Circuit Theory/Dangling Resistors

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100 ohm dangling resistor is only connected to the circuit by one wire
dangling resistor removed

When opening capacitors, inductors or current sources during circuit analysis, sometimes a resistor is left connected to the circuit with only one wire. It can be removed from the circuit.

It can be removed because there is no current through it. This means that the electromotive force is the same through the resistor. The green and the red dot are part of the same node.

The original voltage between green and black is going to be the same voltage between red and black. The total Resistance will be r1+r2.