= Resistance-versus-temperature experiment for superconductivity
The motivating observation is an abrupt disappearance of detectable <electrical resistance> on cooling, rather than a smooth improvement in conduction. The diagram pairs the measuring arrangement with an idealized transition. Its curves are deliberately synthetic; neither their scales nor their abrupt step are a reconstruction of measured mercury data.
\Image[/superconductivity-resistance-experiment.png]
{title=Separate current and voltage leads reveal a synthetic superconducting resistance transition}
{description=The left panel shows <four-terminal sensing>; the right compares an idealized zero-<electrical resistance> branch with a stipulated normal-state continuation. All curves and the resolution band are illustrative, not measured data. The dashed vertical segment marks an idealized jump, not a fitted transition width.}
In a report communicated in November 1911, Heike Kamerlingh Onnes described a mercury thread in seven connected glass U-tubes immersed in a stirred liquid-helium bath. Expansion spaces kept freezing mercury from breaking the glass or interrupting the thread. Separate leads supplied <electric current> and sensed <electric potential difference>. He compensated a troublesome <thermoelectric effect> and reversed the main <electric current> to extract the resistive signal. He reported a rapid fall between $4.21$ and $4.19\,\mathrm K$ on his stated historical <temperature> scale, with <electrical resistance> disappearing at the lower value. The apparatus and control of spurious <electric potential differences> are part of the discovery, not incidental details. https://dwc.knaw.nl/DL/publications/PU00013242.pdf[Kamerlingh Onnes, Communication 124c (1911), §§2–3, pp. 819–821]{ref}
A modern version places a contacted sample and a calibrated <thermometer> close together in a cooling environment. Use <four-terminal sensing>, record the small applied <electric current> $I$, the sensed <electric potential difference> $V$, and the sample <temperature> $T$, then plot $R(T)=V/I$. Repeat on warming as well as cooling, and allow readings to stabilize near <thermal equilibrium>. Disagreement between warming and cooling is a reason to check sample–<thermometer> lag and reproducibility before quoting a <superconducting transition temperature>. Mikhailov and Kordosky's undergraduate experiment uses this strategy with liquid-nitrogen cooling. https://physics.wm.edu/~evmik/classes/2021_fall_Experimental_Atomic_Physics_251/lab_descriptions/superconductivity/[Mikhailov and Kordosky, Physics 251 superconductivity lab, measurement procedure and discussion]{ref}
Choose the measuring <electric current> small enough that <Joule heating> does not appreciably change the sample <temperature>, and repeat with a smaller <electric current> to check that the transition persists. Cancel stable offsets using the reversal described in <four-terminal sensing>. A reading indistinguishable from zero supplies an experimental upper bound, not a proof of exact zero <electrical resistance>. If $\delta V$ bounds the unresolved resistive <electric potential difference>, then
$$
|R|\lesssim\frac{\delta V}{|I|}.
$$
For a stipulated sensitivity $\delta V=20\,\mathrm{nV}$ and $I=1\,\mathrm{mA}$, this is $20\,\mathrm{\mu\Omega}$. The bound applies between the sensing contacts; it is not the <electrical resistance> of the complete wiring. A conducting path through part of an inhomogeneous sample can also make $V$ negligible, so the <Field-cooled Meissner experiment> adds independent evidence about the material's magnetic response.
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