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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?

Vincent Thacker
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  • im not sure , i dont great knowledge about circuits, its quite a new topic in my school –  Jul 26 '21 at 09:41

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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.

R.W. Bird
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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.

TheImperfectCrazy
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  • im confused, does current flow or not? –  Jul 26 '21 at 09:43
  • 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. – TheImperfectCrazy Jul 26 '21 at 09:45
  • ok, thanks !!!! –  Jul 26 '21 at 09:49
  • @MeetLalwani I have edited my post, is this clear enough? – TheImperfectCrazy Jul 26 '21 at 09:51
  • 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. – R.W. Bird Jul 26 '21 at 14:30
  • @R.W.Bird yes that is because practically its hard to get zero resistance materials. In fact, its very hard, you will have to do the experiment with a superconductoring wire. From the question "Is it going to be zero or 1.5 V?", the OP seems to be more interested in an ideal situation. – TheImperfectCrazy Jul 26 '21 at 15:25