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A Practical Problem in E&M



Hi all-
I'm building a 4 A, 30 V power supply, but I want the output
voltage to be variable. The power supply runs off the 115 V household
60 Hz AC. I had a "brilliant" idea for controlling the voltage; I went
to the local hardware store and bought a dimmer, such as you can install
to dim your house lights.
I forgot to say that the output of the power supply is DC; it
uses a step-down transformer, a full-wave bridge rectifier, and a filter
made of a choke followed by a shut capacitor. I put the dimmer in the
primary circuit of the transformer which was fused with a 2 A fuse. I
connected the DC output to a 1 K resistor.
I blew 9 fuses. The fuses blew when I cranked the output up to
about 27 V. So I went to my friendly EE down the hall and asked him
what I did wrong. He explained that it was the harmonics generated by
the dimmer.
So here's the practical physics problem: explain what is wrong
with the following reasoning. The harmonics are all at frequencies
that are multiples of 60 Hz. The only element in the prmary circuit
besides the dimmer is the transformer, which is inductive. Inductive
reactance is proportional to frequency, so the currents from the
high frequency voltage components should go down with increasing frequency.
Conclusion (false): the harmonics generated by the dimmer were not
responsible for blowing the fuses.
Note "shut capacitor" in para 2 should read "shunt capacitor".
Regards,
Jack