How the Kelvin Double Bridge Measures Ultra-Low Resistances

The Kelvin double bridge is a precision instrument designed to measure very low resistances—down to milliohms—where a standard Wheatstone bridge fails due to lead and contact resistances.

Why a Double Bridge?

In low-resistance measurement, the resistance of the connecting leads and contacts becomes significant compared to the unknown resistor. The Kelvin bridge adds a second set of ratio arms to cancel out these parasitic resistances.

Circuit Layout

The bridge has two parallel branches:

• Branch A: Contains the unknown resistance X in series with its lead resistances.
• Branch B: Contains a standard resistor Rₛ and a variable resistor R.

Two additional ratio arms (R₁, R₂ and R₁', R₂') connect the junctions of the unknown and standard resistors to a galvanometer G.

Balancing Procedure

1. Adjust the variable resistor R until the galvanometer reads zero (null condition).
2. At balance, the potential difference between the two intermediate junctions is zero.
3. The unknown resistance is calculated as X = Rₛ × (R₂ / R₁), provided the ratio arms are matched (R₁/R₂ = R₁'/R₂').

Applications

• Calibrating shunts and standard resistors.
• Testing contact resistance of switches, relays, and connectors.
• Measuring winding resistance of transformers and motors.
• Quality control in precision manufacturing.

The Kelvin bridge remains a cornerstone of electrical metrology, enabling accurate characterization of components where even micro-ohms matter.