# Single conductor connecting two parts of a circuit vs two separate circuits

In a textbook exercise, this circuit appears

simulate this circuit – Schematic created using CircuitLab

Solving it was no problem, but checking the answer it stated that i0 must be 0 as no current can flow in a single conductor connecting two parts of a circuit. The consequences raised some questions:

1. Does that mean that the connection between A and B is unnecessary? That the diagram you get by removing this connection is equivalent to the original?

2. With no current flowing, must the voltage between A and B be 0? If these were two separate circuits, couldn't the voltage be anything? If the voltage is non zero, why won't the current flow?

3. From a practical perspective, how can the voltage controlled current source know the value of v0 if there is no connection between the parts. Is there some real world hidden connection in such current sources that are abstracted away in diagrams?

Thanks, from someone just starting out with simple hobby electronics.

• Let me mess a little bit with your mind. Apologies for that, but I believe this is the right time you should face this question as well. Consider the two points above the 500ohm and 2kohm resistors on the right: they are at the same potential, right? And yet a current flows between those two points. Commented Jan 18, 2021 at 15:37