i IEEE Std 118-1978 (Revision of IEEE Std118-1949) IEEE Standard Test Code for Resistance Measurement Sponsor Power Engineering Societyof theInstitute of Electrical and Electronics Engineers Approved September 8, 1977Reaffirmed March 19, 1992 IEEE Standards Board Copyright 1978 by The Institute of Electrical and Electronics Engineers, Inc No part of this publication may be reproduced in any form, in an electronic retrieval system or otherwise, without theprior written permission of the publisher.Authorized licensed use limited to: Pontificia Universidad Catolica Del Peru. Downloaded on February 27,2013 at 20:35:38 UTC from IEEE Xplore.Restrictions apply. ii Approved September 8, 1977 IEEE Standards BoardWilliam R. Kruesi , Chair Irvin N. Howell, Jr , Vice Chair Ivan G. Easton , Secretary William E. AndrusR.O. DuncanDonald T. MichaelJean Jacques ArchambaultCharles W. FlintVoss A. MooreMark BarberJay ForsterWilliam S. MorganEdward J. CohenRalph I. HauserWilliam J. NeiswenderWarren H. CookJoseph L. KoepfingerRalph M. ShowersLouis CostrellIrving KolodnyRobert A. SodermanR. L. CurtisBenjamin J. LeonLeonard W. Thomas, SrDavid B. DobsonThomas J. MartinB, W. WhittingtonAuthorized licensed use limited to: Pontificia Universidad Catolica Del Peru. Downloaded on February 27,2013 at 20:35:38 UTC from IEEE Xplore.Restrictions apply. iii Foreword (This Foreword is not a part of IEEE Std 118-1978, Standard Test Code for Resistance Measurement.) TheWorkingGrouptoreviseIEEEStd118,StandardTestCodeforResistanceMeasurement,wasorganizedbyWilliam J. Johnson, then chairman of the Power System Instrumentation and Measurements Committee. The groupmet initially on March 25, 1971. It was decided that the existing standard required almost completely rewriting andthis was undertaken. The general outline of the original Master Test Code was followed but much new material wasadded to supplement the existing information and to include new techniques which have come into general use sincethe previous version was written.At the time it approved this standard the Working Group had the following membership: P. H. Reynolds , Chair A. AbramowitzS.R. KnudseB. G. BarbW.J.M. MooreE. B. CurdtsR. PailthorpeR. E. GodfreyH.J. SuttonL. JulieT.E. WellsJ. F. KatzmaierH.W. WilderAuthorized licensed use limited to: Pontificia Universidad Catolica Del Peru. Downloaded on February 27,2013 at 20:35:38 UTC from IEEE Xplore.Restrictions apply. iv CLAUSE PAGE 1.General ................................................................................................................................................................11.1 Purpose....................................................................................................................................................... 11.2 Scope.......................................................................................................................................................... 11.3 Units ........................................................................................................................................................... 12.General Measurement Problems and Techniques...............................................................................................32.1 Low-Value Resistance Measurements ....................................................................................................... 32.2 High-Value Resistance Measurements ...................................................................................................... 42.3 Intermediate-Value Resistance Measurements .......................................................................................... 52.4 High-Current Resistance Measurements.................................................................................................... 52.5 High-Voltage Resistance Measurements ................................................................................................... 52.6 Environmental Effects................................................................................................................................ 52.7 Self-Heating Effects................................................................................................................................... 62.8 Interconnected Resistances ........................................................................................................................ 62.9 Substitution Methods ................................................................................................................................. 72.10 Measurement of Resistance in the Presence of Inductance ....................................................................... 72.11 Measurement of Resistance in the Presence of Capacitance ..................................................................... 92.12 Stray Effects............................................................................................................................................... 92.13 Measurement of Resistance with Alternating Currents ............................................................................. 93.Standard Resistors.............................................................................................................................................103.1 Standardization of Apparatus................................................................................................................... 103.2 Reference-Standard Resistors .................................................................................................................. 103.3 Working-Standard Resistors .................................................................................................................... 103.4 Heavy-Current Standard Resistors........................................................................................................... 113.5 Nonreactive Resistors .............................................................................................................................. 113.6 High-Voltage Resistors ............................................................................................................................ 113.7 High-Resistance Standard Resistors ........................................................................................................ 113.8 Combinations of Standard Resistors ........................................................................................................ 124.Instrumentation .................................................................................................................................................134.1 Voltmeter-Ammeter (Drop of Potential) Method .................................................................................... 134.2 Voltmeter Method.................................................................................................................................... 144.3 Ammeter Method ..................................................................................................................................... 154.4 Ratio Devices ........................................................................................................................................... 154.5 Bridges ..................................................................................................................................................... 174.6 Comparators ............................................................................................................................................. 214.7 Ohmmeters ............................................................................................................................................... 224.8 Other Methods.......................................................................................................................................... 245.Applications ......................................................................................................................................................255.1 Preferred Circuits and Measuring Techniques......................................................................................... 255.2 Temperature Measurement by Change in Resistance .............................................................................. 255.3 Computation of Resistance for a Required Temperature......................................................................... 255.4 Measurement of Insulation Resistance..................................................................................................... 265.5 Measurement of Ground Resistance ........................................................................................................ 276.References.........................................................................................................................................................30Authorized licensed use limited to: Pontificia Universidad Catolica Del Peru. Downloaded on February 27,2013 at 20:35:38 UTC from IEEE Xplore.Restrictions apply. Copyright 1978 IEEE All Rights Reserved 1 IEEE Standard Test Code for Resistance Measurement 1. General 1.1 Purpose Thepurposeofthiscodeistopresentmethodsofmeasuringelectricalresistancewhicharecommonlyusedtodetermine the characteristics of electric machinery and equipment. The choice of method in any given case depends onthedegreeofaccuracyrequiredandthenatureofthecircuittobemeasured. Aguideforselectingtheappropriatemethod is given in Table 1. 1.2 Scope The methods presented here are limited to those using direct current or commercial power frequencies of 60 Hz orbelowandtothosemeasurementsrequiredtodeterminetheperformancecharacteristicsofelectricmachineryandequipment. Although methods of measuring insulation and ground resistance are given in this code, more completediscussions may be found in [5], [7], [11]. 