Connecting two circuits with a single conductor

[TheCanadian]

If you have two independent circuits, and then connect them at two points that are at arbitrary voltages by a single conductor, what happens to the system? A moment after the connection happens, I would assume there to be no current between the circuits since the two circuits would try and establish equal potential at the two points they're connected by, right? But would that actually happen? If you had a current I1 going through one of the circuits for example, and then connected the two circuits together by this one conductor, would I1 change at that instant (unless the two points the conductor is connected to is at equal potential)?

 

[nasu]

It may definitely change the currents and voltages in both circuits. In what way will depend on the specifics.

 

[ehild]

If you have two independent circuits, and then connect them at two points that are at arbitrary voltages by a single conductor, what happens to the system? A moment after the connection happens, I would assume there to be no current between the circuits since the two circuits would try and establish equal potential at the two points they're connected by, right? But would that actually happen? If you had a current I1 going through one of the circuits for example, and then connected the two circuits together by this one conductor, would I1 change at that instant (unless the two points the conductor is connected to is at equal potential)?

The potential is defined with respect to a given point. If two circuits have only a single point in common that point can be considered as the zero of potential for both of them. All the voltages (potential differences) are the same as before they get connected.
The situation is different if the circuits are earthed. In this case, connecting them changes the voltages and currents, as they got two points in common, unless the points were at the same potential with respect to the ground.

 

[CWatters]

What ehild said.

There might be some current flow in the single the connecting wire if the "independent" circuits actually have some capacitance that completes the circuit.