This article is from the Antique Radios And Phonographs FAQ, by Hank van Cleef vancleef@netcom with numerous contributions by others.
The heater serves as a voltage divider. Resistance of cold
filaments is much lower than when they are hot, and connecting a bulb in
series will put almost the whole 110 VAC across it until the heaters
warm up. The plate current flows through the bulb/heater to balance the
current once the tubes are warmed up. Note that this also applies to
ballast tube setups---the ballast resistance is designed to increase as
the set warms up. It's a way of putting a cheap light bulb in a cheap
radio. (Historical note: This is an interview question I used to use
when interviewing engineering applicants in the fifties and sixties).
 
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