On Jun 8, 10:30*am, joe wrote:
Here is a thought experiment for you.

* * * * * * * * * *A * * * * *C * * * * *E
* * * *+----\/\/\--+--/\/\/\--+--/\/\/\--+--/\/\/\--+
* * * *| * * * * * * * * * * * * * * * * * * * * * *|
* * * --- * * * * * * * * * * * * * * * * * * * * * -
* * * *- * * * * * * * * * * * * * * * * * * * * * ---
* * * *| * * * * * B * * | * *D * | * * *F * * * * *|
* * * *+-----------+-----||---+---||-----+----------+
* * * * * * * * * * * * *| * * * *|

Four resistors, equal value.
Four DC sources, equal value.
Voltage A-B = 0, no power past here.
Voltage C-D = 0, no power past here.
Voltage E-F = 0, no power past here.

No power crossing the boundaries on either side of the resistor between
A and C. The resistor is not directly connected to a supply, how is it
dissipating power, if any?

(Yes, I do know the answer.)

the first step of the analysis of this circuit is to combine the 4
voltage sources into a single source, thus rendering point b,d,f
irrelevant. you can then analyze for the currents and voltages
through the 4 resistors easily and show that current flows one way
through all 4 of them equally. circuits 101, 2nd day.