## Principles of the ohmmeter. Measurement of four-wire resistance (Kelvin Method)

Suppose we want to measure the resistance of a component located a significant distance from the ohmmeter. This is a complicated situation because the ohmmeter / Ohmmeter measure all resistance in the circuit, which includes the resistance of the cables (R_{wire}) connection and the resistance object (R_{subject}):

Normally the wire resistance is very low (only a few ohms per hundreds of feet of cable, depending on the section of cable) but if the cables are too long or (R_{subject}) have a low value, the error introduce the cables will be substantial.

An ingenious method of measurement of resistance value in cases such as the former involves the use of both a voltmeter and an ammeter. We know from Ohm's Law that resistance is the ratio between voltage and current (R=V/I). Thus we should be able to determine the resistance if we measure the current through and voltage drop:

The current is the same at all points of the circuit since all elements are in series. Since we are only measuring the voltage drop in the measured object (and not the resistance of the cables) the calculated resistance is indicative of the actual value of the resistance (R_{subject}). Our goal, however, is to measure the resistance at a distance, so our voltmeter must be somehow located near the ammeter, it is connected to (R_{subject}) via cables which have a resistance.

Apparently we have introduced a systematic error because now the voltmeter should measure a voltage drop across a long wire resistive torque, which introduces an external resistor in the circuit. However, if we make a detailed study we will not lose any precision at all, this is because the current through the voltmeter has a negligible value. The voltage drop in the wires of the voltmeter is negligible, an indication of the voltmeter being practically the same as if it were directly connected to (R_{subject}).

Any voltage drop in power cables will not be measured by the voltmeter. The measurement accuracy can be improved if the current of the voltmeter is minimized. This measurement method avoids the systematic error would introduce the lead resistance method is called the four-wire or Kelvin. There are special alligator clips (called Kelvin clips) to facilitate this kind of connection resistance.

[Kelvin Clips] | [Metrology] |

The same principle of using different points of contact for current and voltage to drive current and measuring the voltage drop is used to measure high currents, in this case is calibrated resistance (shunt). As mentioned above, the shunt resistor works as a measure of current to reduce a certain amount of voltage per ampere of current passing through it, the voltage drop is measured by a voltmeter then. In this way calibrated shunt resistor "converts" a current value in a voltage proportional. Hence the current can be accurately measured by measuring the voltage drop in the shunt:

The measurement of current through a shunt resistance is particularly suitable for measuring very high currents. For such applications, the shunt resistor must be of the order of milliohms or micro ohms, thus the voltage drop will be low relative to the current value. As low resistance values are comparable to the resistance of the connections to the power cables, this means that the measure of the potential drop should avoid measuring the voltage drop in connections with the resistance wires. To ensure that the voltmeter measure only the voltage drop across the shunt itself, uninfluenced by the potential drops due to connections, shunts are usually equipped with four connections: