An American National Standard

Designation: D 257 – 99 (Reapproved 2005)

Standard Test Methods for

DC Resistance or Conductance of Insulating Materials1
This standard is issued under the fixed designation D 257; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (e) indicates an editorial change since the last revision or reapproval.
This standard has been approved for use by agencies of the Department of Defense.

1. Scope 2. Referenced Documents

1.1 These test methods cover direct-current procedures for 2.1 ASTM Standards: 2
the determination of dc insulation resistance, volume resis- D 150 Test Methods for AC Loss Characteristics and Per-
tance, volume resistivity, surface resistance, and surface resis- mittivity Dielectric Contant of Solid Electrical Insulation
tivity of electrical insulating materials, or the corresponding D 374 Test Methods for Thickness of Solid Electrical Insu-
conductances and conductivities. lation
1.2 These test methods are not suitable for use in measuring D 618 Practice for Conditioning Plastics for Testing
the electrical resistivity/conductivity of moderately conductive D 1169 Test Method for Specific Resistance (Resistivity) of
materials. Use Test Method D 4496 to evaluate such materials. Electrical Insulating Liquids
1.3 The test methods and procedures appear in the follow- D 1711 Terminology Relating to Electrical Insulation
ing sections: D 4496 Test Method for DC Resistance or Conductance of
Test Method or Procedure Section Moderately Conductive Materials
Calculation 13 D 5032 Practice for Maintaining Constant Relative Humid-
Choice of Apparatus and Test Method 7
Cleaning Solid Specimens 10.1
ity by Means of Aqueous Glycerin Solutions
Conditioning of Specimens 11 E 104 Practice for Maintaining Constant Relative Humidity
Effective Area of Guarded Electrode Appendix by Means of Aqueous Solutions
X2
Electrode Systems 6
Factors Affecting Insulation Resistance or Conductance Appendix
3. Terminology
Measurements X1 3.1 Definitions—The following definitions are taken from
Humidity Control 11.2
Liquid Specimens and Cells 9.4
Terminology D 1711 and apply to the terms used in these test
Precision and Bias 15 methods.
Procedure for the Measurement of Resist- 12 3.1.1 conductance, insulation, n—the ratio of the total
ance or Conductance
Referenced Documents 2 volume and surface current between two electrodes (on or in a
Report 14 specimen) to the dc voltage applied to the two electrodes.
Sampling 8 3.1.1.1 Discussion—Insulation conductance is the recipro-
Significance and Use 5
Specimen Mounting 10 cal of insulation resistance.
Summary of Test Methods 4 3.1.2 conductance, surface, n—the ratio of the current
Terminology 3 between two electrodes (on the surface of a specimen) to the dc
Test Specimens for Insulation, Volume, and Surface 9
Resistance or Conductance Determination voltage applied to the electrodes.
Typical Measurement Methods Appendix 3.1.2.1 Discussion—(Some volume conductance is un-
X3 avoidably included in the actual measurement.) Surface con-
1.4 This standard does not purport to address all of the ductance is the reciprocal of surface resistance.
safety concerns, if any, associated with its use. It is the 3.1.3 conductance, volume, n—the ratio of the current in the
responsibility of the user of this standard to establish appro- volume of a specimen between two electrodes (on or in the
priate safety and health practices and determine the applica- specimen) to the dc voltage applied to the two electrodes.
bility of regulatory limitations prior to use. For a specific 3.1.3.1 Discussion—Volume conductance is the reciprocal
hazard statement, see 6.1.8. of volume resistance.

1
These test methods are under the jurisdiction of ASTM Committee D09 on
2
Electrical and Electronic Insulating Materials and are the direct responsibility of For referenced ASTM standards, visit the ASTM website, www.astm.org, or
Subcommittee D09.12 on Electrical Tests. contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
Current edition approved Sept. 1, 2005. Published October 2005. Originally Standards volume information, refer to the standard’s Document Summary page on
approved in 1925. Last previous edition approved in 1999 as D 257 – 99. the ASTM website.

Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.

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 D 257 – 99 (2005)
3.1.4 conductivity, surface, n—the surface conductance 4. Summary of Test Methods
multiplied by that ratio of specimen surface dimensions (dis- 4.1 The resistance or conductance of a material specimen or
tance between electrodes divided by the width of electrodes of a capacitor is determined from a measurement of current or
defining the current path) which transforms the measured of voltage drop under specified conditions. By using the
conductance to that obtained if the electrodes had formed the appropriate electrode systems, surface and volume resistance
opposite sides of a square. or conductance may be measured separately. The resistivity or
3.1.4.1 Discussion—Surface conductivity is expressed in conductivity can then be calculated when the required speci-
siemens. It is popularly expressed as siemens/square (the size men and electrode dimensions are known.
of the square is immaterial). Surface conductivity is the
reciprocal of surface resistivity. 5. Significance and Use
3.1.5 conductivity, volume, n—the volume conductance 5.1 Insulating materials are used to isolate components of an
multiplied by that ratio of specimen volume dimensions electrical system from each other and from ground, as well as
(distance between electrodes divided by the cross-sectional to provide mechanical support for the components. For this
area of the electrodes) which transforms the measured conduc- purpose, it is generally desirable to have the insulation resis-
tance to that conductance obtained if the electrodes had formed tance as high as possible, consistent with acceptable mechani-
the opposite sides of a unit cube. cal, chemical, and heat-resisting properties. Since insulation
3.1.5.1 Discussion—Volume conductivity is usually ex- resistance or conductance combines both volume and surface
pressed in siemens/centimetre or in siemens/metre and is the resistance or conductance, its measured value is most useful
reciprocal of volume resistivity. when the test specimen and electrodes have the same form as
3.1.6 moderately conductive, adj—describes a solid mate- is required in actual use. Surface resistance or conductance
rial having a volume resistivity between 1 and 10 000 000 changes rapidly with humidity, while volume resistance or
V-cm. conductance changes slowly although the final change may
3.1.7 resistance, insulation, (Ri), n—the ratio of the dc eventually be greater.
voltage applied to two electrodes (on or in a specimen) to the 5.2 Resistivity or conductivity may be used to predict,
total volume and surface current between them. indirectly, the low-frequency dielectric breakdown and dissi-
pation factor properties of some materials. Resistivity or
3.1.7.1 Discussion—Insulation resistance is the reciprocal
contivity is often used as an indirect measure of moisture
of insulation conductance.
content, degree of cure, mechanical continuity, and deteriora-
3.1.8 resistance, surface, (Rs), n—the ratio of the dc voltage tion of various types. The usefulness of these indirect measure-
applied to two electrodes (on the surface of a specimen) to the ments is dependent on the degree of correlation established by
current between them. supporting theoretical or experimental investigations. A de-
3.1.8.1 Discussion—(Some volume resistance is unavoid- crease of surface resistance may result either in an increase of
ably included in the actual measurement.) Surface resistance is the dielectric breakdown voltage because the electric field
the reciprocal of surface conductance. intensity is reduced, or a decrease of the dielectric breakdown
3.1.9 resistance, volume, (Rv), n—the ratio of the dc voltage voltage because the area under stress is increased.
applied to two electrodes (on or in a specimen) to the current 5.3 All the dielectric resistances or conductances depend on
in the volume of the specimen between the electrodes. the length of time of electrification and on the value of applied
3.1.9.1 Discussion—Volume resistance is the reciprocal of voltage (in addition to the usual environmental variables).
volume conductance. These must be known to make the measured value of resistance
3.1.10 resistivity, surface, (rs), n—the surface resistance or conductance meaningful.
multiplied by that ratio of specimen surface dimensions (width 5.4 Volume resistivity or conductivity can be used as an aid
of electrodes defining the current path divided by the distance in designing an insulator for a specific application. The change
between electrodes) which transforms the measured resistance of resistivity or conductivity with temperature and humidity
to that obtained if the electrodes had formed the opposite sides may be great (1, 2, 3, 4),3 and must be known when designing
of a square. for operating conditions. Volume resistivity or conductivity
3.1.10.1 Discussion—Surface resistivity is expressed in determinations are often used in checking the uniformity of an
ohms. It is popularly expressed also as ohms/square (the size of insulating material, either with regard to processing or to detect
the square is immaterial). Surface resistivity is the reciprocal of conductive impurities that affect the quality of the material and
surface conductivity. that may not be readily detectable by other methods.
5.5 Volume resistivities above 1021 V·cm (1019 V·m), ob-
3.1.11 resistivity, volume, (rv), n—the volume resistance
tained on specimens under usual laboratory conditions, are of
multiplied by that ratio of specimen volume dimensions
doubtful validity, considering the limitations of commonly
(cross-sectional area of the specimen between the electrodes
used measuring equipment.
divided by the distance between electrodes) which transforms
5.6 Surface resistance or conductance cannot be measured
the measured resistance to that resistance obtained if the
accurately, only approximated, because some degree of volume
electrodes had formed the opposite sides of a unit cube.
3.1.11.1 Discussion—Volume resistivity is usually ex-
pressed in ohm-centimetres (preferred) or in ohm-metres. 3
The boldface numbers in parentheses refer to the list of references appended to
Volume resistivity is the reciprocal of volume conductivity. these test methods.

