Two-Point and Four-Point Methods for Measuring Small Resistances

Abstract

Objective

The goal of this project is to determine which method for measuring small resistances (<1 kohm) is best: the two-point or four-point resistance measurement method?

Credits

Written by Charlie Zhai,  

Edited by Andrew Olson, Ph.D., Science Buddies

Sources

• Kuphaldt, T.R., 2003. "Kelvin (4-wire) Resistance Measurement," All About Circuits: Volume I—DC [accessed April 12, 2006] http://www.allaboutcircuits.com/vol_1/chpt_8/9.html.

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Introduction

You probably have learned how to measure the resistance of a copper wire by using a multimeter. Ohmmeter measurements are normally made with just a two-point measurement method (one probe on each of the two resistor leads). However, when measuring very small resistances, in the milli- or micro-ohm range, the two-point method is not satisfactory because test contact resistance becomes a significant factor. A similar problem occurs when making ground mat resistance tests, because long lead lengths (up to 1000 feet) are used. Here also, the lead resistance, due to long lead length, will affect the measurement results. The four-point resistance measurement method eliminates lead resistance or contact resistance. In this project, we will show you a scientific way to accurately measure resistance by minimizing the contributon of contact resistance.

The following description, from Tony Kuphaldt's website, AllAboutCircuits.com (Kuphaldt, 2003), explains:

• what contact resistance is,
• why it poses a problem when measuring small resistances, and
• how the four-point method for measuring resistance provides better accuracy for measuring small resistances.

"Suppose we wished to measure the resistance of some component located a significant distance away from our ohmmeter. Such a scenario would be problematic, because an ohmmeter measures all resistance in the circuit loop, which includes the resistance of the wires (R_wire) connecting the ohmmeter to the component being measured (R_subject):

"Usually, wire resistance is very small (only a few ohms per hundreds of feet, depending primarily on the gauge (size) of the wire), but if the connecting wires are very long, and/or the component to be measured has a very low resistance anyway, the measurement error introduced by wire resistance will be substantial.

"An ingenious method of measuring the subject resistance in a situation like this involves the use of both an ammeter and a voltmeter. We know from Ohm's Law that resistance is equal to voltage divided by current (R = V/I). Thus, we should be able to determine the resistance of the subject component if we measure the current going through it and the voltage dropped across it:

"Current is the same at all points in the circuit, because it is a series loop. Because we're only measuring voltage dropped across the subject resistance (and not the wires' resistances), though, the calculated resistance is indicative of the subject component's resistance (R_subject) alone.

"Our goal, though, was to measure this subject resistance from a distance, so our voltmeter must be located somewhere near the ammeter, connected across the subject resistance by another pair of wires containing resistance:

"At first it appears that we have lost any advantage of measuring resistance this way, because the voltmeter now has to measure voltage through a long pair of (resistive) wires, introducing stray resistance back into the measuring circuit again. However, upon closer inspection it is seen that nothing is lost at all, because the voltmeter's wires carry miniscule current. Thus, those long lengths of wire connecting the voltmeter across the subject resistance will drop insignificant amounts of voltage, resulting in a voltmeter indication that is very nearly the same as if it were connected directly across the subject resistance:

"Any voltage dropped across the main current-carrying wires will not be measured by the voltmeter, and so do[es] not factor into the resistance calculation at all. Measurement accuracy may be improved even further if the voltmeter's current is kept to a minimum, either by using a high-quality (low full-scale current) movement and/or a potentiometric (null-balance) system.

"This method of measurement which avoids errors caused by wire resistance is called the Kelvin, or 4-wire method, or 4-point method. Special connecting clips called Kelvin clips are made to facilitate this kind of connection across a subject resistance:

"In regular, 'alligator' style clips, both halves of the jaw are electrically common to each other, usually joined at the hinge point. In Kelvin clips, the jaw halves are insulated from each other at the hinge point, only contacting at the tips where they clasp the wire or terminal of the subject being measured. Thus, current through the 'C' ('current') jaw halves does not go through the 'P' ('potential,' or voltage) jaw halves, and will not create any error-inducing voltage drop along their length: (Kuphaldt, 2003)"

Terms and Concepts

To do this project, you should do research that enables you to understand the following terms and concepts:

• resistance,
• contact resistance,
• 2-point resistance measurement,
• 4-point Kelvin resistance measurement.

