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I find the voltage of electric wire in between point 1 and point 2. I want to know if I use the differrent wire,long one and short one,the voltage will be equal or not?

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The answer is "it depends." Wires are not ideal, but in some cases the difference will be negligible. It all depends on your particular circuit and its design.

As an answer to a question you did not ask, you might be interested in 4-wire sensing. 4-wire sensing is a process used for measuring very small resistance. In such test setups, the current drop along wires is non-negligable, so the 4 wire setup is designed to minimize voltage drop across the wires included in the measurements. In those situations, there is indeed a very important difference in voltage across a "wire." Those wires do not act like ideal wires.

Also, in transmission line theory, which matters a bunch for high frequency situations, you can actually get different phasing for short and long wires that has meaningful impacts on the behavior of the entire circuit. For example, one of my college projects was to cut a stub of coaxial wire which, when put in parallel with a normal TV signal, would prevent exactly 1 channel from working properly. Due to the way the signals reflect around in that circuit, one channel's voltages were dropped to nearly 0V, while the others were unaffected.

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  • $\begingroup$ About 4-wire sensing,as I understand if I use a very long wire(such as 100m),The voltage drop between point will be less than the short wire(such as 1m) right? Sorry I’m not good at english much. $\endgroup$ – hajaJa Sep 7 at 5:36
  • $\begingroup$ The idea with 4-wire sensing is that if you want to measure a very low resistance, you need a lot of current to get a meaningful voltage drop across the object you are testing. This also means a lot of current through your wires, which means you'll measure not only the resistance of the object, but the resistance of the wires too. In 4 wire sensing, you run the current through 2 thick wires, and then measure the voltage drop across the object with smaller wires that carry almost no current, so they have almost no voltage drop. $\endgroup$ – Cort Ammon - Reinstate Monica Sep 7 at 5:50

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