In a series heater string each tube heater is actually a resistance. Each resistance drops or uses a certain voltage. The voltage drops must add to approximate the supply voltage. A good way to check this out is to look inside of an old transformerless tube type radio. You can add the first two numbers of the tubes which are your operating voltages and come up with somewhere near line voltage.
You may want to get to know the basics of electronics to get a decent understanding of things like series circuit arrangements as opposed to parallel. There are even combinations of the two which is a bit more difficult to grasp. Frankly, this knowledge IMO is essential to anyone expecting to be a radio or TV doctor. We live in a plug and play age of electronics, but really the old stuff I think required a good knowledge base of the understanding of circuits, components, and the tools of the trade and how to use them being volt, ampere, and resistance meters to keep it basic.
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"Face piles of trials with smiles, for it riles them to believe that you perceive the web they weave, and keep on thinking free"
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