1 1.3 Units Themeasurementofelectricalresistanceisbaseduponthesystemofelectricalunitsmaintainedbythecountriesadherent to the International Convention of the Meter. These countries cooperate ofcially through the InternationalGeneralConferenceofWeightsandMeasures.UnderthisGeneralConference,theInternationalCommitteeofWeightsandMeasures,aidedbytheadvisorycommittees,includingtheAdvisoryCommitteeonElectricity,hascharge of the International Bureau of Weights and Measures, Sevres, France.The National Bureau of Standards (NBS), Department of Commerce, Washington, DC, is responsible for establishingandmaintainingstandardsforthelegalizedelectricalunitsandisthenalauthorityintheUnitedStatesfortheirvalues. In other countries, legal authority is granted to national standardizing agencies.The unit of resistance, the ohm, is intended to be the closest practical approximation to the International System (SI)unit of resistance. A more complete discussion of SI units may be found in ANSI/IEEE Std 268-1976, Standard MetricPractice. The value of the unit of resistance was adopted in 1948 by international agreement and has been maintainedsince then with negligible uctuation by a group of standard resistors. This unit is usually designated as the legal ohm, 1 Numbers in brackets correspond to those of the references listed at the end of this standard, in Section 6.Authorized licensed use limited to: Pontificia Universidad Catolica Del Peru. Downloaded on February 27,2013 at 20:35:38 UTC from IEEE Xplore.Restrictions apply. 2 Copyright 1978 IEEE All Rights ReservedIEEE Std 118-1978 IEEE STANDARD TEST CODE the absolute ohm, or simply the ohm. Before 1948, the unit was designated as the international ohm and was 495 partsper million larger than the present unit.Knowledge of the amount by which the legal unit differs from the dened SI unit depends upon the results of absolutemeasurements; on the basis of measurements made at NBS and other national standardizing laboratories, it may beconcluded that the two units are unlikely to differ by more than one part per million. Table 1Applications of Resistance Measuring Methods Resistance to be MeasuredAccuracy Required Note (5) Bridge Methods Note (2) Direct Reading MethodsAlternative Methods Low Resistance (see 2.1) (less than approximately 5 Greater than 0.1% Kelvin (4.5.3), current comparator(4.5.6) Note generally applicable Note (4)0.1%1% Kelvin (4.5.3)dual-slope in tegration meter (4.4.3) ratio device, crossed coil (4.4.1)Note (4)less than 1 % any bridge-type circuitdirect-reading ohmmeter (4.7.4) ratio device, crossed coil (4.4.1)ammeter (4.3)Intermediate value resistance (see 2.3) (between approximately 5 and 10 )Greater than 0.01% Wheatstone (4.5.1) ratio (4.5.2) comparators (4.6.1) current comparator (4.5.6) Not generally applicable0.01%1%Wheatstone (4.5.1) ratio (4.5.2)dual-slope in gration tion meter (4.4.3) Operational amplifier (4.4.2), ohmmeter, constant-current type (4.7.3)less than 1%any bridge-type circuit direct-reading ahmmeter (4.4.3) voltmeter/ammeter (4.1), volt- meter (4.2), ratio device, crossed coil (4.4.1), note (3)High Resistance (see 2.2) (above approx- imately 10 M)Greater than 0.1%Modified Wheatstone (4.5.4) ratio (4.5.2) comparators (4.6.1) current comparator (4.5.6)Not generally applicable01.%1%modified Wheatstone (4.5.4) ratio (4.5.2)operational amplifier (4.4.2)Voltmeter/ammeter,modified (4.1.1)less than 1% Wheatstone (4.5.1)radio device, crossed coil (4.4.1)direct deflection (4.6.2) loss of charge (4.8.1) voltmeter/ammeter (4.1 and 4.1.1)NOTES:1 Numbers in parentheses refer to section numbers in the text.2 Limit and deviation techniques may be applicable in all cases (see 4.5.5).3 Almost any of the measuring circuits described can be adapted for use in this category.4 Other bridge, ratio, and comparator circuits may be used.5 This column indicates long-term accuracy, including stability and temperature effects.Authorized licensed use limited to: Pontificia Universidad Catolica Del Peru. Downloaded on February 27,2013 at 20:35:38 UTC from IEEE Xplore.Restrictions apply. Copyright 1978 IEEE All Rights Reserved 3 FOR RESISTANCE MEASUREMENT IEEE Std 118-1978 2. General Measurement Problems and Techniques 2.1 Low-Value Resistance Measurements In low-value resistance measurements, contact resistances may seriously limit accuracy; however, their effects can bereduced considerably by using resistor with four terminals. A resistor of this type is shown in Fig 1. The four-terminalresistance is the resistance between the internal junctions J 1 and J 2 and is dened as(1)where I ab is the current into terminal A and out of terminal B and E cd is the potential between terminals C and D (andtherefore between junctions J 1 and J 2 ). Figure 1Four Terminal Representation of a Resistor Averyusefulpropertyofafour-terminalresistor,derivablefromthereciprocitytheorem,isthatthefour-terminalresistance is unchanged if the two potential terminals are used as current terminals while the two current terminals areused as potential terminals. In other words,(2)Thisstatementassumesthattheself-heatingeffects,ifsignicant,remainthesamewhenthecurrentandpotentialterminals are reversed. Since this assumption is not always valid when high currents are used and signicant heatingoccurs in the terminal resistances R a , R b , R c , and R d , the precise position of these terminals may be critical.Basedontheabovedenitionoffour-terminalresistance,theterminalsonsucharesistorareoftenreferredtoascurrent terminals and potential terminals. However, it is not necessary to measure a four-terminal resistor as implied inthedenition(thatis,withzerocurrentattwooftheterminals),andmanyfour-terminalresistancemeasuringinstruments operate with current in all four leads.Some four-terminal resistance measuring instruments and techniques measure R(x) almost independently of the valuesofterminalresistancesR a ,R b ,R c ,andR d ,theresistanceoftheleadsconnectedtotheterminals,andthecontactresistance between the leads and the terminals. Other measuring instruments and techniques only reduce the effect ofthese resistances by putting them in series with resistances in the measuring circuit whose values are higher than R(x)or by connecting them in other less sensitive parts of the measuring circuit.The advantages of a four-terminal resistance measurement can be realized when measuring two-terminal resistors byconnecting two leads to each end of the resistor to convert it into a four-terminal resistor, as shown in Fig 2. The effectof the four contact resistances and lead resistances can then be effectively eliminated or reduced. It is important to notethat the resistance measured with be the resistance between the contacts at each end that are closest to the resistor.RxEcdIab =EcdIab EabIcd Rx= =Authorized licensed use limited to: Pontificia Universidad Catolica Del Peru. Downloaded on February 27,2013 at 20:35:38 UTC from IEEE Xplore.Restrictions apply. 4 Copyright 1978 IEEE All Rights ReservedIEEE Std 118-1978 IEEE STANDARD TEST CODE Thevalueofresistancebelowwhichitisdesirabletousethefour-terminaltechniquedependssomewhatontheaccuracy required and the quality of the contact surface. The value often chosen is 5 . Figure 2Four Terminal Connections to a Two Terminal Resistor 2.2 High-Value Resistance Measurements In high-value resistance measurements, insulation resistances may seriously limit accuracy. The equivalent circuit ofan undesirable insulation is shown in Fig 3(A), where the resistance to be measured (R x ) is shunted by the resistanceof an insulator (R i ). This would result, for instance, if both supports or test clips for a resistor were mounted on thesame piece of insulation.The equivalent circuit of a more desirable situation is shown in Fig 3(B). This circuit would result, for instance, if thesupports or test clips at each end of the resistor to be measured were mounted on individual insulators that separatedby a conductor to E. It would then be possible to measure R x with the effects of the insulation resistances (R i1 ) and R i2 )reduced or eliminated.The effects of insulation resistances may be controlled by means of a three-terminal resistance measurement. This isdoneinthemeasuringcircuitbyconnectingtheinsulationresistances(R il )andR i2 )wheretheywillnotaffecttheresult at all, or where they will shunt resistors that are lower in value than R x , or by reducing the voltage across one oftheinsulationresistancestozerosothatallofthecurrentinoneofthemeasurementterminalspassesthroughtheresistor being measured. (See also 4.5.4.)Some standard resistors of higher value are of three-terminal construction (see also 3.7), with measurement terminalsmounted on separate insulators and an additional terminal connected to the case.Toavoidproblemswithtestconnectionsinathree-terminalmeasurement,twoseparatelyshieldedleadsshouldbeused for connections to the measurement themselves. Figure 3(A) -- Equivalent Circuit for a Resistor Shunted by Insulation Leakage. (B) -- Equivalent Circuit Showing Method of Reducing the Effect of Insulation Leakage.Authorized licensed use limited to: Pontificia Universidad Catolica Del Peru. Downloaded on February 27,2013 at 20:35:38 UTC from IEEE Xplore.Restrictions apply. Copyright 1978 IEEE All Rights Reserved 5 FOR RESISTANCE MEASUREMENT IEEE Std 118-1978 2.3 Intermediate-Value Resistance Measurements In intermediate-value resistance measurements of moderate accuracy, usually no serious limitations on accuracy resultfrom either contact resistances or insulation resistances. On the other hand, in resistance measurements of the highestaccuracy, both contact resistances and insulation resistances can limit the accuracy.Contact and insulation resistance problems can be handled simultaneously by combining the features of four-terminaland three-terminal measurements in the same measurement. The equivalent circuit of a resistor whose measurementcould be limited by both of these factors is shown in Fig 4. The effects of the contact and insulation resistances arecontrolled as described in 2.1 and 2.2.A measurement that controls the effects of contact and insulation resistances simultaneously can be referred to as ave-terminal measurement. Some standard resistors are of ve-terminal construction. (See Section 3.) Figure 4Equivalent Circuit of a Resistor Incorporating Techniques of Fig 1 and Fig 3(B) 2.4 High-Current Resistance Measurements Whenmeasuringresistorsathighcurrents,contactresistanceeffects,discussedin2.1,andself-heatingeffects,discussed in 2.7, usually must be taken into account. An additional source of uncertainty in the effective resistance ofa high-current resistor of the four-terminal type can arise from nonuniform distribution of current resulting from theplacement of leads at different locations at the current terminals or nonuniform potential on the potential terminals.These effects can be minimized by increasing the length-to-width ratio of the conductors between the terminals and thefour-terminal junctions. (See also 3.4.) 