2
 D 257 – 99 (2005)
resistance or conductance is always involved in the measure-
ment. The measured value is also affected by the surface
contamination. Surface contamination, and its rate of accumu-
lation, is affected by many factors including electrostatic
charging and interfacial tension. These, in turn, may affect the
surface resistivity. Surface resistivity or conductivity can be
considered to be related to material properties when contami-
nation is involved but is not a material property in the usual
sense.

6. Electrode Systems
6.1 The electrodes for insulating materials should be of a
material that is readily applied, allows intimate contact with the
specimen surface, and introduces no appreciable error because
of electrode resistance or contamination of the specimen (5).
The electrode material should be corrosion-resistant under the
conditions of test. For tests of fabricated specimens such as
feed-through bushings, cables, etc., the electrodes employed
are a part of the specimen or its mounting. Measurements of
insulation resistance or conductance, then, include the contami-
nating effects of electrode or mounting materials and are
generally related to the performance of the specimen in actual
use.
6.1.1 Binding-Post and Taper-Pin Electrodes, Fig. 1 and
Fig. 2, provide a means of applying voltage to rigid insulating
materials to permit an evaluation of their resistive or conduc-
tive properties. These electrodes simulate to some degree the
actual conditions of use, such as binding posts on instrument
panels and terminal strips. In the case of laminated insulating
FIG. 2 Taper-Pin Electrodes
materials having high-resin-content surfaces, somewhat lower
insulation resistance values may be obtained with taper-pin
than with binding posts, due to more intimate contact with the
body of the insulating material. Resistance or conductance
values obtained are highly influenced by the individual contact
between each pin and the dielectric material, the surface
roughness of the pins, and the smoothness of the hole in the
dielectric material. Reproducibility of results on different
specimens is difficult to obtain.
6.1.2 Metal Bars in the arrangement of Fig. 3 were prima-
rily devised to evaluate the insulation resistance or conduc-
tance of flexible tapes and thin, solid specimens as a fairly
simple and convenient means of electrical quality control. This
arrangement is somewhat more satisfactory for obtaining

FIG. 3 Strip Electrodes for Tapes and Flat, Solid Specimens

approximate values of surface resistance or conductance when

the width of the insulating material is much greater than its
thickness.
6.1.3 Silver Paint, Fig. 4, Fig. 5, and Fig. 6, is available
commercially with a high conductivity, either air-drying or
low-temperature-baking varieties, which are sufficiently po-
FIG. 1 Binding-Post Electrodes for Flat, Solid Specimens rous to permit diffusion of moisture through them and thereby

3
 D 257 – 99 (2005)
trodes may be obtained with a fine-bristle brush. However, for
circular electrodes, sharper edges can be obtained by the use of
a ruling compass and silver paint for drawing the outline circles
of the electrodes and filling in the enclosed areas by brush. A
narrow strip of masking tape may be used, provided the
pressure-sensitive adhesive used does not contaminate the
surface of the specimen. Clamp-on masks also may be used if
the electrode paint is sprayed on.
6.1.4 Sprayed Metal, Fig. 4, Fig. 5, and Fig. 6, may be used
if satisfactory adhesion to the test specimen can be obtained.
Thin sprayed electrodes may have certain advantages in that
they are ready for use as soon as applied. They may be
sufficiently porous to allow the specimen to be conditioned, but
this should be verified. Narrow strips of masking tape or
clamp-on masks must be used to produce a gap between the
guarded and the guard electrodes. The tape shall be such as not
to contaminate the gap surface.
6.1.5 Evaporated Metal may be used under the same con-
ditions given in 6.1.4.
6.1.6 Metal Foil, Fig. 4, may be applied to specimen
surfaces as electrodes. The usual thickness of metal foil used
for resistance or conductance studies of dielectrics ranges from
6 to 80 µm. Lead or tin foil is in most common use, and is
usually attached to the test specimen by a minimum quantity of
Volume Resistivity g |Ls 2t Surface Resistivity petrolatum, silicone grease, oil, or other suitable material, as an
FIG. 4 Flat Specimen for Measuring Volume and Surface
adhesive. Such electrodes shall be applied under a smoothing
Resistances or Conductances
pressure sufficient to eliminate all wrinkles, and to work excess
adhesive toward the edge of the foil where it can be wiped off
with a cleansing tissue. One very effective method is to use a
hard narrow roller (10 to 15 mm wide), and to roll outward on
the surface until no visible imprint can be made on the foil with
the roller. This technique can be used satisfactorily only on
specimens that have very flat surfaces. With care, the adhesive
film can be reduced to 2.5 µm. As this film is in series with the
specimen, it will always cause the measured resistance to be
too high. This error may become excessive for the lower-
resistivity specimens of thickness less than 250 µm. Also the
hard roller can force sharp particles into or through thin films
(50 µm). Foil electrodes are not porous and will not allow the
test specimen to condition after the electrodes have been
applied. The adhesive may lose its effectiveness at elevated
temperatures necessitating the use of flat metal back-up plates
under pressure. It is possible, with the aid of a suitable cutting
device, to cut a proper width strip from one electrode to form
a guarded and guard electrode. Such a three-terminal specimen
normally cannot be used for surface resistance or conductance
measurements because of the grease remaining on the gap
surface. It may be very difficult to clean the entire gap surface
D0 = (D1 + D2)/2 L > 4t g |La 2t Volume Resistivity g |Ls 2t Surface Resistivity
FIG. 5 Tubular Specimen for Measuring Volume and Surface
without disturbing the adjacent edges of the electrode.
Resistances or Conductances 6.1.7 Colloidal Graphite, Fig. 4, dispersed in water or other
suitable vehicle, may be brushed on nonporous, sheet insulat-
allow the test specimen to be conditioned after the application ing materials to form an air-drying electrode. Masking tapes or
of the electrodes. This is a particularly useful feature in clamp-on masks may be used (6.1.4). This electrode material is
studying resistance-humidity effects, as well as change with recommended only if all of the following conditions are met:
temperature. However, before conductive paint is used as an 6.1.7.1 The material to be tested must accept a graphite
electrode material, it should be established that the solvent in coating that will not flake before testing,
the paint does not attack the material so as to change its 6.1.7.2 The material being tested must not absorb water
electrical properties. Reasonably smooth edges of guard elec- readily, and

4
 D 257 – 99 (2005)

FIG. 6 Conducting-Paint Electrodes

6.1.7.3 Conditioning must be in a dry atmosphere (Proce-

dure B, Methods D 618), and measurements made in this same
atmosphere.
6.1.8 Mercury or other liquid metal electrodes give satisfac-
tory results. Mercury is not recommended for continuous use
or at elevated temperatures due to toxic effects. (Warning—
Mercury metal vapor poisoning has long been recognized as a
hazard in industry. The maximum exposure limits are set by the
American Conference of Governmental Industrial Hygienists.4
The concentration of mercury vapor over spills from broken
thermometers, barometers, or other instruments using mercury
can easily exceed these exposure limits. Mercury, being a
liquid and quite heavy, will disintegrate into small droplets and
seep into cracks and crevices in the floor. The use of a
commercially available emergency spill kit is recommended
whenever a spill occurs. The increased area of exposure adds
significantly to the mercury vapor concentration in air. Mer-
cury vapor concentration is easily monitored using commer-
cially available sniffers. Spot checks should be made periodi-
cally around operations where mercury is exposed to the
atmosphere. Thorough checks should be made after spills.) The
metal forming the upper electrodes should be confined by
stainless steel rings, each of which should have its lower rim NOTE 1—Warning: See 6.1.8
reduced to a sharp edge by beveling on the side away from the FIG. 7 Mercury Electrodes for Flat, Solid Specimens
liquid metal. Fig. 7A and Fig. 7B show two electrode arrange-
ments.
with the specimen, considerable pressure is usually required.
6.1.9 Flat Metal Plates, Fig. 4, (preferably guarded) may be
Pressures of 140 to 700 kPa have been found satisfactory (see
used for testing flexible and compressible materials, both at
material specifications).
room temperature and at elevated temperatures. They may be
6.1.9.1 A variation of flat metal plate electrode systems is
circular or rectangular (for tapes). To ensure intimate contact
found in certain cell designs used to measure greases or filling
compounds. Such cells are preassembled and the material to be
4
Available from American Conference of Governmental Industrial Hygienists, tested is either added to the cell between fixed electrodes or the
Inc. (ACGIH), 1330 Kemper Meadow Dr., Suite 600, Cincinnati, OH 45240. electrodes are forced into the material to a predetermined

5
 D 257 – 99 (2005)
constant, K, (equivalent to the A/t factor from Table 1) can be
derived from the following equation:
K 5 3.6 p C 5 11.3 C (1)
where:
K has units of centimetres, and
C has units of picofarads and is the capacitance of the electrode system with
air as the dielectric. See Test Methods D 150 for methods of measurement
for C.

