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Theoretically, Ohm's Law stablishes a linear dependence between voltage and current intensity of the form:

$V(I)=CI$

being the constant $C$ the resistance $R$.

When measuring voltage an current intensity in a DC circuit and then analysing the data collected frequently is obtained an equation of the form:

$V(I)=CI+V_o$

Where $V_o$ is the intercept of the fitted line. This last equation doesn't match the theoretical one, so I was wondering if the independent term $V_o$ has a physical meaning.

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  • $\begingroup$ It would depend a lot on the test equipment you use to measure V and I in this experiment. $\endgroup$
    – The Photon
    Dec 3, 2020 at 0:36
  • $\begingroup$ Note that Ohm's law applies to ideal resistors where $V$ is the voltage across the resistor and $I$ is the current through. Ohm's law does not apply otherwise. In your DC circuit, what is the voltage $V(I)$ across? The reason I ask is that the second equation might apply if the voltage is across a voltage source with a series or internal resistance. $\endgroup$ Dec 3, 2020 at 0:43
  • $\begingroup$ @AlfredCentauri No ceramic resitors used. Only a cable made of a conductor material connected to a power supply in both ends. The purpose was to determine its electrical resistivity. $\endgroup$
    – Syn1110
    Dec 3, 2020 at 0:52
  • $\begingroup$ Most likely a measurement or setup error. If your resistance is very low, than the internal resistance of the current meter and the cables and connectors start to matter. Please provide details about your measurement setup including the measurement devices. $\endgroup$
    – Hilmar
    Dec 3, 2020 at 1:51
  • $\begingroup$ Could also be thermal: as you increase the voltage you heat up the resistor more and depending how it's made the resistance will go up with temperature. $\endgroup$
    – Hilmar
    Dec 3, 2020 at 1:54

1 Answer 1

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Yes, there are phenomena that can generate that kind of offset:

  1. Thermoelectric voltage. Owing to the Seebeck effect, when there is a temperature gradient along an inhomogeneous circuit, a voltage is produced. This voltage does not depend on the current direction but only on the temperature gradient and is typically of the order of tens of microvolts. In a resistance measurement, to cancel this offset, one makes two measurements: a first one with the current driven in one direction, and a second one with the current driven in the opposite direction. The difference between the two results cancels the offset term.
  2. Voltmeter offset. All voltmeters, also the autozeroing ones, have small residual offsets which can be relevant in certain circumstances. These offsets can be cancelled as in 1.
  3. Fitting a curve which is not a straight line. The resistance of a resistor depends on the operating temperature of the resistor which, in turn, depends on the dissipated power (that is, the square of the current). Thus, a better modelling of a real resistor is given by $$V(I) = R(1+kI^2)I$$ where $R$ is the resistance at zero dissipated power and $k$ is a coefficient that depends on the resistor construction. If you fit that curve with a straight line, you obtain a non-zero intercept. That is, the term $V_0$ that you observe may be an artifact due to the fact that you're using an inadequate model of the behaviour of the resistor.
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