2.5 High-Voltage Resistance Measurements When measuring resistors at high voltage, insulation effects, discussed in 2.2, and self-heating effects, discussed in2.7, usually must be taken into account. In addition, some high-voltage resistors have a voltage coefcient, that is, theirvalue is affected by voltage in addition to self-heating. In measurements where regions of high electrical stress exist,care must be taken to minimize the effects of partial discharges (corona). (See also 3.6.) 2.6 Environmental Effects Thevalueofmostresistorsisaffectedbyenvironmentalparameterssuchastemperature,humidity,atmosphericpressure, and chemical and biological corrosion. When measurements of the highest precision are undertaken, all ofAuthorized licensed use limited to: Pontificia Universidad Catolica Del Peru. Downloaded on February 27,2013 at 20:35:38 UTC from IEEE Xplore.Restrictions apply. 6 Copyright 1978 IEEE All Rights ReservedIEEE Std 118-1978 IEEE STANDARD TEST CODE these factors must be taken into account. In most practical situations, however, temperature is the principal concern.Most pure metals have a temperature coefcient of approximately 0.4 percent per degree Celsius. Several precisionresistoralloyshavetemperaturecoefcientsbelow0.0005percentperdegreeCelsiusoverarangeofatleast50degrees. 2.7 Self-Heating Effects It is usually essential that the resistance under test not be changed in value to a signicant extent by the current whichisnecessarilyusedinthemeasurement.Thisrequirementsometimeslimitsthepermissiblecurrentandhencethesensitivity of the measurement. When measuring the resistance of a copper (or aluminum) winding, the error from thiscause is proportional to the square of the measuring current. For small windings, the current should not exceed 15percentoftheratedcurrentofthewinding.Ifthewindingissomassivethattheresistancemeasurementcanbecompleted before the full temperature rise that would result from continued application of the measuring current isreached, the error will be less and currents of up to 25 percent (or in extreme cases, 50 percent) of rated current maybeused.Itisimportantthatthetemperatureofthewindingatthetimeoftheresistancemeasurementbeknowndenitely,whethertheresistancemeasurementisdesiredforcalculatingefciency(afterbeingcorrectedtoanappropriate reference temperature) or as a basis for measuring temperature rise. Any heating by previous operation orby unduly prolonged measuring currents should be avoided [19], [20]. 2.8 Interconnected Resistances When a resistor, low enough in value to have its measurement seriously affected by contact resistances, is part of aninterconnected network of resistors that can shunt it (that is, a closed loop of resistors), it is still possible to measureits value precisely using six-terminal techniques.Apracticalsituationinvolvingthisproblemisthemeasurementofawindingresistanceinadelta-connectedtransformerwhenitisdifcultorundesirabletodisconnectthemeasuredwindingfromtheothers. Theequivalentcircuit is shown in Fig 5, where R x is the resistance to be measured, R a , R b , R c , R d , R f , and R g are terminal resistances,and R y and R z are resistances with values usually comparable to R x . Figure 5A Six Terminal Resistor MeasurementAuthorized licensed use limited to: Pontificia Universidad Catolica Del Peru. Downloaded on February 27,2013 at 20:35:38 UTC from IEEE Xplore.Restrictions apply. Copyright 1978 IEEE All Rights Reserved 7 FOR RESISTANCE MEASUREMENT IEEE Std 118-1978 The value of R x can be measured as follows:(3)where I b is the current out of terminal B, E cd is the potential between terminals C and D (and between J 1 and J 2 ), and E gd is the potential between terminals G and D (and between J 3 and J 2 ). E gd is brought to zero by adjusting the currentout of terminal F. The current into terminal A is the sum of the currents out of terminals B and F. (See also 4.1.1andFig11.)Asix-terminaltechniquecanalsobeusedonthree-terminalnetworksbyapplyingthemethodsdescribed in 2.1. 2.9 Substitution Methods If a known resistance ( R s ) is available which has about the same value as the unknown resistance ( R x ), each should beconnectedinsuccessiontothemeasuringapparatusandmeasured.Mostofthesystematicerrorsinthemeasuringapparatus will be the same in both measurements and will disappear when R x is expressed as the product of R s and afactor derived from the two readings; thus(4)In resistance measurements for determining temperature rise, this principle comes into use almost automatically. Insuch cases, by proceeding so that all leads, contacts, etc, are changed as little as possible while the test specimen heatsup, temperature rise measurements of a very high accuracy are possible.If several known resistors are available, a large number of dial settings of the measuring circuit can be calibrated bymeasuring groups of these resistors in series and parallel combinations. 2.10 Measurement of Resistance in the Presence of Inductance When the circuit being measured has such a high inductance that its time constant ( L/R ) is also very large, considerableinconvenience is caused by the delay in reaching steady conditions. In measuring the resistance of a heated windingwhich is cooling rapidly, any such delay may impair the measurement.The inductive effect may be reduced by the following methods:1) Use a higher voltage supply with a high resistance in series to reduce the time constant ( L/R )2) Apply a higher voltage initially, then decrease it as the current increases, either manually or by automaticcurrent regulation3) Withiron-coredinductorswhencircumstancespermit,sufcientvoltagemaybeappliedinanauxiliarywinding to saturate the magnetic material4) Whenmeasuringresistanceswheremorethanonewindingispresent,anidlewindingmaybeusedeffectively (see Fig 6). WARNING: When making measurements on highly inductive windings,hazardousvoltagemaybeinduced.Eachindividualsituationmustbecarefully evaluated to avoid danger to personnel.RxEcdIb if Egd0 = =RxRsratio of measured value ofRx:Rs( ) =Authorized licensed use limited to: Pontificia Universidad Catolica Del Peru. Downloaded on February 27,2013 at 20:35:38 UTC from IEEE Xplore.Restrictions apply. 8 Copyright 1978 IEEE All Rights ReservedIEEE Std 118-1978 IEEE STANDARD TEST CODE Figure 6Use of an Idle Winding When Measuring Resistance in the Presence of Inductance If the total resistance ( R c + R y ) in the compensating circuit is adjusted to satisfy the relation(5)where N x and N y are the numbers of turns of windings X and Y, respectively, the current induced by the changing coreux,whichiscommontoXand Y,willnotcirculateinthegalvanometer.Thebridgemaybebalancedbytheadjustment of R n (or R b ) without waiting for the current to become constant. An alternate circuit (shown in Fig 7) maybe used if the number of turns of the idle winding is equal to or greater than that of the winding whose resistance isbeingmeasured. ThevoltagedividershouldbeadjustedtoprovideunityvoltagegainbetweenwindingXandthegalvanometer; that is, its ratio should be set to N x /N y .This technique is most often used with the Wheatstone bridge (see 4.5.1), but similar compensating circuits may beapplied to other types of bridges. Figure 7Alternate Circuit to Fig 6 WARNING: Damage to instrumentation or injury or paranel may resultfrom the induced electromotive force if the circuit is opened while largecurrents are present.RcRyRaRxNyNx------- + = +Authorized licensed use limited to: Pontificia Universidad Catolica Del Peru. Downloaded on February 27,2013 at 20:35:38 UTC from IEEE Xplore.Restrictions apply.Copyright 1978 IEEE All Rights Reserved 9 FOR RESISTANCE MEASUREMENT IEEE Std 118-1978 2.11 Measurement of Resistance in the Presence of Capacitance When the resistance being measured is high and has an appreciable shunt capacitance (either discrete or distributed),the charging current of the capacitance will cause a considerable delay in reaching a steady voltage. This delay can bereduced by using a supply whose internal resistance is low. If a resistance ( R x ) shunted by a capacitance ( C ) is beingsupplied from a source whose effective internal resistance is R i , the time constant ( T c ) of the circuit is derived from thefollowing equation:(6)When a constant supply voltage, the current must be allowed to decay for a period equal to 2.3 T c for an accuracy of10 percent, 4.6 T c for an accuracy of 1 percent, and 6.9 T c for an accuracy of 0.1 percent, etc. If the dielectric showsmarkedabsorption,evenlongerperiodswillberequired.Ifthevoltageappliedtotheresistorvariesby P percentduring one time constant, the error in the measured resistance will be P percent.2.12 Stray EffectsMostresistancemeasuringcircuitscontainundesirablecurrentsthatresultfrompickupofexternalnoiseandhum,internal signal sources that are not pure direct current or pure alternating current, spurious electromotive forces suchas those due to