Electrical measurements unit-1-measuring instruments

UNIT–I: MEASURING INSTRUMENTS

Classification – Deflecting, control and damping torques – Ammeters and Voltmeters –PMMC, MI type, dynamometer and electrostatic instruments – Expression for the deflecting torque and control torque – Errors and compensations– Extension of range using shunts and series resistance –CT and PT: Ratio and phase angle errors – Numerical problems.

1. ELECTRICAL MEASUREMENTS
P.NARESH(PH.D), ASST. PROF.,
EEE DEPARTMENT,
RAGHU ENGG. COLLEGE(A)
VISAKHAPATNAM

2. ▪MEASURING INSTRUMENTS
▪MEASUREMENT OF POWER AND POWER FACTOR
▪MEASUREMENT OF ENERGY
▪POTENTIOMETERS
▪MEASUREMENT OF RESISTANCE, INDUCTANCE AND CAPACITANCE
▪MAGNETIC MEASUREMENTs
P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)
ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

3. P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)
ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

4. P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)
ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

5. P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)
ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

6. P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)
ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

7. P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)
ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

8. P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)
ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

9. P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)
ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

10. P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)
ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

11. P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)
ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

12. P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)
ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

13. Functional elements of a measurement system
Themainfunctionalelementsofameasurementsystemare
1.Primarysensingelement
2.Variableconversionelement
3.Variablemanipulationelement
4.Signalconditioningelement
5.Datatransmissionelement
6.Datapresentationelement.
Primary Sensing
Element
Variable Conversion
Element
Variable
Manipulation
Element
Data
Transmission
Element
Data
Presentation
Element
Data Storage &
Playback Element
Quantity to be measured
(Measurand)
Observer
Data Conditioning Elements
Figure:FunctionalElementsofaMeasurementSystem
P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)
ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

14. Classification of measuring instruments
Digital
Instrument
Secondary
Instrument
Absolute
Instrument
Instruments
Mechanical
Instrument
Electrical
Instrument
Electronic
Instrument
Analog
Instrument
Null
Instrument
Indicating
Instrument
Integrating
Instrument
Recording
Instrument
P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)
Figure:Classificationofmeasuringinstruments
ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

15. P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)
Types of Electrical Instruments
ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

16. P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)
indicating Instruments
ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

17. P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)
Essentials of indicating instruments
•Indicating instruments consist essentially of a pointer which moves over a calibrated scale and which is attached to a
moving system pivoted in jewelled bearings.
•Themovingsystemissubjectedtothefollowing3torques:
1.Deflectingtorqueoroperatingtorque
2.Controllingtorqueorrestoringtorque
3.Dampingtorque
•The deflecting or operating torque (Td) is produced by utilizing one or other effects, e.g., magnetic,
electrostatic,electrodynamic, thermal, or inductive.
•Controllingtorque controls the movement of the pointer on a particular scale according to the quantity of the electricity,
passing through it. The controlling forces are required to control the deflection or rotation and bring the pointer to zero
position when there is no force or stop the rotation of the disc when there is no power.
•Damping torque is one which acts on the moving system of the instrument only when it is moving and always opposes
its motion. Such damping force is necessary to bring the pointer to rest quickly, otherwise due to inertia of the
movingsystem,the pointer will oscillate about its final deflected position for quite some time before coming to rest in
the steady position.
ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

18. P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)
Theactualmethodoftorqueproductiondependsonthetypeofinstrument.Thedeflectingtorquecausesthemoving
system(andhencethepointerattachedtoit)tomovefromitszeroposition.
Deflecting torque
ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

19. Controlling torque
Spring
control
Gravity
control
P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)
Methods of controlling torque
ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

20. P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)
Spring control
ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS
Twophosphorbronzehairspringsofspiralshapesareattachedtothe
spindleofthemovingsystemoftheinstrument.Theyarewoundin
oppositedirection.
T
dαI
AndforspringcontrolT
cα
AsT
c=T
d
Iα
SincedeflectionqisdirectlyproportionaltocurrentI,thespring-
controlledinstrumenthaveauniformorequallyspacedscalesoverthe
wholeoftheirrange.

21. P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)
Gravity control
ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS
Gravitycontrolisobtainedbyattachinga
smalladjustableweighttosomepartofthe
movingsystemsuchthatthetwoexert
torquesintheoppositedirections.
Asshowninthefigure,thecontrollingor
restoringtorqueisproportionaltothesineof
theangleofdeflection,i.e.,TcαSin.