6.1.10 Conducting Rubber has been used as electrode ma-

terial, as in Fig. 4, and has the advantage that it can quickly and
easily be applied and removed from the specimen. As the
electrodes are applied only during the time of measurement,
they do not interfere with the conditioning of the specimen.
The conductive-rubber material must be backed by proper
plates and be soft enough so that effective contact with the
specimen is obtained when a reasonable pressure is applied.
NOTE 1—There is evidence that values of conductivity obtained using
conductive-rubber electrodes are always smaller (20 to 70 %) than values
obtained with tinfoil electrodes (6). When only order-of-magnitude
accuracies are required, and these contact errors can be neglected, a
properly designed set of conductive-rubber electrodes can provide a rapid
means for making conductivity and resistivity determinations.

6.1.11 Water is widely employed as one electrode in testing

NOTE 1—Warning: See 6.1.8 insulation on wires and cables. Both ends of the specimen must
FIG. 7 Mercury Cell for Thin Sheet Material (continued) be out of the water and of such length that leakage along the
insulation is negligible. Guard rings may be necessary at each
electrode spacing. Because the configuration of the electrodes end. It may be desirable to add a small amount of sodium
in these cells is such that the effective electrode area and the chloride to the water to ensure high conductivity. Measure-
distance between them is difficult to measure, each cell ments may be performed at temperatures up to about 100°C.

TABLE 1 Calculation of Resistivity or ConductivityA

Type of Electrodes or Specimen Volume Resistivity, V-cm Volume Conductivity, S/cm
A t
rv 5 R gv 5 G
t v A v
Circular (Fig. 4) p~D1 1 g! 2
A 5
4
Rectangular A = (a + g) (b + g)
Square A = (a + g) 2
Tubes (Fig. 5) A = pD0(L + g)
Cables 2pLRv
rv 5
D2
ln
D1
D2
ln
D1
gv 5
2pLRv

Surface Resistivity, V (per square) Surface Conductivity, S (per square)

P g
ps 5 Rs gs 5 G
g P s
Circular (Fig. 4) P = pD0
Rectangular P = 2(a + b + 2g)
Square P = 4(a + g)
Tubes (Figs. 5 and 6) P = 2p D2
Nomenclature:
A = the effective area of the measuring electrode for the particular arrangement employed,
P = the effective perimeter of the guarded electrode for the particular arrangement employed,
Rv = measured volume resistance in ohms,
Gv = measured volume conductance in siemens,
Rs = measured surface resistance in ohms,
Gs = measured surface conductance in siemens,
t = average thickness of the specimen,
D0, D1, D2, g, L = dimensions indicated in Figs. 4 and 6 (see Appendix X2 for correction to g),
a, b, = lengths of the sides of rectangular electrodes, and
ln = natural logarithm.
A
All dimensions are in centimetres.

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 D 257 – 99 (2005)
7. Choice of Apparatus and Test Method
7.1 Power Supply—A source of very steady direct voltage is
required (see X1.7.3). Batteries or other stable direct voltage
supplies may be used.
7.2 Guard Circuit—Whether measuring resistance of an
insulating material with two electrodes (no guard) or with a
three-terminal system (two electrodes plus guard), consider
how the electrical connections are made between the test
instrument and the test sample. If the test specimen is at some
distance from the test instrument, or the test specimen is tested
under humid conditions, or if a relatively high (1010 to 1015
ohms) specimen resistance is expected, spurious resistance
paths can easily exist between the test instrument and test
specimen. A guard circuit is necessary to minimize interference
from these spurious paths (see also X1.9).
7.2.1 With Guard Electrode—Use coaxial cable, with the
core lead to the guarded electrode and the shield to the guard
electrode, to make adequate guarded connections between the
test equipment and test specimen. Coaxial cable (again with the
shield tied back to the guard) for the unguarded lead is not
mandatory here (or in 7.2.2), although its use provides some
reduction in background noise (see also Fig. 8).
7.2.2 Without Guard Electrode—Use coaxial cable, with the
core lead to one electrode and the shield terminated about 1 cm FIG. 9 Connections to Unguarded Electrodes for Unguarded
from the end of the core lead (see also Fig. 9). Surface Measurements
7.3 Direct Measurements—The current through a specimen
at a fixed voltage may be measured using any equipment that nometers. Typical methods and circuits are given in Appendix
has the required sensitivity and accuracy (610 % is usually X3. When the measuring device scale is calibrated to read
adequate). Current-measuring devices available include elec- ohms directly no calculations are required.
trometers, d-c amplifiers with indicating meters, and galva- 7.4 Comparison Methods—A Wheatstone-bridge circuit
may be used to compare the resistance of the specimen with
that of a standard resistor (see Appendix X3).
7.5 Precision and Bias Considerations:
7.5.1 General—As a guide in the choice of apparatus, the
pertinent considerations are summarized in Table 2, but it is not
implied that the examples enumerated are the only ones
applicable. This table is not intended to indicate the limits of
sensitivity and error of the various methods per se, but rather
is intended to indicate limits that are distinctly possible with
modern apparatus. In any case, such limits can be achieved or
exceeded only through careful selection and combination of the
apparatus employed. It must be emphasized, however, that the
errors considered are those of instrumentation only. Errors such
as those discussed in Appendix X1 are an entirely different
matter. In this latter connection, the last column of Table 2 lists
the resistance that is shunted by the insulation resistance
between the guarded electrode and the guard system for the
various methods. In general, the lower such resistance, the less
probability of error from undue shunting.
NOTE 2—No matter what measurement method is employed, the
highest precisions are achieved only with careful evaluation of all sources
of error. It is possible either to set up any of these methods from the
component parts, or to acquire a completely integrated apparatus. In
general, the methods using high-sensitivity galvanometers require a more
permanent installation than those using indicating meters or recorders. The
methods using indicating devices such as voltmeters, galvanometers, d-c
amplifiers, and electrometers require the minimum of manual adjustment
FIG. 8 Connections to Guarded Electrode for Volume and Surface and are easy to read but the operator is required to make the reading at a
Resistivity Measurements (Volume Resistance hook-up shown) particular time. The Wheatstone bridge (Fig. X1.4) and the potentiometer

7
 D 257 – 99 (2005)
TABLE 2 Apparatus and Conditions for Use
Ohms Shunted by
Reference Maximum Ohms Maximum Ohms Insulation Resistance
Type of
Method Detectable Measurable to from Guard to
Measurement
Section Figure at 500 V 66 % at 500 V Guarded
Electrode
Voltmeter-ammeter (galvanometer) X3.1 X1 1012 1011 deflection 10 to 105
Comparison (galvanometer) X3.4 X3 1012 1011 deflection 10 to 105
Voltmeter-ammeter (dc amplifica- X3.2 X2(a) deflection 102 to 109
tion, electrometer) (Position 1) 1015 1013
X2(a) deflection 102 to 103
(Position 2) 1015 1013 deflection 103 to 1011
X2(b) 1017 1015 null 0 (effective)
X2(b) 1017 1015
Comparison (Wheatstone bridge) X3.5 X4 1015 1014 null 105 to 106
Voltage rate-of-change X3.3 X5 ;100 MV·F deflection unguarded
Megohmmeter (typical) commercial instruments 1015 1014 direct-reading 104 to 1010

