EXPERIMENT 7
PHYSICS 250
FOUR-LEAD MEASUREMENTS
Apparatus:
Digital multimeter (4½ digit)
Semiconductor strip
Liquid four-lead apparatus
NaCl solution
Mounted wire sets
Introduction
During this laboratory period you will study a special technique used in high-precision DC
electrical measurements. Two preliminary comments provide helpful background for this type of
study:
First, it is important to review the distinction between the words precision and accuracy. As
was noted in the handout for lab #5, precision involves the ability to measure with great sensitivity
and to measure repeatedly a very small difference. Accuracy further implies that the measured value
can be related to an absolute scale. That is, accuracy involves reference to some standard, whereas
precision implies simply the ability to observe very small changes. Precision has to do with a relative
measurement, and accuracy has to do with an absolute measurement. Note that high precision is
required before high accuracy can be considered, but it is more difficult to obtain accuracy.
Second, in high-precision measurements you must exercise great care to control or eliminate
spurious or random effects. It is foolish to talk about the measurement of a quantity to within one
part in 106 if the quantity is fluctuating in time with a variation of a few parts in 104 or if there is a
large spatial variation in the quantity. Stability and uniqueness are axiomatic to high-precision
measurements.
In this lab, you will be introduced to the four-lead technique for measuring small resistances
or resistances for which the contact or connecting resistance is relatively high. Examples of such
measurements are the resistances of liquids or semi-conductors. This technique eliminates the
problem of lead resistance, which is present no matter how precise the multimeter used. Since lead
resistances and contact resistances for meters are usually a few ohms or less, you can measure large
resistances reasonably precisely with a digital multimeter, but for resistances of a few ohms or less,
or when surface films are present, you must exercise more care in making such measurements.
7-1
If the resistance you desire to
measure is small and remote so that
A
Voltage
long lead wires are necessary or if the
connections to the resistance are
Source
unreliable or have large resistances
Rlead
R
Rlead
a
themselves,
any
attempt
at
b
high-precision measurement of the
resistance by standard means will have
Rlead
large uncertainties due to the effect of
Rlead
the leads and contacts. To avoid this
V
situation, consider the simple technique
illustrated in Fig. 1, where a known
current is passed through the resistance Figure 1. Connections for a typical four-lead measurement.
and two auxiliary leads are attached to
the resistance at the two points (a) and
(b) between which the resistance is desired. The voltage is measured between these two leads with
a voltmeter that has a high internal resistance so that very little (effectively none) of the current passes
through the voltmeter. The resistance R=V/I. Note that the lead resistances have absolutely no effect
on the measurement and that the resistance in the leads produces error only if the resistance is
comparable to the internal resistance of the voltmeter. If you use an electronic voltmeter with Rm =
107 ohms, a resistance of 1000 ohms in the voltage leads gives errors of only one part in 104, and you
can tolerate resistances of any size in the current leads provided you can maintain the current through
R constant.
Objective: To become acquainted with high-precision electrical measurements and to gain an
appreciation for the care required to make such measurements.
Procedure
During this laboratory period you will use the four-lead measurement technique to measure
with modest accuracy a resistance that could not be measured with any degree of reliability using the
electronic meter. You should contrast resistance measurements made with the electronic multimeter
with measurements made with the more precise technique discussed above.
Caution: When making measurements in a four-lead configuration you should usually start with a
small current and slowly increase it until you can accurately measure the voltage across your sample.
This is especially important if your sample can be damaged or modified by the current. “Small” often
means that the initial current should be measured in milliamps or tens of milliamps - NOT in amps.
On some samples you may eventually reach currents of amps before an accurate measurement can
be made, but in many cases currents of milliamps are adequate.
Select two of the following three situations to study using the four-lead measurement
technique.
1. Measure the resistance R of an 80-cm length of one of the mounted bare wires provided in
the laboratory. Now measure the resistance for a 40-cm length and comment on the results.
7-2
Could you measure a resistance this small using the electronic meter? Try it. Using a
micrometer, you can measure the diameter of the wires and can thus determine the resistivity
of the metal. Determine for at least two of the metals.
2. Measure the resistance R of a weak molar solution of NaCl or KCl in water. A glass tube that
can be filled with the solution and fitted with four-lead configuration contacts will be
available. Determine the conductivity for two of the solutions provided. Try to repeat this
measurement using the electronic meter.
3. Measure the resistance of a chosen length of the semi-conductor strip provided, and determine
the resistivity of the sample. Try to repeat these measurements using the electronic meter.
7-3