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Shouldn't the ammeter between A and B read zero because A and B are maintained at the same potential, and for current to flow, a potential difference is required?

On the other hand, the current that entered the resistances has to return to the circuit through AB, which means that the ammeter's reading will be a non-zero value.

Diagram

Resistances in Parallel
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    They're the same potential because the current meter has zero resistance? sure. But that's like saying "a wire can never carry current because two adjacent points on a wire with no resistor between them are at teh same potential" – AXensen Apr 04 '23 at 09:36
  • Right! I thought about that, I guess we'll have to use the junction rule to calculate the current in that portion. – Resistances in Parallel Apr 04 '23 at 13:16
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    Voting to re-open. Clearly a conceptual question (how can current flow between points with the same potential ?) rather than a calculation or check-my-work question. – gandalf61 Apr 04 '23 at 15:21
  • @gandalf61 I agree. It should have been closed as a duplicate instead: https://physics.stackexchange.com/questions/45040/how-electric-currents-can-flow-between-2-points-at-the-same-potential?rq=1 – Dale Apr 05 '23 at 11:04
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    "for current to flow, a potential difference is required?" Only when the conductor has non-zero resistance, and the only electromotive force is due to different potentials (electrostatic force). Sometimes there can be current in real conductor even though there is no potential difference - this is because there can be other electromotive forces pushing the current against the resistance, such as induced electric force. In this case, there are only electrostatic forces, so ideal ammeter has zero difference of potential, and real ammeter will have some non-zero difference of potential.

     – Ján Lalinský Apr 05 '23 at 15:52

2 Answers2

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You are using Ohm's law in the form

$V_{AB}=I_{AB}R_{AB}$

to say that if $V_{AB}$ (the potential difference between A and B) is $0$ then $I_{AB}$ (the current flowing between A and B) is $0$. This would be true if $R_{AB}$ (the resistance between A and B) were not zero. But since $R_{AB}$ is $0$ we have

$0 = I_{AB} \times 0$

which is true for any value of $I_{AB}$ whatsoever. So you cannot use Ohm's law directly - you have to use it indirectly by finding the current through each of the other resistors in the circuit. Then add the currents through the two resistors that end at A to find $I_{AB}$.

gandalf61
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As gandalf61 said, you have to go through every part of the wires instead of the whole thing. It is not because two point has the same potential that the path of the energy/electron has the same potential everywhere.

In general relativity, an electron wouldn't see the same potential at both point I believe.

Correct me if wrong, I'm here to learn as well. Cheers

Laurier
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