thermoelectric effects, and current or voltage offsets of the detectors. The accuracy of the measurementwill be limited by the response of the detectors to these undesirable signals. In alternating-current measurements, thisproblem is usually solved by using a detector tuned to respond only to the desirable signal frequency. In direct-currentmeasurement, this problem is solved by using detectors with adequate alternating-current rejection (that is, those thatdonotindicateasignicantdirect-currentsignalduetoanalternating-currentinput)andbyuseofthefalse-zeroprocedure.The false-zero procedure refers to taking as the zero point of the measuring apparatus its indication when the spuriouseffects are present but when the power supply is disconnected. This false zero is then used as the null point. In bridgemeasurementsadoublingofsensitivitymayalsobeachievedbydeningthebalancepointasthatforwhichthedetector indication does not change with reversal of the polarity of the power supply.2.13 Measurement of Resistance with Alternating CurrentsThe measurement of resistance by means of alternating currents is attractive because it permits the use of very stableformerratiotechniquesandeliminatestheeffectofthermalelectromotiveforces.However,theresistancetoalternating current may differ from the resistance to direct current for the following reasons:1) Shunt or Series Reactance Inductance in series and capacitance in shunt with a resistance, either discreteor distributed, will alter the impedance (or the effective resistance, or both) to alternating current2) Skin Effect Magnetic elds produced by the current within the conductor, which increases the impedanceat the conductor's center, force the current to concentrate near the outside surface or skin. The effective cross-sectional area of the conductor is therefore reduced. Skin effect is most noticeable in conductors of large crosssection. This effect increases with frequency and, in conductors of ferromagnetic material, is a function of therelative permeabilityWARNING:Damagetoinstrumentationorinjurytopersonnelmayoccurasaresultofvoltagethatmaybedevelopedfromchargesstillabsorbedinthedielectricofacapacitorthathasbeenapparentlydischarged.TcRxR1CRxR1+------------------ -CRiwhen RxRi =Authorized licensed use limited to: Pontificia Universidad Catolica Del Peru. Downloaded on February 27,2013 at 20:35:38 UTC from IEEE Xplore.Restrictions apply. 10 Copyright 1978 IEEE All Rights ReservedIEEE Std 118-1978 IEEE STANDARD TEST CODE3) Proximity Effect The magnetic eld produced by currents in other conductors which are in close proximitywill inuence the current distribution in the resistance being measured and cause an increase in its effectivevalue similar to that due to skin effect4) Stray CouplingEddy Currents Coupled losses may result from currents induced in nearby conductingmaterial5) StrayCouplingHysteresisHysteresislossesmayresultfrommagneticeldsinducedinnearbyferromagnetic material6) Dielectric Losses Dielectric losses may occur in shunt capacitances.Theresistiveequivalentoftheseeffectsaddedtothedirect-currentresistanceisknownasthealternating-currentresistance. However, it is often possible to assume from the design of the resistor that these effects are negligible andhence that the alternating-current resistance is the same as the direct-current resistance.3. Standard Resistors3.1 Standardization of ApparatusBeforeusinganinstrument,theusershouldhavesomeassuranceofitsabilitytogiveresultstotheaccuracyorprecision required. If the instrument is to be used for measurements at a limited number of points, it may be possibleto use a substitution method (see 2.9) to calibrate the instrument. In the general case, where the instrument will be usedto measure either a wide range of values, or values for which no standard is available, a complete calibration of theinstrument may be required. Some instruments are designed for self-calibration, that is, they can be calibrated usinglittle or no additional apparatus. The calibration of other apparatus may be so involved that it may be desirable to sendit back to the manufacturer or to a commercial testing laboratory for calibration.3.2 Reference-Standard ResistorsThese standards (also called precision resistors, standard resistors, or shunts) are resistors demonstrating a high degreeof stability and are intended for use as reference standards in accurate dc resistance measurements. These resistors areconstructed from alloys having low temperature coefcients of resistance. They may be of the two-, three-, four-, orve-terminaldesign,dependingupontheresistancevalueandtheprecision. Althoughthestandardmaybeofanyrequiredvalue,valuesarepredominantlydecimalmultiplesorsubmultiplesof1.Thesestandardsmaybeintercompared with the National Standards (of resistance) on a periodic basis. (Specications for Reference-StandardElectrical Resistors are given in [6].)3.3 Working-Standard ResistorsThese may be similar in construction to reference-standards, differing only in their application, or they may be adaptedby construction or dimension to some specic measuring procedure. Thus, in the routine testing of copper wire andcable, working standards of copper of the same temperature coefcient as the test specimens are frequently used sothatthemeasuredvalueoftheresistanceofthespecimenisautomaticallycorrectedtoastandardtemperature,providedthestandardandthetestspecimenareatthesametemperaturewhenthespecimenistestedandthattheworking standard was at the standard temperature when it was compared with the reference-standard.Working standards may also be resistance boxes which consist of a number of resistors enclosed in a container and soarrangedthatnumerouscombinationsofresistorscanbeconnectedbetweentheterminalsoftheboxbysuitablemanipulation of dial switches, links, or plug contacts. Some specic types of working standards are described in 3.4through 3.7.Authorized licensed use limited to: Pontificia Universidad Catolica Del Peru. Downloaded on February 27,2013 at 20:35:38 UTC from IEEE Xplore.Restrictions apply. Copyright 1978 IEEE All Rights Reserved 11FOR RESISTANCE MEASUREMENT IEEE Std 118-19783.4 Heavy-Current Standard ResistorsForuseinmeasurementsinvolvinglargecurrents,thestandardresistormustbeprovidedwitheffectivecooling,usually by increasing its surface area and by circulating oil, air, or water as a cooling medium. If the resistance is adenite function of the temperature of the cooling medium only (that is, if any heat developed by current through theresistor is carried off by the coolant without materially affecting the temperature of the resistance alloy), the standardresistoristhermallyself-containedand,ifpreviouslytestedoveraparticularcurrentrange,issuitableformeasurements of high accuracy in this range. Standard resistors with short, thick current terminals, such as the usualforms of switchboard shunt, are not thermally self-contained. The resistance may depend to an appreciable extent uponthe heat developed at the current terminal contacts or conducted inward or outward by the current leads. For precisework with such standard resistors, the temperature of the resistance alloy must be measured both when the shunt istested initially and when it is used.Acommonsourceofuncertaintyintheeffectiveresistanceofheavy-currentshuntsofthefour-terminaltypeisnonuniformdistributionofcurrentwhenconnectionsaremadeatdifferentlocationsonthecurrentterminals.Inextreme cases, errors of 1 percent may occur. These effects are minimized by locating the potential taps on the axis ofsymmetry and by providing resistance between the current contact surface and the potential tap. (See also 2.4.)3.5 Nonreactive ResistorsFor alternating-current measurements, it is essential that the inductive and capacitive reactance and skin effect of thestandard resistors used are either negligible or so small and denite that corrections for their effects can be applied. Inwire-woundstandardresistors,inductivereactancepredominatesinresistorsoflessthan1,whilecapacitivereactance predominates in resistors of over 100 . In the intermediate range, time constants as low as 10-8 s can beobtained.Inlow-resistancestandardresistorsofthefour-terminaltype,thenetinductancemayoftenbemadeverysmallbyarrangingthepotentialleadssothatthemutualinductancebetweenthemandthecurrentcircuitoffsetstheself-inductance of the current circuit between tap points. For use in precise alternating-current measurements, the standardshouldeitherhavesuchageometricalcongurationthatitsinductanceiscomputableoritsinductanceshouldbedetermined experimentally by comparison with a standard resistor of known inductance.In wire-wound resistors of higher value, used with alternating voltages, serious errors may arise from the shuntingeffect of capacitance. Above 50 000 it is usually necessary to subdivide the resistor and to provide shields for thecomponent sections. If the shields are connected to points on a parallel guard circuit which have approximately thesame potentials as the portions of the resistor which they shield, the capacitive currents to ground occur only in theguard circuit and their effect on the shielded resistor is greatly reduced.3.6 High-Voltage ResistorsResistorsusedinhigh-voltagecircuitsmustbecapableofdissipatingalargeamountofheatorbeofveryhighresistance. These resistors are usually subdivided to reduce self-heating, and the component sections are shielded asdescribed in 3.5 so that any partial discharges (corona) produce currents in the guard circuit only. If the shields areshaped with rounded edges of proper design, corona may be avoided. On direct-current circuits, such rounded shieldsmay be tied to the working circuit. (A high-voltage standard resistor is described in [8].) (See also 2.5.)3.7 High-Resistance Standard ResistorsWire-woundresistorswithvaluesof100Mormorethathaveahighdegreeofstabilityandlowtemperaturecoefcients have been made, but they are very bulky and expensive. For some uses, resistors of 1 M or larger aremade by putting a semiconducting material on an insulating form which is then hermetically sealed. These resistorsmayhaverelativelypoorstability,hightemperaturecoefcientsofresistance,andlargeandnonlinearvoltageAuthorized licensed use limited to: Pontificia Universidad Catolica Del Peru. Downloaded on February 27,2013 at 20:35:38 UTC from IEEE Xplore.Restrictions apply. 