method (Fig. X1.2 (b)) require the undivided attention of the operator in available. If 10-mV input to the amplifier or electrometer gives
keeping a balance, but allow the setting at a particular time to be read at full-scale deflection with an error not greater than 2 % of full
leisure.
scale, with 500 V applied, a resistance of 5000 TV can be
7.5.2 Direct Measurements: measured with a maximum error of 6 % when the voltmeter
7.5.2.1 Galvanometer-Voltmeter—The maximum percent- reads full scale, and 10 % when it reads 1⁄3 scale.
age error in the measurement of resistance by the 7.5.2.3 Comparison-Galvanometer—The maximum per-
galvanometer-voltmeter method is the sum of the percentage centage error in the computed resistance or conductance is
errors of galvanometer indication, galvanometer readability, given by the sum of the percentage errors in Rs, the galvanom-
and voltmeter indication. As an example: a galvanometer eter deflections or amplifier readings, and the assumption that
having a sensitivity of 500 pA/scale division will be deflected the current sensitivities are independent of the deflections. The
25 divisions with 500 V applied to a resistance of 40 GV latter assumption is correct to well within 62 % over the useful
(conductance of 25 pS). If the deflection can be read to the range (above 1⁄10 full-scale deflection) of a good, modern
nearest 0.5 division, and the calibration error (including Ayrton galvanometer (probably 1⁄3 scale deflection for a dc current
Shunt error) is 62 % of the observed value, the resultant amplifier). The error in Rs depends on the type of resistor used,
galvanometer error will not exceed 64 %. If the voltmeter has
but resistances of 1 MV with a limit of error as low as 0.1 %
an error of 62 % of full scale, this resistance can be measured
are available. With a galvanometer or d-c current amplifier
with a maximum error of 66 % when the voltmeter reads full
having a sensitivity of 10 nA for full-scale deflection, 500 V
scale, and 610 % when it reads one-third full scale. The
applied to a resistance of 5 TV will produce a 1 % deflection.
desirability of readings near full scale are readily apparent.
At this voltage, with the preceding noted standard resistor, and
7.5.2.2 Voltmeter-Ammeter—The maximum percentage er-
with Fs = 105, ds would be about half of full-scale deflection,
ror in the computed value is the sum of the percentage errors
with a readability error not more than 61 %. If dx is approxi-
in the voltages, Vx and Vs, and the resistance, Rs. The errors in
mately 1⁄4 of full-scale deflection, the readability error would
Vs and Rs are generally dependent more on the characteristics
not exceed 64 %, and a resistance of the order of 200 GV
of the apparatus used than on the particular method. The most
could be measured with a maximum error of 651⁄2 %.
significant factors that determine the errors in Vs are indicator
errors, amplifier zero drift, and amplifier gain stability. With 7.5.2.4 Voltage Rate-of-Change—The accuracy of the mea-
modern, well-designed amplifiers or electrometers, gain stabil- surement is directly proportional to the accuracy of the
ity is usually not a matter of concern. With existing techniques, measurement of applied voltage and time rate of change of the
the zero drift of direct voltage amplifiers or electrometers electrometer reading. The length of time that the electrometer
cannot be eliminated but it can be made slow enough to be switch is open and the scale used should be such that the time
relatively insignificant for these measurements. The zero drift can be measured accurately and a full-scale reading obtained.
is virtually nonexistent for carefully designed converter-type Under these conditions, the accuracy will be comparable with
amplifiers. Consequently, the null method of Fig. X1.2 (b) is that of the other methods of measuring current.
theoretically less subject to error than those methods employ- 7.5.2.5 Comparison Bridge—When the detector has ad-
ing an indicating instrument, provided, however, that the equate sensitivity, the maximum percentage error in the com-
potentiometer voltage is accurately known. The error in Rs is to puter resistance is the sum of the percentage errors in the arms,
some extent dependent on the amplifier sensitivity. For mea- A, B, and N. With a detector sensitivity of 1 mV/scale division,
surement of a given current, the higher the amplifier sensitivity, 500 V applied to the bridge, and RN = 1 GV, a resistance of
the greater likelihood that lower valued, highly precise wire- 1000 TV will produce a detector deflection of one scale
wound standard resistors can be used. Such amplifiers can be division. Assuming negligible errors in RA and RB, with RN = 1
obtained. Standard resistances of 100 GV known to 62 %, are GV known to within 62 % and with the bridge balanced to one

8
 D 257 – 99 (2005)
detector-scale division, a resistance of 100 TV can be mea- the measurement (this is particularly important for high-input-
sured with a maximum error of 66 %. impedance instruments, such as electrometers). If the gap is
made equal to twice the specimen thickness, as suggested in
8. Sampling 9.3.3, so that the specimen can be used also for surface
8.1 Refer to applicable materials specifications for sam- resistance or conductance determinations, the effective area of
pling instructions. electrode No. 1 can be taken, usually with sufficient accuracy,
as extending to the center of the gap. If, under special
9. Test Specimens conditions, it becomes desirable to determine a more accurate
9.1 Insulation Resistance or Conductance Determination: value for the effective area of electrode No. 1, the correction
9.1.1 The measurement is of greatest value when the speci- for the gap width can be obtained from Appendix X2. Elec-
men has the form, electrodes, and mounting required in actual trode No. 3 may have any shape provided that it extends at all
use. Bushings, cables, and capacitors are typical examples for points beyond the inner edge of electrode No. 2 by at least
which the test electrodes are a part of the specimen and its twice the specimen thickness.
normal mounting means. 9.2.4 For tubular specimens, electrode No. 1 should encircle
9.1.2 For solid materials, the test specimen may be of any the outside of the specimen and its axial length should be at
practical form. The specimen forms most commonly used are least four times the specimen wall thickness. Considerations
flat plates, tapes, rods, and tubes. The electrode arrangements regarding the gap width are the same as those given in 9.2.3.
of Fig. 2 may be used for flat plates, rods, or rigid tubes whose Electrode No. 2 consists of an encircling electrode at each end
inner diameter is about 20 mm or more. The electrode of the tube, the two parts being electrically connected by
arrangement of Fig. 3 may be used for strips of sheet material external means. The axial length of each of these parts should
or for flexible tape. For rigid strip specimens the metal support be at least twice the wall thickness of the specimen. Electrode
may not be required. The electrode arrangements of Fig. 6 may No. 3 must cover the inside surface of the specimen for an axial
be used for flat plates, rods, or tubes. Comparison of materials length extending beyond the outside gap edges by at least twice
when using different electrode arrangements is frequently the wall thickness. The tubular specimen (Fig. 5) may take the
inconclusive and should be avoided. form of an insulated wire or cable. If the length of electrode is
9.2 Volume Resistance or Conductance Determination: more than 100 times the thickness of the insulation, the effects
9.2.1 The test specimen may have any practical form that of the ends of the guarded electrode become negligible, and
allows the use of a third electrode, when necessary, to guard careful spacing of the guard electrodes is not required. Thus,
against error from surface effects. Test specimens may be in the the gap between electrodes No. 1 and No. 2 may be several
form of flat plates, tapes, or tubes. Fig. 4 and Fig. 7 illustrate centimetres to permit sufficient surface resistance between
the application and arrangement of electrodes for plate or sheet these electrodes when water is used as electrode No. 1. In this
specimens. Fig. 5 is a diametral cross section of three elec- case, no correction is made for the gap width.
trodes applied to a tubular specimen, in which electrode No. 1
9.3 Surface Resistance or Conductance Determination:
is the guarded electrode, electrode No. 2 is a guard electrode
consisting of a ring at each end of electrode No. 1, and 9.3.1 The test specimen may be of any practical form
electrode No. 3 is the unguarded electrode (7, 8). For materials consistent with the particular objective, such as flat plates,
that have negligible surface leakage, the guard rings may be tapes, or tubes.
omitted. Convenient and generally suitable dimensions appli- 9.3.2 The arrangements of Fig. 2 and Fig. 3 were devised for
cable to Fig. 4 in the case of test specimens that are 3 mm in those cases where the volume resistance is known to be high
thickness are as follows: D3 = 100 mm, D2 = 88 mm, and relative to that of the surface (2). However, the combination of
D1 = 76 mm, or alternatively, D3 = 50 mm, D2 = 38 mm, and molded and machined surfaces makes the result obtained
D1 = 25 mm. For a given sensitivity, the larger specimen generally inconclusive for rigid strip specimens. The arrange-
allows more accurate measurements on materials of higher ment of Fig. 3 is somewhat more satisfactory when applied to
resistivity. specimens for which the width is much greater than the
9.2.2 Measure the average thickness of the specimens in thickness, the cut edge effect thus tending to become relatively
accordance with one of the methods in Test Methods D 374 small. Hence, this arrangement is more suitable for testing thin
pertaining to the material being tested. The actual points of specimens such as tape, than for testing relatively thicker
measurement shall be uniformly distributed over the area to be specimens. The arrangements of Fig. 2 and Fig. 3 should never
covered by the measuring electrodes. be used for surface resistance or conductance determinations
9.2.3 It is not necessary that the electrodes have the circular without due considerations of the limitations noted previously.
symmetry shown in Fig. 4 although this is generally conve- 9.3.3 The three electrode arrangements of Fig. 4, Fig. 6 and
nient. The guarded electrode (No. 1) may be circular, square, or Fig. 7 may be used for purposes of material comparison. The
rectangular, allowing ready computation of the guarded elec- resistance or conductance of the surface gap between elec-
trode area for volume resistivity or conductivity determination trodes No. 1 and No. 2 is determined directly by using
when such is desired. The diameter of a circular electrode, the electrode No. 1 as the guarded electrode, electrode No. 3 as the
side of a square, or the shortest side of a rectangular electrode, guard electrode, and electrode No. 2 as the unguarded electrode
should be at least four times the specimen thickness. The gap (7, 8). The resistance or conductance so determined is actually
width should be great enough so that the surface leakage the resultant of the surface resistance or conductance between
between electrodes No. 1 and No. 2 does not cause an error in electrodes No. 1 and No. 2 in parallel with some volume

