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Dennis:
I am back to answer your question.
You are assuming the lamp resistance is constant relative to voltage. This is not what actually happens. Tungsten has a positive coefficient of resistance with respect to temperature. When you raise the temperature by raising the voltage you increase the resistance. Edison's carbon filament had a negative temperature coefficient.
See my web site at
http://beta-a2.com/EE-photos.html . Use Microsoft Internet Explorer. At photo P9 is a plot of power vs voltage for a 75 W tungsten filament bulb. At photo P11 is an Edison carbon filament.
For the tungsten lamp at 120 V and 75 W the resistance is 192 ohms. At 60 V it is about 27 W and 133 ohms. For the Edison bulb 192 ohms at 120 V and about 240 ohms at 60 V.
Note: the power curve is more straight for the tungsten lamp than for the carbon lamp.
When I set up actual 75 W and 100 W bulbs in series across 240 V I used the actual components as their own analog computer to determine the current and voltages. You could now adjust supply voltage and get current and voltages vs total voltage for the individual components.
Graphically you can calculate the operating point in the following way. This was or is typically done in vacuum tube or transistor circuits.
Create a graph of current vs voltage for each bulb. Make a new graph with the Y axis current, and X voltage. Mark X from 0 to 240 V. Pick the plot for one of the bulbs and put it on this new plot in the same orientation. The second plot is mirrored about the Y axis and its 0 voltage point placed at 240 V. Where these two curves intersect is the steady state operating point.
When I applied power to my series string there was a very short moment when the 75 W was brighter than its steady state value. This is because its thermal time constant is shorter than the 100 W.
Also on my web site, in photos P1 and P2, is shown the effect on peak inrush current of turn on at a voltage peak vs a zero crossing.
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