12 Copyright 1978 IEEE All Rights ReservedIEEE Std 118-1978 IEEE STANDARD TEST CODEcoefcients; and despite being hermetically sealed, they may still be affected by humidity due to surface conduction onthe container. Whenever high accuracy is required, the standard should be calibrated as soon as possible before or afteruse. (See also 2.2.)3.8 Combinations of Standard ResistorsToreducethenumberofreference-standardresistorsrequired,somemeansofaccuratelycomparingresistorsofdifferentnominalvaluesisnecessary.Onemethodofdoingthisisbyusingseriesandparallelcombinationsofstandard resistors (commonly known as transfer standards), a common type having n (n=10 usually) nominally equalresistors connected in series and arranged so that they can be connected in parallel.With n nominally equal resistors having the value(7A)(where M is the mean value of the n resistors and mi is the departure of the ith resistor from the mean of the group), thetotal resistance of the group connected in series S will be(7B)If P is equal to the resistance of the group, connected in parallel,(8A)by neglecting terms of third and higher order, since by the denition of mi,(8B)Then,(9)Since there is no problem in matching resistors to 0.1 percent or better, the error term can be reduced to less than 1 part per million if the effects of leakage are made negligible and the resistanceof the conductors used in making the series and parallel connections can be neglected or accounted for. For resistorshavinganominalvalueof10kormore,thereisnoprobleminmeetingtheserequirementsusingtwo-terminalresistors; but for 10 resistors, the resistance of the connecting conductor would make it very difcult to get a part permillionorbetteraccuracyusingtwo-terminalresistors.Hamondescribedamethodofconnectingfour-terminalresistors in parallel such that the parallel resistance would satisfy equation 9. (See [9].)Since the square root of 10 is not an integer, this method cannot be used to make to 10-to-1 jump in resistance value;however, each of the 10 resistors can be measured against a reference resistor having the same nominal value, and thena standard of either 10 times or 1/10 the value of the reference resistor can be measured against the transfer standardconnected in either mode.M1M 1 ( m1) + M2M 1 ( = m2) MnM 1 ( mn) + =, , + , =S nM =1P---1M-----11 mi+--------------- nM----- 11n--- + mi2i 1 =n =i 1 =n=mi0 =i 1 =nS n2P11n--- + mi2i 1 =n =1 n ( ) mi2i 1 =nAuthorized licensed use limited to: Pontificia Universidad Catolica Del Peru. Downloaded on February 27,2013 at 20:35:38 UTC from IEEE Xplore.Restrictions apply. Copyright 1978 IEEE All Rights Reserved 13FOR RESISTANCE MEASUREMENT IEEE Std 118-19784. Instrumentation4.1 Voltmeter-Ammeter (Drop of Potential) MethodThe basic circuits and operations for this method are shown in Figs 8 and 9.The following equation is used for measuring with the circuit shown in Fig 8:(10)where V is the voltmeter reading, I is the ammeter reading, and Rv is the internal resistance of the voltmeter.Figure 8Voltmeter-Ammeter Measurement--Low Value ResistorsThe equation used for measuring with the circuit shown in Fig 9 is as follows:(11)where the nomenclature is the same as that used in equation 10, and where Ra is the ammeter resistance.Fig 8 shows the circuit preferred for low-value resistors, while the circuit shown in Fig 9 is preferable for high-valueresistors.Eithercircuitmaybeusedforintermediate-valueresistors.Dependinguponthedesiredaccuracy,thecorrection terms (due to Rv and Ra) may frequently be neglected. For low-value resistors, Rx may be a four-terminaldevice and the voltmeter may be a millivoltmeter used with calibrated leads. For high-value resistors, the ammeter maybe a microammeter or a more sensitive instrument, such as an electronic electrometer. In such cases, it is necessary toemploy guarding and to bypass the leakage current around the current meter, as shown in Fig 10.Figure 9Voltmeter-Ammeter MeasurementMedium Value ResistorsRxVI V Rv ---------------------- =RxV I RaI------------------ =Authorized licensed use limited to: Pontificia Universidad Catolica Del Peru. Downloaded on February 27,2013 at 20:35:38 UTC from IEEE Xplore.Restrictions apply. 14 Copyright 1978 IEEE All Rights ReservedIEEE Std 118-1978 IEEE STANDARD TEST CODEFigure 10Voltmeter-Ammeter Measurement-High Value Resistors4.1.1 Modified Voltmeter-Ammeter Method for Measuring Six-Terminal ResistorsThecircuitforthismethodisshowninFig11.(Seealso2.8.)RheostatR1isadjusteduntilthegalvanometer(G)indicates a null. R2 is adjusted to obtain the desired current in the unknown resistor (Rx). For these conditions,(12)Figure 11Modified Voltmeter-Ammeter Method (Six Terminal Resistor)4.2 Voltmeter MethodThecircuitusedinthismethodisshowninFig12.Thevoltmetermethodpermitsbothvoltageandcurrenttobemeasured by one instrument. Two readings are taken: with the switch (S) in position one, the supply voltage (V1) ismeasured; with the switch in position two, V2 is read. Rx is given by the following equation:(13)where Rv is the internal resistance of the voltmeter.RxVcdIb =RxV1V2V2------------------- Rv=Authorized licensed use limited to: Pontificia Universidad Catolica Del Peru. Downloaded on February 27,2013 at 20:35:38 UTC from IEEE Xplore.Restrictions apply. Copyright 1978 IEEE All Rights Reserved 15FOR RESISTANCE MEASUREMENT IEEE Std 118-1978Figure 12Voltmeter Method of Resistance Measurement4.3 Ammeter MethodFor low-value resistors the ammeter method is more suitable than the voltmeter method. The basic circuit is given inFig 13. An ammeter reading (I) is taken with the switch open. The switch (S) is then closed and a reading (I2) is taken.Forlargevaluesofthelimitingresistor(givingessentiallyaconstantcurrentsource), Rxisgivenbythefollowingequation:(14)where Ra is the resistance of the ammeter.Figure 13Ammeter Method of Resistance Measurement4.4 Ratio Devices4.4.1 Crossed-Coil TypeSeveral meter movements are available which indicate the ratio of two currents. Most incorporate two moving coilsarrangedsothatthemeterdeectionisproportionaltotheratioofthevoltageandcurrentappliedtoanunknownresistance. Such devices may be powered by internal or external sources, and they can be calibrated to indicate theunknown resistance directly. The basic circuit is shown in Fig 14.Whilesuchinstrumentsgivereadingswhichare,withinwidelimits,independentofthesourcevoltage,constantvoltage sources are frequently provided to avoid charging-current effects when the resistance of electric cables or othercapacitive specimens is measured. Instruments of this type are available for measuring wide ranges of resistance andcan be built with provisions for guarding and for measuring four-terminal resistors.RxI2RaI1I2--------------- =Authorized licensed use limited to: Pontificia Universidad Catolica Del Peru. Downloaded on February 27,2013 at 20:35:38 UTC from IEEE Xplore.Restrictions apply. 16 Copyright 1978 IEEE All Rights ReservedIEEE Std 118-1978 IEEE STANDARD TEST CODEFigure 14Crossed-Coil Type Ratio Ohmmeter4.4.2 Operational Amplifier TypeResistance can be measured by means of an operational amplier and a direct-current voltmeter. Extensive literatureexists describing operational amplier techniques in detail. Fig 15 shows a typical circuit.(15)Figure 15Operational Amplifier Resistance Measurement4.4.3 Dual-Slope, Integration-Type Digital Ratio MeterIn this method, illustrated in Fig 16A, a constant current source, derived from a voltage reference (Vref), produces acurrent(I)intheunknownresistor(Rx).(ThiscircuitwasoriginatedandpatentedbyGilbert[21].)TheresultingvoltagegeneratedacrossRxchargesthecapacitorofanintegratingcircuit[seeFig16B]inaknowntime(T1)determinedbyastableoscillatorproducing N1clockpulses. Attheendofthisperiod,thecounterwhichhasbeencounting the pulses is returned to zero. The reference voltage is then reversed across the input of the integrating circuit,causing the capacitor to discharge.When the capacitor is fully discharged (output voltage zero) in time T2, the counter is stopped and shows count N2.Rx is then derived by the following equation:(16)TheresultingvalueofRxisindependentoftheclockrateandthetimeconstant(RC)oftheintegratingcircuit.Itdepends primarily upon Vref and the value of the resistor used to generate the constant current (I). Range changing isdone by varying the current either manually or automatically.VoutRxRs------ Vin andRxVout RsVin------- = =RxVrefI---------N2N1------- KN2= =Authorized licensed use limited to: Pontificia Universidad Catolica Del Peru. Downloaded on February 27,2013 at 20:35:38 UTC from IEEE Xplore.Restrictions apply. Copyright 1978 IEEE All Rights Reserved 17FOR RESISTANCE MEASUREMENT IEEE Std 118-1978Figure 16A Dual Slope, Integration-Type Digital Ratio Ohmmeter. B Capacitor Integrating Circuit-Dual Slope Integrator. C Alternative Integration MethodAnother method consists in rst charging the capacitor by means of the IRx drop in the unknown resistor, as shown inFig 16C. This again occurs in time T1 and count N1. The capacitor is discharged by the drop IRs in the standard resistorin time T2 and count N2. For this condition,(17)Thusthemeasurementdependsupononlythestandardresistor(Rs).Rangechangingisclonemanuallyorautomatically by changing Rs. This method requires either an isolated power supply or isolated inputs for both IRx andIRs.4.5 BridgesUndermostcircumstances,abridgecircuitisthemostaccuratemethodofmeasuringresistance.Thefollowingsubsections describe some of the bridge circuits most commonly used for resistance measurement.4.5.1 Basic Wheatstone BridgeThe circuit of a Wheatstone bridge, shown in Fig 17, consists of four resistance arms, a source of current (usually abattery),andadetector.ThemeasurementoftheunknownRxismadeintermsofthethreeknownresistances.Adjustment of the three resistances is made for zero current in the detector at balance; therefore, this is a null balancemethod of resistance measurement.RxRsN2N1------------- KN2= =Authorized licensed use limited to: Pontificia Universidad Catolica Del Peru. Downloaded on February 27,2013 at 20:35:38 UTC from IEEE Xplore.Restrictions apply. 