The heating current is not common to the bias current. There is .01575 amps of heating current flowing across the two 200 ohm resistors in series but that current does not flow to or from ground nor does it flow across the vacuum to the plate. The heating current only flows through the filament and the 'two resistors in series' which are in parallel to the filament. There is a total of 100ma of bias current flowing through the two 200 ohm resistors. That current flows from ground to the filament and across the vacuum to the plate. Each resistor has the same amount of bias current flowing through it and in the same direction, from ground to the filament. Each resistor has the same amount of heating current flowing through it in one direction (negative to positive of the filament DC supply) and only appears to be flowing in opposite directions when looked at WRT the ground reference. I don't think just measuring the voltages WRT ground when there are two different voltage sources, one where ground is part of the current path and one where ground is not part of the current path, gives the correct answer. Tre'
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