9
 D 257 – 99 (2005)
resistance or conductance between the same two electrodes. 12.3.1 Measure the electrode dimensions and the distance
For this arrangement the surface gap width, g, should be between the electrodes, g. Measure the surface resistance or
approximately twice the specimen thickness, t, except for thin conductance between electrodes No. 1 and 2 with a suitable
specimens, where g may be much greater than twice the device having the required sensitivity and accuracy. Unless
material thickness. otherwise specified, the time of electrification shall be 60 s, and
9.3.4 Special techniques and electrode dimensions may be the applied direct voltage shall be 500 6 5 V.
required for very thin specimens having such a low volume 12.3.2 When the electrode arrangement of Fig. 3 is used, P
resistivity that the resultant low resistance between the guarded is taken as the perimeter of the cross section of the specimen.
electrode and the guard system would cause excessive error. For thin specimens, such as tapes, this perimeter effectively
9.4 Liquid Insulation Resistance—The sampling of liquid reduces to twice the specimen width.
insulating materials, the test cells employed, and the methods 12.3.3 When the electrode arrangements of Fig. 6 are used
of cleaning the cells shall be in accordance with Test Method (and the volume resistance is known to be high compared to the
D 1169. surface resistance), P is taken to be the length of the electrodes
or circumference of the cylinder.
10. Specimen Mounting
13. Calculation
10.1 In mounting the specimens for measurements, it is 13.1 Calculate the volume resistivity, rv, and the volume
important that there shall be no conductive paths between the conductivity, gv, using the equations in Table 1.
electrodes or between the measuring electrodes and ground that 13.2 Calculate the surface resistivity, rs, and the surface
will have a significant effect on the reading of the measuring conductivity, gs, using the equations in Table 1.
instrument (9). Insulating surfaces should not be handled with
bare fingers (acetate rayon gloves are recommended). For 14. Report
referee tests of volume resistivity or conductivity, the surfaces 14.1 Report the following information:
should be cleaned with a suitable solvent before conditioning. 14.1.1 A description and identification of the material
When surface resistance is to be measured, the surfaces should (name, grade, color, manufacturer, etc.),
be cleaned or not cleaned as specified or agreed upon. 14.1.2 Shape and dimensions of the test specimen,
14.1.3 Type and dimensions of electrodes,
11. Conditioning 14.1.4 Conditioning of the specimen (cleaning, predrying,
11.1 The specimens shall be conditioned in accordance with hours at humidity and temperature, etc.),
Practice D 618. 14.1.5 Test conditions (specimen temperature, relative hu-
11.2 Circulating-air environmental chambers or the methods midity, etc., at time of measurement),
described in Practices E 104 or D 5032 may be used for 14.1.6 Method of measurement (see Appendix X3),
controlling the relative humidity. 14.1.7 Applied voltage,
14.1.8 Time of electrification of measurement,
12. Procedure 14.1.9 Measured values of the appropriate resistances in
ohms or conductances in siemens,
12.1 Insulation Resistance or Conductance—Properly
14.1.10 Computed values when required, of volume resis-
mount the specimen in the test chamber. If the test chamber and
tivity in ohm-centimetres, volume conductivity in siemens per
the conditioning chamber are the same (recommended proce-
centimetre, surface resistivity in ohms (per square), or surface
dure), the specimens should be mounted before the condition-
conductivity in siemens (per square), and
ing is started. Make the measurement with a suitable device
14.1.11 Statement as to whether the reported values are
having the required sensitivity and accuracy (see Appendix ).
“apparent” or “steady-state.”
Unless otherwise specified, the time of electrification shall be
60 s and the applied direct voltage shall be 500 6 5 V. 15. Precision and Bias
12.2 Volume Resistivity or Conductivity—Measure the di- 15.1 Precision and bias are inherently affected by the choice
mensions of the electrodes and width of guard gap, g. Make the of method, apparatus, and specimen. For analysis and details
measurement with a suitable device having the required see Sections 7 and 9, and particularly 7.5.1-7.5.2.5.
sensitivity and accuracy. Unless otherwise specified, the time
of electrification shall be 60 s, and the applied direct voltage 16. Keywords
shall be 500 6 5 V. 16.1 DC resistance; insulation resistance; surface resistance;
12.3 Surface Resistance or Conductance: surface resistivity; volume resistance; volume resistivity

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 D 257 – 99 (2005)
APPENDIXES

(Nonmandatory Information)

X1. FACTORS AFFECTING INSULATION RESISTANCE OR CONDUCTANCE MEASUREMENTS

X1.1 Inherent Variation in Materials—Because of the NOTE X1.1—The resistance of an electrical insulating material may be
variability of the resistance of a given specimen under similar affected by the time of temperature exposure. Therefore, equivalent
test conditions and the nonuniformity of the same material temperature conditioning periods are essential for comparative measure-
ments.
from specimen to specimen, determinations are usually not NOTE X1.2—If the insulating material shows signs of deterioration after
reproducible to closer than 10 % and often are even more conditioning at elevated temperatures, this information must be included
widely divergent (a range of values from 10 to 1 may be with the test data.
obtained under apparently identical conditions).
X1.3 Temperature and Humidity—The insulation resis-
X1.2 Temperature—The resistance of electrical insulating tance of solid dielectric materials decreases both with increas-
materials is known to change with temperature, and the ing temperature as described in X1.2 and with increasing
variation often can be represented by a function of the form: humidity (1, 2, 3, 4). Volume resistance is particularly sensitive
(18) to temperature changes, while surface resistance changes
widely and very rapidly with humidity changes (2, 3). In both
R 5 Bem/T (X1.1)
cases the change is exponential. For some materials a change
where: from 25 to 100°C may change insulation resistance or conduc-
R = resistance (or resistivity) of an insulating material or tance by a factor of 100 000, often due to the combined effects
system, of temperature and moisture content change; the effect of
B = proportionality constant, temperature change alone is usually much smaller. A change
m = activation constant, and from 25 to 90 % relative humidity may change insulation
T = absolute temperature in kelvin (K). resistance or conductance by as much as a factor of 1 000 000
This equation is a simplified form of the Arrhenius equation or more. Insulation resistance or conductance is a function of
relating the activation energy of a chemical reaction to the both the volume and surface resistance or conductance of the
absolute temperature; and the Boltzmann principle, a general specimen, and surface resistance changes almost instanta-
law dealing with the statistical distribution of energy among neously with change of relative humidity. It is, therefore,
large numbers of minute particles subject to thermal agitation. absolutely essential to maintain both temperature and relative
The activation constant, m, has a value that is characteristic of humidity within close limits during the conditioning period and
a particular energy absorption process. Several such processes to make the insulation resistance or conductance measurements
may exist within the material, each with a different effective in the specified conditioning environment. Another point not to
temperature range, so that several values of m would be needed be overlooked is that at relative humidities above 90 %, surface
to fully characterize the material. These values of m can be condensation may result from inadvertant fluctuations in hu-
determined experimentally by plotting the natural logarithm of midity or temperature produced by the conditioning system.
resistance against the reciprocal of the absolute temperature. This problem can be avoided by the use of equivalent absolute
The desired values of m are obtained from such a plot by humidity at a slightly higher temperature, as equilibrium
measuring the slopes of the straight-line sections of the plot. moisture content remains nearly the same for a small tempera-
This derives from (Eq X1.1), for it follows that by taking the ture change. In determining the effect of humidity on volume
natural logarithm of both sides: resistance or conductance, extended periods of conditioning
1 are required, since the absorption of water into the body of the
1n R 5 ln B 1 m T (X1.2) dielectric is a relatively slow process (10). Some specimens
require months to come to equilibrium. When such long
The change in resistance (or resistivity) corresponding to a
periods of conditioning are prohibitive, use of thinner speci-
change in absolute temperature from T1 to T2, based on Eq
mens or comparative measurements near equilibrium may be
X1.1, and expressed in logarithmic form, is:
reasonable alternatives, but the details must be included in the
S1 1
D S D
DT
ln ~R2/R1! 5 m T 2 T 5 m T T
2 1 1 2
(X1.3) test report.

