Lead-wire resistance: sensitivity loss and apparent strain in 2-, 3- and 4-wire connection

What is calculated?

With a full bridge the cable is outside the bridge: the supply leads form a divider with the bridge resistance, reducing sensitivity, and cable temperature changes alter it. With half and quarter bridges the leads are part of the arms: they lower the effective gauge factor, and in two-wire connection every thermal change of lead resistance acts as apparent strain. Keil's example: 3 m, 0.8 mm², 40 K give 0.0216 Ω and 90 µm/m at 120 Ω. Ruge's three-wire connection places the leads in adjacent arms and cancels this effect.

Equations

R_K = ρ·L/q

Vollbrücke: E*/E = R_B/(R_B+2R_K) (Keil Gl. 6.1); ΔE/E = −2ΔR_K/(R_B+2R_K) (Gl. 6.2)

Viertel-/Halbbrücke: ΔR/(R_DMS+R_L) = k*·ε ⇒ k* = k·R/(R+R_L) (Keil Gl. 6.4)

Zweileiter: ε_s = ΔR_L/(k·(R+R_L)) mit R_L = 2R_K

Step by step

1. Enter connection type, cable length and cross-section.
2. Account for the sensitivity loss when calibrating or correct the instrument gauge factor accordingly.
3. Always use three-wire connection for quarter bridges exposed to temperature change.

Typical mistake

Entering the doubled cable length (out and back) a second time – the calculator already accounts for the number of leads via the connection type.

Application and limits

Planning measurement cables for multi-channel setups, judging zero drift of long two-wire connections and correcting the gauge factor for long half-bridge leads.

Ohmic effects only; cable capacitance (phase shift, amplitude loss at carrier frequency, Keil sec. 6.3) and six-wire sensing are not modelled.

Technical basis

Keil, Dehnungsmessstreifen, 2nd ed. 2017, secs. 6.2.2–6.2.3 ohmic cable resistance, eqs. (6.1)–(6.4), figs. 6.1–6.3; sec. 6.7.

The source supports the equation structure and worked examples; this calculator does not replace calibration of the measuring chain.

Frequently asked questions

In the same cluster

• Strain-gauge basic equation: resistance change from strain and gauge factor
• Transverse sensitivity: correction for two perpendicular gauges
• Temperature response: apparent strain of a gauge under temperature change
• Bridge excitation voltage and gauge self-heating
• Wheatstone bridge: output voltage of the unbalanced bridge
• Basic strain-gauge bridge equation: signal from four strains

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