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I was reflecting on the functioning of a balanced Wheatstone bridge circuit:

Point C and D are at the same electric potential V (zero potential difference). Even if they are connected by an ideal zero resistance wire, current will not split at either node C or D to flow through that section between C and D.

So what are the conditions for a current to flow along a path between two points in a circuit?

In the a basic DC circuit below composed of a battery with ##\Delta V=12 V##, perfectly conducting wires (zero resistance), and single resistor with ##R=2 \Omega##, a nonzero electrical current ##I =6A## flows between points a and b (##V_a- V_b \ne 0## and nonzero resistance) and between points c and d (##V_a- V_b = 0## and zero resistance between them).

I would say that nonzero current ALWAYS flows if there is nonzero potential difference AND a finite resistance between two points (ex: current flowing from a to b).

A nonzero current CAN also flow there is zero potential difference between the points but the resistance must be zero between them (ex: current I flowing from c to d). But that is not always the case as it happens in balanced Wheatstone bridge between point C and D...

Is my thinking that correct? More fundamentally, a current will flow if there is a nonzero E field inside the path between the points to push and move the electric charges.

Thanks!