These equations are valid over a temperature range only if X1.4 Time of Electrification—Measurement of a dielectric
the material does not undergo a transition within this tempera- material is not fundamentally different from that of a conductor
ture range. Extrapolations are seldom safe since transitions are except that an additional parameter, time of electrification, (and
seldom obvious or predictable. As a corollary, deviation of a in some cases the voltage gradient) is involved. The relation-
plot of the logarithm of R against 1/T from a straight line is ship between the applied voltage and the current is involved in
evidence that a transition is occurring. Furthermore, in making both cases. For dielectric materials, the standard resistance
comparisons between materials, it is essential that measure- placed in series with the unknown resistance must have a
ments be made over the entire range of interest for all relatively low value, so that essentially full voltage will be
materials. applied across the unknown resistance. When a potential

11
 D 257 – 99 (2005)
difference is applied to a specimen, the current through it X1.6 Contour of Specimen:
generally decreases asymptotically toward a limiting value
X1.6.1 The measured value of the insulation resistance or
which may be less than 0.01 of the current observed at the end
conductance of a specimen results from the composite effect of
of 1 min (9, 11). This decrease of current with time is due to
its volume and surface resistances or conductances. Since the
dielectric absorption (interfacial polarization, volume charge,
relative values of the components vary from material to
etc.) and the sweep of mobile ions to the electrodes. In general,
material, comparison of different materials by the use of the
the relation of current and time is of the form I(t) = At −m, after
electrode systems of Fig. 1, Fig. 2, and Fig. 3 is generally
the initial charge is completed and until the true leakage current
inconclusive. There is no assurance that, if material A has a
becomes a significant factor (12, 13). In this relation A is a
higher insulation resistance than material B as measured by the
constant, numerically the current at unit time, and m usually,
use of one of these electrode systems, it will also have a higher
but not always, has a value between 0 and 1. Depending upon
the characteristics of the specimen material, the time required resistance than B in the application for which it is intended.
for the current to decrease to within 1 % of this minimum value X1.6.2 It is possible to devise specimen and electrode
may be from a few seconds to many hours. Thus, in order to configurations suitable for the separate evaluation of the
ensure that measurements on a given material will be compa- volume resistance or conductance and the approximate surface
rable, it is necessary to specify the time of electrification. The resistance or conductance of the same specimen. In general,
conventional arbitrary time of electrification has been 1 min. this requires at least three electrodes so arranged that one may
For some materials, misleading conclusions may be drawn select electrode pairs for which the resistance or conductance
from the test results obtained at this arbitrary time. A measured is primarily that of either a volume current path or a
resistance-time or conductance-time curve should be obtained surface current path, not both (7).
under the conditions of test for a given material as a basis for
selection of a suitable time of electrification, which must be X1.7 Deficiencies in the Measuring Circuit:
specified in the test method for that material, or such curves X1.7.1 The insulation resistance of many solid dielectric
should be used for comparative purposes. Occasionally, a specimens is extremely high at standard laboratory conditions,
material will be found for which the current increases with approaching or exceeding the maximum measurable limits
time. In this case either the time curves must be used or a given in Table 2. Unless extreme care is taken with the
special study undertaken, and arbitrary decisions made as to insulation of the measuring circuit, the values obtained are
the time of electrification. more a measure of apparatus limitations than of the material
itself. Thus errors in the measurement of the specimen may
X1.5 Magnitude of Voltage: arise from undue shunting of the specimen, reference resistors,
X1.5.1 Both volume and surface resistance or conductance or the current-measuring device, by leakage resistances or
of a specimen may be voltage-sensitive (4). In that case, it is conductances of unknown, and possibly variable, magnitude.
necessary that the same voltage gradient be used if measure- X1.7.2 Electrolytic, contact, or thermal emf’s may exist in
ments on similar specimens are to be comparable. Also, the the measuring circuit itself; or spurious emf’s may be caused
applied voltage should be within at least 5 % of the specified by leakage from external sources. Thermal emf’s are normally
voltage. This is a separate requirement from that given in insignificant except in the low resistance circuit of a galva-
X1.7.3, which discusses voltage regulation and stability where nometer and shunt. When thermal emf’s are present, random
appreciable specimen capacitance is involved. drifts in the galvanometer zero occur. Slow drifts due to air
X1.5.2 Commonly specified test voltages to be applied to currents may be troublesome. Electrolytic emf’s are usually
the complete specimen are 100, 250, 500, 1000, 2500, 5000, associated with moist specimens and dissimilar metals, but
10 000 and 15 000 V. Of these, the most frequently used are emf’s of 20 mV or more can be obtained in the guard circuit of
100 and 500 V. The higher voltages are used either to study the a high-resistance detector when pieces of the same metal are in
voltage-resistance or voltage-conductance characteristics of contact with moist specimens. If a voltage is applied between
materials (to make tests at or near the operating voltage the guard and the guarded electrodes a polarization emf may
gradients), or to increase the sensitivity of measurement. remain after the voltage is removed. True contact emf’s can be
X1.5.3 Specimen resistance or conductance of some mate- detected only with an electrometer and are not a source of
rials may, depending upon the moisture content, be affected by error. The term “spurious emf’’ is sometimes applied to
the polarity of the applied voltage. This effect, caused by electrolytic emf’s. To ensure the absence of spurious emf’s of
electrolysis or ionic migration, or both, particularly in the whatever origin, the deflection of the detecting device should
presence of nonuniform fields, may be particularly noticeable be observed before the application of voltage to the specimen
in insulation configurations such as those found in cables and after the voltage has been removed. If the two deflections
where the test-voltage gradient is greater at the inner conductor are the same, or nearly the same, a correction can be made to
than at the outer surface. Where electrolysis or ionic migration the measured resistance or conductance, provided the correc-
does exist in specimens, the electrical resistance will be lower tion is small. If the deflections differ widely, or approach the
when the smaller test electrode is made negative with respect deflection of the measurement, it will be necessary to find and
to the larger. In such cases, the polarity of the applied voltage eliminate the source of the spurious emf (5). Capacitance
shall be specified according to the requirements of the speci- changes in the connecting shielded cables can cause serious
men under test. difficulties.

12
 D 257 – 99 (2005)
X1.7.3 Where appreciable specimen capacitance is in- should be connected together until the measurement is to be
volved, both the regulation and transient stability of the applied made to prevent any build-up of charge from the surroundings.
voltage should be such that resistance or conductance measure-
ments can be made to prescribed accuracy. Short-time tran- X1.9 Guarding:
sients, as well as relatively long-time drifts in the applied X1.9.1 Guarding depends on interposing, in all critical
voltage may cause spurious capacitive charge and discharge insulated paths, guard conductors which intercept all stray
currents which can significantly affect the accuracy of mea- currents that might otherwise cause errors. The guard conduc-
surement. In the case of current-measuring methods particu- tors are connected together, constituting the guard system and
larly, this can be a serious problem. The current in the forming, with the measuring terminals, a three-terminal net-
measuring instrument due to a voltage transient is I0 = CxdV/dt. work. When suitable connections are made, stray currents from
The amplitude and rate of pointer excursions depend upon the spurious external voltages are shunted away from the measur-
following factors: ing circuit by the guard system.
X1.7.3.1 The capacitance of the specimen, X1.9.2 Proper use of the guard system for the methods
X1.7.3.2 The magnitude of the current being measured, involving current measurement is illustrated in Figs. X1.1-
X1.7.3.3 The magnitude and duration of the incoming X1.3, inclusive, where the guard system is shown connected to
voltage transient, and its rate of change, the junction of the voltage source and current-measuring
X1.7.3.4 The ability of the stabilizing circuit used to pro- instrument or standard resistor. In Fig. X1.4 for the
vide a constant voltage with incoming transients of various Wheatstone-bridge method, the guard system is shown con-
characteristics, and nected to the junction of the two lower-valued-resistance arms.
X1.7.3.5 The time-constant of the complete test circuit as In all cases, to be effective, guarding must be complete, and
compared to the period and damping of the current-measuring must include any controls operated by the observer in making
instrument. the measurement. The guard system is generally maintained at
X1.7.4 Changes of range of a current-measuring instrument a potential close to that of the guarded terminal, but insulated
may introduce a current transient. When Rm [Lt ] Rx and Cm[Lt from it. This is because, among other things, the resistance of
]Cx, the equation of this transient is many insulating materials is voltage-dependent. Otherwise, the
direct resistances or conductances of a three-terminal network
I 5 ~V0 / Rx!@I 2 e2t/RmCx# (X1.4)
are independent of the electrode potentials. It is usual to ground
where: the guard system and hence one side of the voltage source and
V0 = applied voltage, current-measuring device. This places both terminals of the
Rx = apparent resistance of the specimen, specimen above ground. Sometimes, one terminal of the
Rm = effective input resistance of the measuring instru- specimen is permanently grounded. The current-measuring
ment, device usually is then connected to this terminal, requiring that
Cx = capacitance of the specimen at 1000 Hz, the voltage source be well insulated from ground.
Cm = input capacitance of the measuring instrument, and X1.9.3 Errors in current measurements may result from the
t = time after Rm is switched into the circuit. fact that the current-measuring device is shunted by the
For not more than 5 % error due to this transient, resistance or conductance between the guarded terminal and
RmCx # t/3 (X1.5) the guard system. This resistance should be at least 10 to 100
times the input resistance of the current measuring device. In
Microammeters employing feedback are usually free of this
some bridge techniques, the guard and measuring terminals are
source of error as the actual input resistance is divided,
brought to nearly the same potentials, but a standard resistor in
effectively, by the amount of feedback, usually at least by 1000.
the bridge is shunted between the unguarded terminal and the
guard system. This resistance should be at least 1000 times that
X1.8 Residual Charge—In X1.4 it was pointed out that the
of the reference resistor.
current continues for a long time after the application of a
potential difference to the electrodes. Conversely, current will
continue for a long time after the electrodes of a charged
specimen are connected together. It should be established that
the test specimen is completely discharged before attempting
the first measurement, a repeat measurement, a measurement of
volume resistance following a measurement of surface resis-
tance, or a measurement with reversed voltage (9). The time of
discharge before making a measurement should be at least four
times any previous charging time. The specimen electrodes FIG. X1.1 Voltmeter-Ammeter Method Using a Galvanometer

