy equation (1) would be slightly too high if the temperature increase were large. For those wishing more precise control, this factor can be taken into account for heaters used in particular environments.
104
/
Journal o f Chemical Education
Figure 1 shows a typical relationship between wattage and applied voltage for a heater which supplies 100 watts a t 110 v. The ordinate divided by 100 gives a simple multiplying factor for each voltage A copy of this figure would be a handy reference to remind users of this bit of fundamental physics.
Figure 1. Heat output in woth for various voItagos for a heater which gives 1 0 0 woth a t 1 1 0 volts.
