When a Kelvin connection is used, current is supplied via a pair of force connections (current leads). These generate a voltage drop across the impedance to be measured according to Ohm's law V=IR. A pair of sense connections (voltage leads) are made immediately adjacent to the target impedance, so that they do not include the voltage drop in the force leads or contacts. Since almost no current flows to the measuring instrument, the voltage drop in the sense leads is negligible.
It is usual to arrange the sense wires as the inside pair, while the force wires are the outside pair. If the force and sense connections are exchanged, accuracy can be affected, because more of the lead resistance is included in the measurement. The force wires may have to carry a large current when measuring very small resistances, and must be of adequate gauge; the sense wires can be of a small gauge.
The technique is commonly used in low-voltage power supplies, where it is called remote sensing, to measure the voltage delivered to the load independent of the voltage drop in the supply wires.
It is common to provide 4-wire connections to current-sensing shunt resistors of low resistance operating at high current.
A variant uses three wires, with separate load and sense leads at one end, and a common wire on the other. Voltage drop in the common wire is compensated for by assuming that it is the same as in the load wire, of the same gauge and length. This technique is widely used in resistance thermometers, also known as resistance temperature detectors or RTDs. It is not as accurate as 4-wire sensing but can remove most of the error caused by cable resistance and is accurate enough for most applications.
Another example is in the ATX power supply standard, which includes a remote sense wire connected to the 3.3 V supply line at connector pin 13, but no sense connection for the ground wires.
Chandra, H., et al. Open-Source Automated Mapping Four-Point Probe. Materials 2017, 10(2), 110. doi: 10.3390/ma10020110 https://www.academia.edu/31083196/Open-Source_Automated_Mapping_Four-Point_Probe ↩
Manual for the Racal-Dana Databridge 9343M: "If the resistance value is low, less than 100 ohms, make a four-terminal connection..." ↩