Bibliography

• Kuphaldt, T.R., 2003. "Kelvin (4-wire) Resistance Measurement," All About Circuits: Volume I—DC [accessed April 12, 2006] http://www.allaboutcircuits.com/vol_1/chpt_8/9.html.
• Nuckolls, B., 2004. "Practical Low Resistance Measurements," The AeroElectric Connection [accessed April 13, 2006] http://www.aeroelectric.com/articles/LowOhmsAdapter_3.pdf.
• If you need to brush up on the basics of current, voltage, and resistance, the following references should be helpful:
  • Click here to see the Science Buddies page on Using a Multimeter.
  • Mastascusa, E.J., 2006. "An Introduction to Electrical Measurements," Department of Electrical Engineering, Bucknell University [accessed March 14, 2006] http://www.facstaff.bucknell.edu/mastascu/elessonshtml/Measurements/MeasIntro.htm.
  • An online source for information on Kirchoff's Laws is:
    Burley, I. et al., date unknown, "Kirchoff's Laws," Introductory Physics Notes, University of Winnipeg [accessed March 14, 2006] http://theory.uwinnipeg.ca/physics/curr/node8.html.

Materials and Equipment

To do this experiment you will need the following materials and equipment:

• 4 12-inch lengths of insulated electric wire (copper) for 4-wire resistance measurement,
• 4 banana plugs (for connecting to probe wires to multimeters),
• 4 alligator connectors (for connecting probe wires to resistors),
• 2 AA batteries (1.5v each),
• holder for 2 AA batteries,
• two digital multimeters, available at Amazon.com,
• a selection of standard 1/4 watt resistors for higher-resistance comparison (e.g., 3 ohm, 30 ohm, 300 ohm, 3000 ohm),
• any conductor you can find that you think has small resistance. For example, try a dime, a segment of copper pipe (used in plumbing), etc. The smaller resistance they have, the more advantage the 4-point test has over the 2-point test.

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Experimental Procedure

Making 4-Point Resistance Measurements

1. Strip the ends of the 1-foot wires to expose a short segment of bare wire.
2. Solder an alligator connector to one end of each wire.
3. Solder a banana plug connector to the other end of each wire.
4. Label two of the wires as A1 and A2 (label both the plug end and the alligator clip end).
5. Label the other two wires as B1 and B2 (again, labeling both the plug end and the alligator clip end).
6. Connect the two meters, wires and battery as shown in Figure 1, below. Make sure that the ammeter is initially set to its highest DC current range (you can later decrease the current range, if necessary).

   Figure 1. Diagram for making 4-wire resistance measurements using two digital multimeters.

7. Read the ammeter and voltmeter data.
8. Divide the voltmeter reading by ammeter reading to calculate R_subject.
9. Repeat the measurement for each of the resistors and conductors you are testing.

Making 2-Point Resistance Measurements

1. Disconnect leads A1 and B1 (refer to Figure 1, above).
2. Change the setting of multimeter at the place of voltmeter to Ohms (resistance) measurement.
3. Directly measure the resistance, R_subject.
4. Repeat the measurement for each of the resistors and conductors you are testing.

Questions

1. Compare the values you measured for R_subject with each method. Over what range of resistance values do the methods produce similar results?
2. Over what range of resistance values do the methods produce different results?
3. Can you explain the differences?

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Variations

• What do you think would happen if you used 2-foot long pieces of wire to make your 4-wire connectors?
• Investigate the temperature dependence of resistance by repeating the measurements at different temperatures. You can use a hair dryer to heat up the resistors and conductors (or put them in the refrigerator or freezer for awhile). Keep in mind that the metals are normally very good thermally conductive material, so their temperatures can change rapidly.
• For a slightly more advanced project, see the article by Bob Nuckolls in the Bibliography (Nuckolls, 2004) on building a simple circuit for making accurate 4-wire resistance measurements with a single multimeter.

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