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I have had this doubt for quite a while and I have tried reading answers to similar questions but I'm still not sure.

If I connect a voltmeter at A and B, what would be the reading? Is it going to be zero or 1.5 V? If it's zero, how can current flow through the wire?

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  • $\begingroup$ im not sure , i dont great knowledge about circuits, its quite a new topic in my school $\endgroup$
    – user287374
    Commented Jul 26, 2021 at 9:41

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In a circuit like you show, with a resistor connected to a power source by relativity short pieces of copper wire, the resistance of the wires is very small compared with that if the resistor, and the voltage drop across a segment of the wire would be close to zero. Most of the voltage drop occurs across the resistor.

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It is zero (provided your diagram is an idealized circuit, meaning the resistance of connecting wires are zero), that is, there is not potential difference between point A and B.

Current flows from higher potential to lower potential is the fact.

How do you conclude that current cannot flow if there is NO potential difference? You simply don't / you can't conclude.

From a logic theory point of view, how do you argue this conclusion?

Consider the proposition.

  • IF there is a potential difference, THEN the current flows.

This is an IF THEN statement, and this particular instance where IF statement is wrong to start with, is called Ex-Falso Quodlibet in deduction logic. What it means is since the starting IF statement itself is wrong /FALSE, the followup THEN statement is always TRUE.

Current flows when there is a potential difference, DOES NOT mean current doesn't flow when there is NO potential difference. As a matter of fact a better statement that expresses this fact would be,

Current flows across a resistor ONLY when there is a potential difference, and the direction of flow is taken to be from higher potential to lower, by convention.

From this it is clear that you don't necessarily require a potential difference for current to flow, when you don't have any resistance.

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  • $\begingroup$ im confused, does current flow or not? $\endgroup$
    – user287374
    Commented Jul 26, 2021 at 9:43
  • $\begingroup$ Yes, it does. What I meant to say was that, Current flows when there is a potential difference, DOES NOT mean current doesn't flow when there is NO potential difference. I will add this and a bit more in my answer. $\endgroup$
    – TheImperfectCrazy
    Commented Jul 26, 2021 at 9:45
  • $\begingroup$ ok, thanks !!!! $\endgroup$
    – user287374
    Commented Jul 26, 2021 at 9:49
  • $\begingroup$ @MeetLalwani I have edited my post, is this clear enough? $\endgroup$
    – TheImperfectCrazy
    Commented Jul 26, 2021 at 9:51
  • $\begingroup$ In physics labs which I supervised many times over a period of 40 years, we applied a voltage across a length of nichrome wire. A high resistance voltmeter always showed that the voltage drop across any segment of the wire was proportional to the length of the segment. $\endgroup$
    – R.W. Bird
    Commented Jul 26, 2021 at 14:30