13
 D 257 – 99 (2005)

FIG. X1.2 Voltmeter-Ammeter Method Using DC Amplification

FIG. X1.3 Comparison Method Using a Galvanometer

FIG. X1.4 Comparison Method Using a Wheatstone Bridge

X2. EFFECTIVE AREA OF GUARDED ELECTRODE

X2.1 General—Calculation of volume resistivity from the X2.2 Fringing:

measured volume resistance involves the quantity A, the
X2.2.1 If the specimen material is homogeneous and isotro-
effective area of the guarded electrode. Depending on the
pic, fringing effectively extends the guarded electrode edge by
material properties and the electrode configuration, A differs
an amount (14, 19):
from the actual area of the guarded electrode for either, or both,
of the following reasons. ~g/2! 2 d (X2.1)
X2.1.1 Fringing of the lines of current in the region of the where:
electrode edges may effectively increase the electrode dimen-
d 5 t$~2/p! ln cosh [~p/4!~g/t!#%, (X2.2)
sions.
X2.1.2 If plane electrodes are not parallel, or if tubular and g and t are the dimensions indicated in Fig. 4 and Fig. 6.
electrodes are not coaxial, the current density in the specimen The correction may also be written
will not be uniform, and an error may result. This error is g[1 2 ~2d/g!# 5 Bg (X2.3)
usually small and may be ignored.

14
 D 257 – 99 (2005)
where B is the fraction of the gap width to be added to the 0.4 0.85 2.0 0.41
diameter of circular electrodes or to the dimensions of rectan- 0.5 0.81 2.5 0.34
0.6 0.77 3.0 0.29
gular or cylindrical electrodes. 0.8 0.71
X2.2.2 Laminated materials, however, are somewhat aniso-
tropic after volume absorption of moisture. Volume resistivity NOTE X2.1—The symbol “ln” designates logarithm to the base
e = 2.718. ... When g is approximately equal to 2t, d is determined with
parallel to the laminations is then lower than that in the sufficient approximation by the equation:
perpendicular direction, and the fringing effect is increased.
With such moist laminates, d approaches zero, and the guarded d 5 0.586t (X2.4)
electrode effectively extends to the center of the gap between NOTE X2.2—For tests on thin films when t << g, or when a guard
electrode is not used and one electrode extends beyond the other by a
guarded and unguarded electrodes (14).
distance which is large compared with t, 0.883t should be added to the
X2.2.3 The fraction of the gap width g to be added to the diameter of circular electrodes or to the dimensions of rectangular
diameter of circular electrodes or to the electrode dimensions electrodes.
of rectangular or cylindrical electrodes, B, as determined by the NOTE X2.3—During the transition between complete dryness and
preceding equation for d, is as follows: subsequent relatively uniform volume distribution of moisture, a laminate
g/t B g/t B is neither homogeneous nor isotropic. Volume resistivity is of questionable
0.1 0.96 1.0 0.64 significance during this transition and accurate equations are neither
0.2 0.92 1.2 0.59 possible nor justified, calculations within an order of magnitude being
0.3 0.88 1.5 0.51 more than sufficient.

X3. TYPICAL MEASUREMENT METHODS

X3.1 Voltmeter-Ammeter Method Using a Galvanometer: electrometer are connected to the voltage source and the
X3.1.1 A dc voltmeter and a galvanometer with a suitable specimen as illustrated in Fig. X1.2. The applied voltage is
shunt are connected to the voltage source and to the test measured by a dc voltmeter having the same characteristics as
specimen as shown in Fig. X1.1. The applied voltage is prescribed in X3.1.1. The current is measured in terms of the
measured by a dc voltmeter, having a range and accuracy that voltage drop across a standard resistance, Rs.
will give minimum error in voltage indication. In no case shall X3.2.2 In the circuit shown in Fig. X1.2(a) the specimen
a voltmeter be used that has an error greater than 62 % of full current, Ix, produces across the standard resistance, Rs, a
scale, nor a range such that the deflection is less than one third voltage drop which is amplified by the dc amplifier, and read
of full scale (for a pivot-type instrument). The current is on an indicating meter or galvanometer. The net gain of the
measured by a galvanometer having a high current sensitivity amplifier usually is stabilized by means of a feedback resis-
(a scale length of 0.5 m is assumed, as shorter scale lengths will tance, Rf, from the output of the amplifier. The indicating meter
lead to proportionately higher errors) and provided with a can be calibrated to read directly in terms of the feedback
precision Ayrton universal shunt for so adjusting its deflection voltage,Vf, which is determined from the known value of the
that the readability error does not, in general, exceed 62 % of resistance of Rf, and the feedback current passing through it.
the observed value. The galvanometer should be calibrated to When the amplifier has sufficient intrinsic gain, the feedback
within 62 %. Current can be read directly if the galvanometer voltage, Vs, differs from the voltage, IxRs, by a negligible
is provided with an additional suitable fixed shunt. amount. As shown in Fig. X1.2(a) the return lead from the
X3.1.2 The unknown resistance, Rx, or conductance, Gx, is voltage source, Vx, can be connected to either end of the
calculated as follows: feedback resistor, Rf. With the connection made to the junction
Rx 5 1/Gx 5 Vx/Ix 5 Vx/KdF (X3.1) of Rs andRf (switch in dotted position l), the entire resistance of
Rs is placed in the measuring circuit and any alternating
where: voltage appearing across the specimen resistance is amplified
K = galvanometer sensitivity, in amperes per scale divi-
only as much as the direct voltage Ix Rs , across Rs. With the
sion,
connection made to the other end of Rf (switch position 2), the
d = deflection in scale divisions,
F = ratio of the total current, Ix, to the galvanometer apparent resistance placed in the measuring circuit is Rs times
current, and the ratio of the degenerated gain to the intrinsic gain of the
Vx = applied voltage. amplifier; any alternating voltage appearing across the speci-
men resistance is then amplified by the intrinsic amplifier gain.
X3.2 Voltmeter-Ammeter Method Using DC Amplification X3.2.3 In the circuit shown in Fig. X1.2(b), the specimen
or Electrometer: current, Ix, produces a voltage drop across the standard
X3.2.1 The voltmeter-ammeter method can be extended to resistance, Rs which may or may not be balanced out by
measure higher resistances by using dc amplification or an adjustment of an opposing voltage, Vs, from a calibrated
electrometer to increase the sensitivity of the current measuring potentiometer. If no opposing voltage is used, the voltage drop
device (6, 15, 16). Generally, but not necessarily, this is across the standard resistance, Rs, is amplified by the dc
achieved only with some sacrifice in precision, depending on amplifier or electrometer and read on an indicating meter or
the apparatus used. The dc voltmeter and the dc amplifier or galvanometer. This produces a voltage drop between the

