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We measured the resistance of a wire by setting the multimeter to ohmmeter mode and connected the ends of the ohmmeter to the ends of the wire; and we also calculated the theoretical value using a table of resistivity. The given wire is made of nichrome material. But the measured value deviates about 40% of the theoretical one. Do the connectors made of copper contribute to the measured resistance?

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    $\begingroup$ Without telling us how exactly you "measured the resistance", this is impossible to answer. $\endgroup$
    – ACuriousMind
    Apr 13, 2015 at 12:36
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    $\begingroup$ In order to exclude contact/lead resistance, you should do a proper four point measurement. Meaning, the outer contacts serve as current source and sink and the center contacts are used for a voltage measurement. $\endgroup$
    – engineer
    Apr 13, 2015 at 12:42
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    $\begingroup$ @engineer: Note that measurement-problem is not about problems with measurements, but about "the" measurement problem $\endgroup$
    – ACuriousMind
    Apr 13, 2015 at 12:47
  • $\begingroup$ @ACuriousMind Is it possible that there is an internal resistance in the multimeter which contributed to the increase in resistance measurement? Or maybe the copper connector itself has resistance? $\endgroup$
    – Ace Carter
    Apr 13, 2015 at 13:13

2 Answers 2

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Short answer - yes, everything in the circuit can contribute. But usually, an ohmmeter is zeroed with the probes in place - in other words, whatever resistance the probes represent is taken out by the meter.

There are two other factors that play a role, especially when you try to measure small resistance. The first of these is contact resistance: it is possible that there is a small amount of oxidation on the wire you are measuring, and this can represent a significant resistance. This is represented by this first diagram:

enter image description here

The small resistance in the probe wires (and contacts) is included in the measurement - this will affect your precision.

The way to avoid this problem is to use a Kelvin (four point) configuration - four wires used for precision resistance measurement. In this configuration, you use two wires to generate the current through the test object, and two different wires to measured the voltage generated. This ensures that the voltage measured is due ONLY to the resistance in the device under test - resistance of probe wires and contact resistance is eliminated.

enter image description here

It is usual to have the voltage measurement as the inside pair. Some multimeter probes actually have two connections on the clip precisely to make this measurement easier.

The second factor is a result of differences in materials. As you know, in a junction of unlike materials a small thermally induced voltage is generated (this is the principle behind the thermocouple). If your device under test does not have uniform temperature, then this thermal difference will result in a bias in the measured voltage (even with a Kelvin configuration). This can be mitigated by using an AC measurement - or more simply, by reversing your multimeter and measuring again. If there is a DC bias, it is always in the same direction; and measuring in both directions will subtract out the bias, leaving you with just the contribution of the resistivity of the device under test (D.U.T).

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As noted by Floris, the best way to measure small-value resistance is to use a four-point Kelvin connection; unless the current drawn by the voltage meter is significant (in which case there are other problems) then provided that current-source probes are either the inner two or the outer two (as opposed to being interleaved with the voltage-reading ones) the device will measure the resistance of the portion of the device under test which is between the two inner probes, regardless of how much resistance the connections have or well-matched they are.

If the connection resistance is unknown but the resistances of at least two of the connections can be presumed to be well-matched, it's possible to use three wires rather than four by using a circuit which uses a zero-current wire to sense the voltage drop across one of the high-current wires and subtracts twice that value from the voltage drop observed between the two current-carrying wires. This approach may be good if a significant portion of the resistance between the measurement apparatus and the device under test will be in the form of wire resistance and will always be well-matched.

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