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Keithley Instruments is an instrument manufacturer associated with precision electrical measurement. Its Low Level Measurements Handbook, Seventh Edition by Keithley Instruments explains how current sources, voltmeters and connection arrangements determine what a low-level reading means, with concrete treatments of lead resistance and thermoelectric offset.^[ref]

A useful example is the handbook's comparison of two-wire resistance measurement with four-terminal sensing. In two-wire measurement, current and voltage readout share the leads, so their resistance contributes to the measured drop. Separate voltage-sensing connections can avoid including that lead drop when sensing current is negligible.^[ref]

For an original ideal calculation, a $1\Omega$ resistor has two current leads of $0.1\Omega$ each. At $10\mathrm{mA}$, the total drop is $12\mathrm{mV}$, giving $1.2\Omega$ if all of it is attributed to the specimen. A separate voltmeter connected directly across the specimen, with negligible sensing current, instead measures $10\mathrm{mV}$ and gives $1\Omega$.

That result follows from the connection arrangement, rather than from the manufacturer's name. Finite input impedance, contact placement, thermoelectric offset and source uncertainty can still matter. The manufacturer's technical handbook is useful as an apparatus-level account of such limits; its example methods do not establish the accuracy of an unspecified instrument or a particular laboratory setup.

Polarity reversal measurement separates a signal that changes sign on reversal from an additive contribution that does not. If readings in two polarities obeythen the half-difference estimates the signal, $\hat{s}=(y_{+}-y_{-})/2$, while the half-sum estimates the unchanged offset, $\hat{b}=(y_{+}+y_{-})/2$. The procedure depends on reversing the intended signal while preserving the relevant offset.

A primary electrical application is cancellation of thermoelectric offset in low-level measurements. The Keithley handbook describes reversing sources when comparing small electric potential differences, and reversing test current for low-electrical resistance measurements. A thermal offset can arise at dissimilar-metal junctions and remain approximately unchanged during a sufficiently short cycle.^[ref]

For an original resistance example, a bipolar current source applies $+I$ and $-I$ to a resistor while a voltmeter measuresLet $I=10\mathrm{mA}$ and readings be $103$ and $-97\mu \mathrm{V}$. Their half-difference is $100\mu \mathrm{V}$, giving $R=10\mathrm{m\Omega }$; their half-sum reveals a $3\mu \mathrm{V}$ offset. Using only the positive reading would instead give $10.3\mathrm{m\Omega }$.

An offset changing from $b_{+}$ to $b_{-}$ leaves resistance error $(b_{+}-b_{-})/(2I)$. A $2\mu \mathrm{V}$ change in this example therefore leaves $0.1\mathrm{m\Omega }$ error. Allow electrical settling after reversal while keeping the cycle short relative to material temperature changes. The handbook explicitly notes this time-scale requirement.^[ref] Reversal does not automatically remove lead resistance, current-magnitude errors, self-heating or every offset in the circuit. Record the actual reversal operation and timing with the measurement procedure.