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Taking the following circuit:

enter image description here

The path on the left will be on and the same, whereas the path on the right is dependent on what is connected to the base of the transistor (not shown in the above schematic). Is there a differentiation between a path and current through it that is independent (the one on the left) vs. one that is more dependent (the one on the right)? How are these usually distinguished?

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Any resistance is parallel with a 0 ohm Voltage source can be neglected from the rest of the circuit.

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