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 D 257 – 99 (2005)
measuring electrode and the guard electrode which may cause s usually specified). Alternatively, the voltage, DV, appearing
an error in the current measurement unless the resistance on the electrometer in a time, Dt, can be used. Since this gives
between the measuring electrode and the guard electrode is at an average of the rate-of-change of voltage during Dt, the time
least 10 to 100 times that of Rs. If an opposing voltage, Vs, is Dt should be centered at the specified electrification time (time
used, the dc amplifier or electrometer serves only as a very since closing S2).
sensitive, high-resistance null detector. The return lead from X3.3.2 If the input resistance of the electrometer is greater
the voltage source, Vx, is connected as shown, to include the than the apparent specimen resistance and the input capaci-
potentiometer in the measuring circuit. When connections are tance is 0.01 or less of that of the specimen, the apparent
made in this manner, no resistance is placed in the measuring resistance at the time at which dV/dt or DV/Dt is determined is
circuit at balance and thus no voltage drop appears between the
Rx 5 V0/Ix 5 V0dt/C0dVm or, V0Dt/C0DVm (X3.3)
measuring electrode and the guard electrode. However, a
steeply increasing fraction of Rs is included in the measuring depending on whether or not a recorder is used. When the
circuit, as the potentiometer is moved off balance. Any electrometer input resistance or capacitance cannot be ignored
alternating voltage appearing across the specimen resistance is or when Vmis more than a small fraction of V0 the complete
amplified by the net amplifier gain. The amplifier may be either equation should be used.
a direct voltage amplifier or an alternating voltage amplifier Rs 5 $V0 [~Rx 1 Rm!/Rm#Vm% / ~C0 1 Cm!dVm/dt (X3.4)
provided with input and output converters. Induced alternating
voltages across the specimen often are sufficiently troublesome where:
that a resistance-capacitance filter preceding the amplifier is C0 = capacitance of Cx at 1000 Hz,
required. The input resistance of this filter should be at least Rm = input resistance of the electrometer,
100 times greater than the effect resistance that is placed in the Cm = input capacitance of the electrometer,
measurement circuit by resistance Rs. V0 = applied voltage, and
X3.2.4 The resistance Rx, or the conductance,G x, is calcu- Vm = electrometer reading = voltage decrease on Cx.
lated as follows:
X3.4 Comparison Method Using a Galvanometer or DC
Rx 5 1/Gx 5 Vx/Ix 5 ~Vx/Vs!Rs (X3.2)
Amplifier (1):
where: X3.4.1 A standard resistance, Rs, and a galvanometer or dc
Vx = applied voltage, amplifier are connected to the voltage source and to the test
Ix = specimen current, specimen as shown in Fig. X3.1 . The galvanometer and its
Rs = standard resistance, and associated Ayrton shunt is the same as described in X3.1.1. An
Vs = voltage drop across Rs, indicated by the amplifier amplifier of equivalent direct current sensitivity with an
output meter, the electrometer or the calibrated appropriate indicator may be used in place of the galvanometer.
potentiometer. It is convenient, but not necessary, and not desirable if batteries
X3.3 Voltage Rate-of-Change Method: are used as the voltage source (unless a high-input resistance
voltmeter is used), to connect a voltmeter across the source for
X3.3.1 If the specimen capacitance is relatively large, or a continuous check of its voltage. The switch is provided for
capacitors are to be measured, the apparent resistant, Rx, can be shorting the unknown resistance in the process of measure-
determined from the charging voltage, V0, the specimen ment. Sometimes provision is made to short either the un-
capacitance value, C0 (capacitance of Cx at 1000 Hz), and the known or standard resistance but not both at the same time.
rate-of-change of voltage, dV/dt, using the circuit of Fig. X3.1
(17). To make a measurement the specimen is charged by X3.4.2 In general, it is preferable to leave the standard
closing S2, with the electrometer shorting switch S1 closed. resistance in the circuit at all times to prevent damage to the
When S1 is subsequently opened, the voltage across the current measuring instrument in case of specimen failure. With
specimen will fall because the leakage and absorption currents the shunt set to the least sensitive position and with the switch
must then be supplied by the capacitance C0 rather than by V0. open, the voltage is applied. The Ayrton shunt is then adjusted
The drop in voltage across the specimen will be shown by the to give as near maximum scale reading as possible. At the end
electrometer. If a recorder is connected to the output of the of the electrification time the deflection, dx, and the shunt ratio,
electrometer, the rate of change of voltage, dV/dt, can be read Fx, are noted. The shunt is then set to the least sensitive
from the recorder trace at any desired time after S2 is closed (60 position and the switch is closed to short the unknown
resistance. Again the shunt is adjusted to give as near maxi-
mum scale reading as possible and the galvanometer or meter
deflection, ds, and the shunt ratio, Fs, are noted. It is assumed
that the current sensitivities of the galvanometer or amplifier
are equal for nearly equal deflections dxand ds.
X3.4.3 The unknown resistance, Rx, or conductance, Gx, is
calculated as follows:
R 5 1/Gx 5 Rs@~dsFs / dxFx! – 1] (X3.5)

where:
FIG. X3.1 Voltage Rate-of-Change Method

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 D 257 – 99 (2005)

Fxand Fs = ratios of the total current to the galvanometer indicating meter of Fig. X1.2(a) can be replaced by a recording
or dc amplifier with Rx in the circuit, and milliammeter or millivoltmeter as appropriate for the amplifier
shorted, respectively. used. The recorder may be either the deflection type or the
X3.4.4 In case Rs is shorted when Rx is in the circuit or the null-balance type, the latter usually having a smaller error.
ratio of Fs to Fx is greater than 100, the value of Rx or Gx is Null-balance-type recorders also can be employed to perform
computed as follows: the function of automatically adjusting the potentiometer
Rx 5 1/Gx 5 R ~dsFs/dxFx! (X3.6) shown in Fig. X1.2(b) and thereby indicating and recording the
quantity under measurement. The characteristics of amplifier,
X3.5 Comparison Methods Using a Wheatstone Bridge (2): recorder balancing mechanism, and potentiometer can be made
X3.5.1 The test specimen is connected into one arm of a such as to constitute a well integrated, stable, electromechani-
Wheatstone bridge as shown in Fig. X1.4. The three known cal, feedback system of high sensitivity and low error. Such
arms shall be of as high resistance as practicable, limited by the systems also can be arranged with the potentiometer fed from
errors inherent in such resistors. Usually, the lowest resistance, the same source of stable voltage as the specimen, thereby
RA, is used for convenient balance adjustment, with either RBor eliminating the voltmeter error, and allowing a sensitivity and
RNbeing changed in decade steps. The detector shall be a dc precision comparable with those of the Wheatstone-Bridge
amplifier, with an input resistance high compared to any of Method (X3.5).
these arms.
X3.5.2 The unknown resistance, Rx, or conductance, Gx, is X3.7 Direct-Reading Instruments—There are available,
calculated as follows: and in general use, instruments that indicate resistance directly,
Rx 5 1/Gx 5 RBRN / RA (X3.7) by a determination of the ratio of voltage and current in bridge
methods or related modes. Some units incorporate various
where RA, RB, and RN are as shown in Fig. X1.4. When arm
advanced features and refinements such as digital readout.
A is a rheostat, its dial can be calibrated to read directly in
Most direct reading instruments are self-contained, portable,
megohms after multiplying by the factor RBRN which for
and comprise a stable dc power supply with multi-test voltage
convenience can be varied in decade steps.
capability, a null detector or an indicator, and all relevant
X3.6 Recordings—It is possible to record continuously auxiliaries. Measurement accuracies vary somewhat with type
against time the values of the unknown resistance or the of equipment and range of resistances covered; for the more
corresponding value of current at a known voltage. Generally, elaborate instruments accuracies are comparable to those
this is accomplished by an adaptation of the voltmeter-ammeter obtained with the voltmeter-ammeter method using a galva-
method, using dc amplification (X3.2). The zero drift of direct nometer (X3.1). The direct-reading instruments do not neces-
coupled dc amplifiers, while slow enough for the measure- sarily supplant any of the other typical measurement methods
ments of X3.2, may be too fast for continuous recording. This described in this Appendix, but do offer simplicity and conve-
problem can be resolved by periodic checks of the zero, or by nience for both routine and investigative resistance
using an ac amplifier with input and output converter. The measurements.

REFERENCES

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Paper No. 234, pp. 369–417. p. 152.
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