= Reference resistor
{title2=$R_{\rm ref}$}
A <reference resistor> is a <resistor> whose assigned <electrical resistance> supplies the comparison value in a resistance-measurement circuit. Its value may come from <measurement calibration> rather than its nominal marking. The useful reference is its value under the stated <temperature>, loading and connection conditions, together with the associated <measurement uncertainty>.
In a <shared-excitation resistance ratio measurement>, the sensor and <reference resistor> carry the same <electric current>. Measuring their <electric potential differences> gives $r=V_T/V_{\rm ref}=R_T/R_{\rm ref}$, so $R_T=rR_{\rm ref}$. A reference value error therefore sets a scale error even when excitation cancels perfectly. <Reference-resistor error in ratiometric resistance measurement> derives the exact relation and distinguishes a correction from its remaining <measurement uncertainty>.<A Basic Guide to RTD Measurements by Joseph Wu>[§§2.1.3–2.1.4, printed pp. 10–11, reference requirements and conversion equations (17)–(18)]{ref}
The connections define which resistance is compared. In <four-terminal sensing>, two leads carry the <electric current> while a separate high-impedance pair senses the <electric potential difference> at the reference terminals. This avoids including the current-lead drops in the assigned reference value, within the sensing instrument's limitations.
For an original ideal example, a $100\,\Omega$ <reference resistor> carries $1\,\mathrm{mA}$ through two current leads, each of <electrical resistance> $0.20\,\Omega$. The reference element has a potential difference of $0.1000\,\mathrm V$, while a reading outside both leads is $0.1004\,\mathrm V$. If this latter reading is used as the denominator while the calculation assumes $100\,\Omega$, a true $50\,\Omega$ sensor is inferred as
$$
\widehat R_T=100\,\Omega\frac{0.0500\,\mathrm V}{0.1004\,\mathrm V}
=49.8007968\ldots\,\Omega.
$$
Sensing directly at the reference terminals removes this idealized lead contribution. It does not correct a wrong reference value. The circuit guide explicitly shows a Kelvin connection at the reference terminals for this purpose.<A Basic Guide to RTD Measurements by Joseph Wu>[§2.1.3, printed p. 11, reference-terminal sensing]{ref}
A small <temperature> change shifts the value approximately by $\Delta R_{\rm ref}/R_{\rm ref}\simeq\alpha_R\Delta T$, with <temperature coefficient of resistance> $\alpha_R$. Excitation also dissipates <electric power> $I^2R_{\rm ref}$; a reference with a different <temperature> or load from its <measurement calibration> may require a correction or additional <measurement uncertainty>. A proposed check compares the reference before and after the measurement sequence under the same connection and loading conditions. Repeating the comparison at a lower <electric current> tests for a heating contribution. Stability of the observed <ratio> alone cannot certify the reference's assigned value.
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