18 Copyright 1978 IEEE All Rights ReservedIEEE Std 118-1978 IEEE STANDARD TEST CODEFigure 17Wheatstone BridgeWhen the bridge is balanced, as indicated by a null reading of the detector D, the unknown resistance is given by thefollowing equation:(18)where RA and RB are the values of the ratio resistors, while Rs is the value of the standard resistor. These resistors maybe adjustable either continuously or in steps. A protective resistor Rp is used to protect the bridge elements.4.5.2 Julie Ratio-Type BridgeIn order to make use of high-precision voltage dividers, the circuit shown in Fig 18 is used. For this circuit, at balance,(19)where Rd is the total resistance of the divider and K is the divider setting. This circuit can be adjusted so that Rx isproportional to the divider setting k as follows. The resistance of D is adjusted to set the zero offset to zero. Resistor Cis adjusted so that, with Rx replaced by a standard resistor, a range factor M is set in terms of the standard, and(20)This circuit is patented and is described in [15].Figure 18Julie Ratio-Type BridgeRxRARB------- Rs= =RxKRd1 RARB + ( )1 (RdRdet) C + +---------------------------------------------RdetRARB ( ) Rd1(RdRdet) C + +----------------------------------------------+ =RxkM =Authorized licensed use limited to: Pontificia Universidad Catolica Del Peru. Downloaded on February 27,2013 at 20:35:38 UTC from IEEE Xplore.Restrictions apply. Copyright 1978 IEEE All Rights Reserved 19FOR RESISTANCE MEASUREMENT IEEE Std 118-19784.5.3 Kelvin BridgeWhen four-terminal resistors of low value (generally below 5 ) are to be measured, the Kelvin bridge (shown in Fig19) is frequently used. The bridge is similar to the Wheatstone bridge; however, the circuit contains an additional setofratioarms(aandb).Thisarrangementpermitsfour-terminalmeasurementofresistanceelements,essentiallyeliminating the effects of lead and contact resistance errors in the measurement of low resistance (see 2.1). When thebridge is balanced, as indicated by a null reading of the detector D, the unknown resistance is given in the followingequation:(21)where Ra and Rb are the resistance values of the ratio arms a and b and Ry is the value of the yoke Y. If RA/RB is exactlyequal to Ra/Rb, equation 21 becomes(22)equation 21 is useful, because it shows the necessity to keep the resistance of the yoke (Ry) as small as possible in orderto minimize the error caused by lead and contact resistances to the unknown and standard in case of discrepanciesbetweentheratiosRA/RBandRa/Rb.Forthehighestaccuracy,caremustbetakentoensurethattheconnectionresistances are balanced, because Ry is not negligible. For a detailed study of the procedures required for the highestaccuracy, see [16], [17], and [18].Figure 19Kelvin Bridge4.5.4 High-Resistance BridgesThe open-circuit voltage for an almost balanced Wheatstone bridge (see Fig 20) is given by the following equation:(23)where V is the voltage applied to the bridge and Rx is the error in measuring Rx. When Rx becomes high, Equation 23becomes(24)Thebridgeisthenveryinsensitive.ThissituationmaybeimprovedbyincreasingVandusingaverysensitiveelectronic detector. If practical, it is helpful to increase the value of Rs, in which case the simplication of equation 23is not correct.RxRsRARB-------RbRyRaRbRy+ +-------------------------------RARB-------RaRb------ + =RxRsRARB------- =VocVRxRsRsRx+ ( )2------------------------- =VocVRxRsRx2-------------------- =Authorized licensed use limited to: Pontificia Universidad Catolica Del Peru. Downloaded on February 27,2013 at 20:35:38 UTC from IEEE Xplore.Restrictions apply. 20 Copyright 1978 IEEE All Rights ReservedIEEE Std 118-1978 IEEE STANDARD TEST CODESince high-value resistors have leakage resistances comparable to their own values, guarding must be employed asshown in Fig 20. The leakage resistor (M) shunts the relatively low-valued ratio arm (A), while the leakage resistor (N)shunts the detector (D). Other specialized bridge circuits are occasionally used for high-resistance measurements.Figure 20High Resistance Bridge (Modified Wheatstone)4.5.5 Limit and Deviation BridgesFor production purposes, devices are used which permit sorting of resistors into groups with specied deviations froma mean. The simplest method of doing this is by using equation 23 and calibrating the detector reading in terms ofdeviation from null point. However, this method depends upon the bridge voltage (V).By modifying the resistance of the ratio arms (A and B) and adding switches, the ratio RA/RB can be readily changedso that one can determine whether Rx is within production limits. Bridges can be built with auxiliary adjustments thatare direct reading in deviations of parts per million or percentage deviation from the setting of the standard resistor.4.5.6 Kusters and MacMartin Current ComparatorThis device is used primarily in a standards laboratory for high-accuracy resistance measurement. As shown in Fig 21,itoperatesontheprincipleofbalancingtheratiooftwodirectcurrentsuntilthevoltagedrops,asindicatedbyagalvanometer(G),areequalacrosstheunknownandknowresistancestandard.Measurementisaccomplishedbymeans of transformer ratio arms. When the ampere-turns imposed on the magnetic core by the two windings are equalandopposite,theuxinthecoreiszero.Atzerouxcondition,asindicatedbythedetector(D),theunknownresistance is given by(25)Fig 21 shows this circuit in its simplest form. High-precision bridges of this type often have additional complications,including more complex magnetic circuits. This circuit is described in [13] and [14]; some features of the circuit arepatented by the authors of these papers.RxNxNs------- Rs=Authorized licensed use limited to: Pontificia Universidad Catolica Del Peru. Downloaded on February 27,2013 at 20:35:38 UTC from IEEE Xplore.Restrictions apply. Copyright 1978 IEEE All Rights Reserved 21FOR RESISTANCE MEASUREMENT IEEE Std 118-1978Figure 21Kusters and MacMartin Current Comparator4.6 ComparatorsFor many purposes, unknown resistors are compared to standard resistors by a comparison circuit.4.6.1 Direct-Comparison Method Using a Standard Resistor and PotentiometerIn this method, the unknown resistor, the standard resistor, and a current source are connected in series, as shown inFig 22, and a potentiometer is used to measure the voltage drop across each resistor.Figure 22Potentiometer MeasurementThe unknown resistance (Rx) is given by the following equation:(26)where Vx is the voltage measured across Rx and Vs is the voltage measured across Rs. It is essential that the currentremain constant during the two measurements.RxVxVs ( )Rs=Authorized licensed use limited to: Pontificia Universidad Catolica Del Peru. Downloaded on February 27,2013 at 20:35:38 UTC from IEEE Xplore.Restrictions apply. 22 Copyright 1978 IEEE All Rights ReservedIEEE Std 118-1978 IEEE STANDARD TEST CODE4.6.2 Direct-Deflection MethodA modication of the direct-comparison method has been used to measure high-voltage resistors. The basic circuit isshown in Fig 23. For this circuit,(27)whereMisthemultiplyingvalueoftheshuntforeachsettingandDisthedetectorreadingforeachsetting. Thegalvanometer and shunt combination can be replaced by an electronic electrometer.Figure 23Direct Deflection Method4.7 OhmmetersOhmmetersareself-containeddeviceswhichshowresistancereadingsdirectlyinohms.Thebasiccalibrationequations are as follows.4.7.1 Simple OhmmeterIn this instrument, the voltmeter is powered by self-contained batteries. The basic circuit is shown in Fig 24. The initialreading (V1) is brought to full scale by short-circuiting Rx and adjusting R. The unknown resistor is then inserted inseries with the battery-meter combination. Instead of reading V2, the scale is directly calibrated in ohms, so that(28)where m is the fraction of the meter scale indicated and Rv is the resistance of the voltmeter. Rv is assumed to be muchgreater than Rx.Themidscalereadingistheresistanceofthevoltmeter.Theohmmeterrangesarechangedbychangingthemeterresistances and battery voltages. Various circuit modications are used to offset the effects of battery aging.Figure 24Simple OhmmeterRxMsDsMxDx--------------- Rs=Rx1 m m-------------Rv=Authorized licensed use limited to: Pontificia Universidad Catolica Del Peru. Downloaded on February 27,2013 at 20:35:38 UTC from IEEE Xplore.Restrictions apply. Copyright 1978 IEEE All Rights Reserved 23FOR RESISTANCE MEASUREMENT IEEE Std 118-19784.7.2 Modified Comparison MethodThe simple ohmmeter has two disadvantages: its scale is nonlinear and the meter reads from right to left. The circuitshown in Fig 25 circumvents the latter problem. In this case,(29)where m is the fraction of the meter scale read.The voltmeter impedance (V) should be very high compared with the value of Rx and in practice may be an electronictypeselectedforhighinputimpedance.TheelectronicvoltmeterwillreadfullscalewhenRxisinnite(thatis,disconnected). Ranges are changed by changing the value of Rs.Figure 25Modified Comparison Type Ohmmeter4.7.3 Constant-Current SourceA modication of Fig 25 uses a constant-current source, as shown in Fig 26. As in the previous circuit (see Fig 25), thevoltmeter should be of much higher impedance than the value of Rx to be measured. For this case,(30)where K is a constant.Suchaninstrumenthaslinearscales.Rangesarechangedbychangingtheoutputoftheconstant-currentsource.Voltmetersusingelectroniccircuitsornull-balancepotentiometricmethodsareparticularlysuitableandmaybeadapted to direct digital reading.Figure 26Constant-Current Source OhmmeterRxm1 m -------------Rs=RxV I KV = =Authorized licensed use limited to: Pontificia Universidad Catolica Del Peru. Downloaded on February 27,2013 at 20:35:38 UTC from IEEE Xplore.Restrictions apply. 