 Two-wire resistance measurement

A two-wire resistance measurement sends a known electric current through a specimen and measures the resulting electric potential difference using the same two connecting leads. The instrument estimates electrical resistance from their ratio. Because the leads carry the test current, their voltage drops enter the reading along with the specimen’s. Keithley’s primary handbook illustrates the two-wire circuit and identifies added lead resistance as its principal low-resistance limitation.^[ref]

For an original linear series-circuit model, let $R_x$ be the specimen resistance, $r_1+r_2$ the total lead resistance, and $r_c$ an included contact resistance. With actual test current $I\ne 0$ and additive offset potential difference $E$, the terminal reading isThe division assumes the actual current is known and the specified resistive elements are sufficiently linear at that current. Non-ohmic contacts require a different response model.

For $R_x=0.100\Omega$, $r_1=r_2=0.150\Omega$, $r_c=0$ and $I=10\mathrm{mA}$, the true terminal potential difference is $4.00\mathrm{mV}$. The indicated resistance is $0.400\Omega$: a $300\%$ positive error relative to the specimen value. Adding $E=20\mu \mathrm{V}$ raises the reading to $0.402\Omega$. The same $0.300\Omega$ lead contribution is only $0.003\%$ of a $10\mathrm{k\Omega }$ specimen, illustrating why the acceptable arrangement depends on the measurement scale.

Lead-resistance subtraction in two-wire measurements estimates that series contribution using a shorted-lead reading. It can remove a stable offset resistance, but reconnecting clips, moving contacts or changing lead temperature can alter the quantity subtracted. If residual lead resistance changes by $0.020\Omega$ after zeroing, the error is already $20\%$ for the $0.100\Omega$ specimen above. Display resolution alone cannot establish that subtraction’s accuracy.

Reversing the test current cancels a different effect. If $E$ and the resistances remain unchanged between equal-magnitude positive and negative currents,The thermoelectric offset cancels, but the lead resistance remains. In the example, $V_{+}=4.02\mathrm{mV}$ and $V_{-}=-3.98\mathrm{mV}$ yield $0.400\Omega$, not $0.100\Omega$. The handbook treats current reversal separately from the four-wire connection.^[ref]

Four-terminal sensing instead separates the current-carrying connections from potential-sensing connections placed at the desired specimen boundaries. A high-input-impedance sense circuit draws sufficiently little current that its lead drops can be much smaller; the exact contact placement still defines what is measured. Raising the two-wire test current to suppress $E/I$ also raises specimen heating, $I^2{R}_x$. Increasing this example’s current from $10$ to $100\mathrm{mA}$ raises specimen dissipation from $10\mu \mathrm{W}$ to $1\mathrm{mW}$.

A proposed comparison measures the same stable reference specimen with short and long leads, repeats with current reversal, then uses a four-wire connection at fixed specimen terminals. Record current, temperature and connection geometry. Lead-length dependence and reversal dependence distinguish series resistance from additive thermal offsets, while repeating at lower current helps test whether self-heating changed the specimen during the measurement.