24 Copyright 1978 IEEE All Rights ReservedIEEE Std 118-1978 IEEE STANDARD TEST CODE4.7.4 AmmeterThis method is suitable for measuring low-value resistors. The basic circuit is shown in Fig 27. With Rx disconnected,R is adjusted so that the meter reads full scale. The reading is then taken with Rx connected. The value of Rx is givenby the following equation:(31)where Ra is the ammeter resistance and m is the fraction of the meter scale indicated. Ranges are changed by changingthe full-scale current and the ammeter resistance.Figure 27Ammeter Type Low Resistance Ohmmeter4.8 Other Methods4.8.1 Loss-of-Charge MethodInthismethod,usedforveryhighvalueresistors,acapacitorisrstcharged.Itisthendischargedthroughtheunknown high-value resistor. After a measured period of time, the charge remaining on the capacitor is measured by aballistic galvanometer or charge meter. The basic circuit is shown in Fig 28. The charge remaining on the capacitor (C)is given by the following equation:(32)where Q0 is the initial charge and C is the capacitance value.Taking the log of equation 32,(33)Thus, if log Q is plotted against t, the negative slope equals 0.4343 RxC, and Rx can be found.Figure 28Loss-of-Charge Method OhmmeterRxmRa1 m ------------- =Q Q0exp t Rx C ( ) =Q log Q00.4343tRxC------------------ - log =Authorized licensed use limited to: Pontificia Universidad Catolica Del Peru. Downloaded on February 27,2013 at 20:35:38 UTC from IEEE Xplore.Restrictions apply. Copyright 1978 IEEE All Rights Reserved 25FOR RESISTANCE MEASUREMENT IEEE Std 118-19785. Applications5.1 Preferred Circuits and Measuring TechniquesTable 1 indicates the preferred circuits and measuring techniques to be used for various measurements.5.2 Temperature Measurement by Change in ResistanceA commonly used method for determining the average temperature of a winding is to measure the resistance of thewindingattheunknowntemperatureandtocomparethisvaluewiththeresistanceataknowntemperature.Theaverage temperature of the winding may be calculated by the equation:(34)wheretistheunknowntemperatureindegreesCelsius,t1istheknowntemperatureindegreesCelsius,Rtisthemeasuredresistanceatt,R1istheknownresistanceatt1,andCisthezero-resistancetemperatureconstantMoreextensive information about this method is contained in [12].TheconstantsC=234.5forcopperandC=224.1foraluminumhavebeendeducedperimentallyforcommercialgrades of conductors of annealed copper and aluminum of fairly high purity. The experimentally determined linearrelationshipbetweenresistanceandtemperatureoveraconsiderablerange,thededucedtemperaturesforzeroresistance [234.5C (copper) and 224.1C (aluminum)] and the proportionality of corresponding sides of similartriangles permit the relationship to be expressed as(35)from which equation 34 was derived. Temperatures computed by equation 34 are recognized as valid for commercialpurposes.When measuring the resistance of any winding that is highly inductive or of low resistance, or both, readings shouldbedelayeduntilthemeasuringcurrenthasreachedasteadystate.Theinductiveeffectandlowresistanceofthewinding may cause the time constant (L/R) to become quite large, and the measuring current may increase for severalminutes or even hours before the steady-state value is reached. Premature readings may result in gross errors in thecalculated temperature rise, although errors in the measured resistance may be small.Methods have been devised to decrease the delay in resistance measurements for temperature tests to prevent coolingof the apparatus under test. See [12] for additional information on this subject.5.3 Computation of Resistance for a Required TemperatureMeasurements of resistance are usually made at ambient temperatures. For various reasons, such as loss calculationsfor efciencies, the value of resistance required must be the value at a specied temperature. To convert the measuredresistance value to the required value, the relationship described in 5.2 may be rearranged so that(36)where Rt is the resistance at a specied temperature, R1 is the measured resistance at t1, t is the specied temperatureindegreesCelsius,t1isthetemperatureindegreesCelsiusofmeasuredresistance,andCisthezero-resistancetemperature constant.t t1RtR11 ( ) = t1C +t C +t1C +--------------RR1------ =RtR1

t C +t1C +-------------- =Authorized licensed use limited to: Pontificia Universidad Catolica Del Peru. Downloaded on February 27,2013 at 20:35:38 UTC from IEEE Xplore.Restrictions apply. 26 Copyright 1978 IEEE All Rights ReservedIEEE Std 118-1978 IEEE STANDARD TEST CODE5.4 Measurement of Insulation ResistanceThe resistance of the insulation between, and in contact with, two metallic bodies or electrodes is dened as the ratioof the direct voltage applied to the electrodes to the total current between them. The insulation may be a specimen ofa specic material or an assembly of materials constituting an insulation system.The current measured is dependent upon both the volume and surface resistance of the material or system, unless athird electrode is provided to permit a three-terminal measurement using guarding techniques.The volume resistance results from that portion of the current that is distributed throughout the volume of the materialor system, whereas the surface resistance results from that portion of the current which is primarily in a thin layer ofmoisture or other conducting material that may be deposited on its surface.The current that results from the application of a direct voltage to an insulating material or system is principally ionicin nature, as compared to the free-electron charge carried in metals. Semiconductors are intermediate in their ability toconduct electricity. An arbitrary distinction between the realm of semiconductors and that of insulating materials, interms of resistivity, is usually considered to be 1010 .cm.Insulation-resistancemeasurementscanbegreatlyinuencedbyseveralfactors,whichmustbetakenintoconsideration and reported as test conditions:1) The insulation resistance may be voltage sensitive, depending upon the voltage stresses that may exist duringthe test2) The degree of conditioning before making the test determines the dryness and cleanliness of the specimen3) Thetemperatureofthespecimenmaterialorinsulationsystemanditsrelationshiptothedew-pointtemperature of the test environment directly affect the measurement4) The resistance of insulating materials and systems is usually time dependent5) Depending upon moisture content, the resistance of insulating materials and systems may be affected by thepolarityoftheappliedvoltageandbyanyeldnonuniformitythatmayexistasaresultofelectrodeconguration.Formorecompleteinformationonmakingresistancemeasurementsoninsulatingmaterials,see[10],andforinsulation systems, see [11].5.4.1 MethodsThe methods to be used for measuring the resistance or resistivity of relatively small specimens of insulating materialsmay be somewhat different from those used in the case of insulation systems, particularly in regard to sensitivity. Atable of suggested methods or apparatus in terms of conditions of use is given in [10].For insulation systems, where the accuracy requirements may not be so stringent, megohm bridges and ohmmeters oflower sensitivity are commonly used.5.4.2 Testing TechniquesInsulation-resistance measurements customarily fall in the range of 106 to 1015 , and such measurements are greatlyinuenced by the factors noted in 5.4. The techniques referred to must be closely followed and precautions carefullyobservedifmeaningfulresultsaretobeobtained.Furthermore,andparticularlyinthecaseofcertaininsulationsystems, considerable geometric capacitance may be inherent in the system; and if such systems are tested at relativelyhigh voltages, the matter of safety becomes a primary concern.Itisrecommendedtharelevantdocuments,suchas[10]and[11],becarefullyreviewedbeforemakinginsulation-resistance measurements.Authorized licensed use limited to: Pontificia Universidad Catolica Del Peru. Downloaded on February 27,2013 at 20:35:38 UTC from IEEE Xplore.Restrictions apply. Copyright 1978 IEEE All Rights Reserved 27FOR RESISTANCE MEASUREMENT IEEE Std 118-19785.5 Measurement of Ground ResistanceResistancemeasurementofagroundconnectionpresentsanumberofproblemsnotencounteredinmostotherresistance measurements. The conduction of electricity in the soil is electrolytic, and the continued passage of directcurrentproduceschemicalactionandpolarizationpotentialdifferenceswhichmayseriouslyinterferewiththemeasurement. It is therefore almost essential that the measurement be made using alternating current (or periodicallyreversed direct current). Inductive and capacitive effects, however, are usually negligible.Thedistributionofacurrentinthevicinityofagroundelectrodeissuchthattheequipotentialsareroughlyhemispherical surfaces centered on the electrode. Most of the drop in voltage occurs in the region fairly close to theelectrode. Assuming that the soil is of uniform resistivity, approximate calculations indicate that, for driven rods, 90percent of the resistance is localized within a radius equal to twice the depth of the rod and that 99 percent is localizedwithin a radius 20 times the depth of the rod. For plates buried at a considerable depth, 90 percent of the resistance islocalized within a radius of 6 or 7 times the greatest dimension of the plate. The measuring procedure should be suchthat at least 90 percent of the resistance is located inside the auxiliary potential electrode used in the measurement.Still another complication may arise from stray currents, either alternating or direct, which may be present in the earthandevenintheelectrodeundermeasurementatthetimeoftest. Aconvenientwayofmitigatingtheireffectsistoutilize in the measurement a frequency not likely to be present in the stray current.Itisrecommendedthatrelevantdocuments,suchas[5],becarefullyreviewedbeforemakingground-resistancemeasurements.5.5.1 Measurement by Reference GroundTo measure the resistance of a ground, it is essential that a measuring current be passed from the electrode under testintotheground;hence,asecondgroundconnectionmustbeprovidedtocarrythemeasuringcurrent. Thissecondconnectioncanbeadistant,metallicwaterpipesystemwhich,becauseofitslargeextent,maybeofverylowresistance, or it can be formed by connecting in parallel a large number of other driven grounds separated rather widelyfrom each other and also from the test ground. In these cases, it is sufcient to measure the total resistance of the twogroundsinseriesand,neglectingtheresistanceofthesecondorreferenceground,ascribethemeasuredresistanceentirely to the ground under test. The measurement of the total resistance of the two grounds may be made by the drop-of-potentialmethod(see4.1)orbya Wheatstonebridge(see4.5.1),usingalternatingcurrenttoavoidpolarizationeffectsintheground. Asmostsourcesofalternatingcurrentarethemselvesgroundedatsomepoint,aninsulatingtransformermustbeusedtoisolatethemeasuringcircuit.Errorsfromthepresenceofstraycurrentsofthesamefrequency as that used in the measurement may be reduced by reversing the connections at the secondary terminal ofthe isolating transformer and taking the mean of the two sets of data thus obtained.5.5.2 Three-Measurement MethodWhen no reference ground connection of negligible resistance is available, it is necessary to provide both an auxiliarycurrentgroundtoconductthemeasuringcurrentandathirdorpotentialground.Thepotentialgroundservestoseparate the resistance of the ground under test from that of the auxiliary ground connection. The theoretically simplestprocedure would be to drive two auxiliary grounds at a sufcient distance from the test ground and from each other thattheregionsinwhichtheirresistanceislocalizeddonotoverlap. ThenifRab,Rbc,andRcaarethetotalresistancesmeasured successively between the pairs of electrodes indicated by the subscripts, the resistance of the test ground (Ra)is given by(37)This procedure is practical only if all three grounds are of nearly the same resistance. If, as is usually the case, the twoauxiliary grounds are of materially higher resistance than the test ground, Ra will be the difference of two nearly equalRaRabRcaRbc + ( ) 2 =Authorized licensed use limited to: Pontificia Universidad Catolica Del Peru. Downloaded on February 27,2013 at 20:35:38 UTC from IEEE Xplore.Restrictions apply. 28 Copyright 1978 IEEE All Rights ReservedIEEE Std 118-1978 IEEE STANDARD TEST CODEquantities, and errors in the individual readings will be greatly magnied in the nal result. Stray currents and theirchanges between successive readings may be another serious source of error.5.5.3 Ratio OhmmeterAcommonlyusedmethodofmeasuringgroundresistanceisshowninFig29.Currentfromthedirect-currentgenerator is periodically reversed by the current-reversing switch and will exist in the earth between the ground undertest(X)andtheauxiliaryelectrode(C).ThedropofpotentialbetweenXandtheotherauxiliaryelectrode(P)isrectied by the potential-reversing switch, which is operated in synchronism with the current-reversing switch. Thecoils of the ratio ohmmeter carry current proportional to the voltage (XP) and the current through X, respectively, sothat the scale of the instrument can be calibrated to read directly the resistance (Rx) of the test ground. The distance d1must be large enough to span the region in which the desired fraction of Rx is localized. Similarly, d2 must be largeenoughthatthepotentialgradientaroundChasanegligibleeffectatP.ExcessiveresistanceatCwillreducethesensitivity of the measurement, and a less denite balance will be obtained. The resistance (Rp) at P must be negligiblecompared with that of the series resistor. This method is only slightly affected by stray currents if the frequency of thereversals remains different from that of the stray current.Figure 29Crossed-Coil Ratio-Type Ground Resistance Measurement5.5.4 Double-Balance Bridge MethodA convenient bridge method for measuring ground resistance is shown in Fig 30. In this method, currents from thealternating-currentsourceoccurintwoparallelcircuits. ThelowercircuitincludesthexedresistanceRAandtheresistance of the ground under test (Rx) and of the auxiliary current ground (Rc). The upper circuit includes the xedresistance Rs and an adjustable slide rheostat on which two sliders (Sa and Sb) make contact. With the detector switchclosed to the left, slider Sa is adjusted until the detector shows a balance. The currents in the two branch circuits arethen inversely proportional to the resistances RA and RB. The switch is then closed to the right and slider Sb is adjusteduntil the detector again shows a balance. The potential drop between X and P is then equal to the drop in the portionRb of the slide rheostat, and the resistance of the ground under test is then given by(38)The scale over which Sb moves can thus be calibrated to read Rx directly.RxRbRARB =Authorized licensed use limited to: Pontificia Universidad Catolica Del Peru. Downloaded on February 27,2013 at 20:35:38 UTC from IEEE Xplore.Restrictions apply. Copyright 1978 IEEE All Rights Reserved 29FOR RESISTANCE MEASUREMENT IEEE Std 118-1978Figure 30Double Balance Bridge for Ground Resistance MeasurementThealternating-currentsourcemaybeanelectronicorelectromechanicaloscillator,andthedetectormayhaveanaudibleoutput.Thetoneoftheoscillatorcanusuallyberecognizedandbalancedout,eveninthepresenceofconsiderable background noise caused by stray alternating currents. Resistance at P merely reduces the sensitivity ofthedetector.ExcessiveresistanceatCmaylimittherangeofresistancewhichcanbemeasured.Thelocationsofelectrodes P and C are determined by the same considerations as in the crossed-coil ohmmeter method.5.5.5 Single-Balance (Transformer) MethodFig 31 shows a circuit in which a single balance is sufcient to give a measurement of the ground resistance (Rx) of theground (x) if auxiliary potential ground (P) is at a sufcient distance from X so as not to inuence Rx. (See [5]).The current transformer maintains a xed ratio (N) of the secondary current (I2) to the primary current (I1). Hence, atbalance,(39)Various devices may be incorporated into this circuit to minimize the disturbing effects of stray ground currents. Atransformer coupling in the detector circuit eliminates errors from direct currents in the ground. A tuned bypass circuitor a detector excited separately and in synchronism with the alternating-current ground current minimizes the effect ofthephaseangleofthetransformer. Analternativeistouseadirect-currentdetectorwithsynchronousrecticationsuitably phased with the alternating-current source.RxR2N =Authorized licensed use limited to: Pontificia Universidad Catolica Del Peru. Downloaded on February 27,2013 at 20:35:38 UTC from IEEE Xplore.Restrictions apply. 30 Copyright 1978 IEEE All Rights ReservedIEEE Std 118-1978 IEEE STANDARD TEST CODEFigure 31Single Balance (Transformer) Ground Resistance Measurement6. References[1] HARRIS, F. K. Electrical Measurements. New York: Wiley, 1952.[2] STOUT, M. B. Basic Electrical Measurements. Englewood Cliffs, N.J.: Prentice-Hall, 1960.[3] LUPPOLD, D. S. Precision DC Measurements and Standards. Reading, Mass.: Addison-Wesley, 1969.[4]PrecisionMeasurementandCalibrationElectricity-LowFrequency.NBSSpecialPublication300,vol3,Washington, DC: US Government Printing Ofce, 1968.[5] IEEE Std 811962, Recommended Guide for Measuring Ground Resistance and Potential Gradients in the Earth. [6] IEEE Std 3101969 (ANSI C100.31969), Specication for Reference-Standard Electrical Resistors. [7]IEEEStd951977,RecommendedPracticeforInsulation TestingofLarge ACRotatingMachinerywithHighDirect Voltage. [8] PARK, J.H. Special Shielded Resistor for High-Voltage DC Measurement. Journal of Research, vol 166C, Jan-Mar1962.[9] HAMON, B.V. A 11000 Ohm Build-Up Resistor for the Calibration of Standard Resistor. Journal of ScienticInstruments, vol 31, Dec 1954.[10] ASTM D25776, Tests for DC Resistance or Conductance of Insulating Materials.[11] IEEE Std 621958, Recommended Guide for Making Dielectric Measurements in the Field. [12] IEEE Std 1191974, Recommended Practice for General Principles of Temperature Measurement as Applied toElectrical Apparatus. Authorized licensed use limited to: Pontificia Universidad Catolica Del Peru. Downloaded on February 27,2013 at 20:35:38 UTC from IEEE Xplore.Restrictions apply. Copyright 1978 IEEE All Rights Reserved 31FOR RESISTANCE MEASUREMENT IEEE Std 118-1978[13]MACMARTIN,M.P.,andKUSTERS,N.L.ADirect-Current-ComparatorRatio-BridgeforFour-TerminalResistanceMeasurements.IEEETransactionsonInstrumentationandMeasurement,volIM-15,pp212220,Dec1966.[14] KUSTERS, N.L., and MACMARTIN, M.P. A Direct-Current-Comparator Bridge for Measuring Shunts up to 20000 Amperes. IEEE Transactions on Instrumentation and Measurement, vol IM-18, pp 26671, Dec 1969.[15] JULIE, L. US Patent 3 179 800.[16] WENNER, F., and WEIBEL, E. Bulletin of the Bureau of Standards, vol 8, p 559, 1912.[17] WENNER, F., and WEIBEL, E. Bulletin of the Bureau of Standards, vol 11, p 65, 1914.[18] WENNER, F. Bulletin of the Bureau of Standards, vol 25, p 225, 1940.[19] IEEE Std 2621973 (ANSI C57. 12.901973), Test Code for Distribution, Power, and Regulating Transformers. [20] IEEE Std 4621973 (ANSI C57. 12.001973), General Requirements for Distribution, Power, and RegulatingTransformers. [21] GILBERT, R.W. US Patent 3 051 939. Dual-Slope Analog-to-Digital Converter.Authorized licensed use limited to: Pontificia Universidad Catolica Del Peru. Downloaded on February 27,2013 at 20:35:38 UTC from IEEE Xplore.Restrictions apply.