22. Damping torque
Air friction
damping
Eddy current
damping
P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)
Methods of damping torque
ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

23. •Thelightaluminiumpistonattachedtothe
movingsystemoftheinstrumentisarrangedto
travelwithaverysmallclearanceinafixed
chamberclosedatoneend.
•Thecross-sectionofthechamberiseither
circularorrectangular.Dampingofthesystem
isaffectedbythecompressionandsuction
actionsofthepistonontheairenclosedinthe
chamber.
•Inanothermethod,lightaluminiumvaneismountedonthespindleofthemovingsystemwhichmovesinairor
inaclosedsector-shapedbox.Fluid-frictionissimilarisactiontotheair-friction.
•Duetogreaterviscosityoftheoil,thedampingismoreeffective.However,oildampingisnotmuchused
becauseofseveraldisadvantagessuchasobjectionablecreepingofoil,thenecessityofusingtheinstrument
alwaysinverticalpositionanditsobviousunsuitabilityforuseinportableinstruments.
P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)
Air friction damping
ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

24. •Athindiscofaconductingbutnon-
magneticmateriallikecopperor
aluminiumismountedonthespindle.The
discissopositionedthatitsedges,when
inrotation,cutthemagneticfluxbetween
thepolesofapermanentmagnet.
•Henceeddycurrentsareproducedinthediscwhichflowandsoproduceadampingforceinsuchadirectionas
toopposetheverycauseproducingthem(Lenz’slaw).Sincethecauseproducingthem,istherotationofthe
disc,theseeddycurrentsretardthemotionofthediscandmovingsystem.
P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)
Eddy current damping
ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

25. Theinstrumentswhichusethepermanentmagnetforcreatingthestationarymagneticfieldbetweenwhichthecoilmovesis
knownasthepermanentmagnetmovingcoilorPMMCinstrument.Itoperatesontheprinciplethatthetorqueisexertedon
themovingcoilplacedinthefieldofthepermanentmagnet.
1.MovingCoil
2.MagnetSystem
3.Controlsystem
4.Dampingsystem
P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)
Permanent magnet moving coil (pmmc) instrument
ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

26. The deflecting torque
Where,N –Number of turns of coil
B –flux density in the air gap
L, d –the vertical and horizontal length of the side.
I –current through the coil.
The spring provides the restoring torque to the moving coil which is expressed as
Where K = Spring constant.
For final deflection,
By substituting the value of equation (1) and (3) we get,
The above equation shows that the deflection torque is directly proportional to the current passing through the coil.
P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)
Torque Equation for PMMC Instrument
ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

27. Advantages
1.The scale of the PMMC instruments is uniform.
2.The power consumption of the devices is very less.
3.The PMMC instruments have high accuracy because of the high torque weight ratio.
4.The single device measures the different range of voltage and current. This can be done by the use of multipliers and shunts.
Dis-Advantages
1.The PMMC instruments are only used for the direct current. The alternating current varies with the time. The rapid variation
of the current varies the torque of the coil. But the pointer can not follow the fast reversal and the deflection of the torque.
Thus, it cannot use for AC.
2.The cost of the PMMC instruments is much higher as compared to the moving coil instruments.
Errors in PMMC Instruments
In PMMC instruments the error occurs because of the ageing and the temperature effects of the instruments. The magnet,
spring and the moving coil are the main parts of the instruments which cause the error.
P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)
Advantages & Disadvantages of PMMC Instruments
ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

28. P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)
ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS
Thebasicd.c.ammeterisnothingbutaD'Arsonvalgalvanometer.Thecoilwindingofabasicmovementisverysmalland
lightandhenceitcancarryverysmallcurrents.Soasmentionedearlier,forlargecurrents,themajorpartofcurrentis
requiredtobebypassedusingaresistancecalledshunt.ItisshownintheFigure.

29. Iftheordinaryswitchisused,whilerangechanging,theswitch
remainsopenandfullcurrentpassesthroughthemeter.
Themetermaygetdamagedduetosuchhighcurrent.Somake
beforebreakswitchisused.
Thedesignofsuchswitchissothatitmakescontactwithnext
terminalbeforecompletelybreakingthecontactwiththeprevious
terminal.
P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)
ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS
Therangeofthebasicd.c.ammetercanbeextendedbyusingnumberofshuntsandaselectorswitch.Suchameteris
calledmultirangeammeterandisshownintheFigure.

30. P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)
ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS
Inmultirangeammeter,amakebeforebreakswitchismust.TheArytonshuntortheuniversalshunteliminatesthe
possibilityofhavingameterwithoutashunt.ThemeterwiththeArytonshuntisshownintheFigure.

31. P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)
ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS
Thebasicd.c.voltmeterisnothingbutaPMMCD'Arsonovalgalvanometer.Theresistanceisrequiredtobeconnectedin
serieswiththebasicmetertouseitasavoltmeter.Thisseriesresistanceiscalledamultiplierthemainfunctionofthe
multiplieristolimitthecurrentthroughthebasicmetersothatthemetercurrentdoesnotexceedthefull-scaledeflection
value.

32. •TheR
1,R
2,R
3andR
4arethefourseriesmultipliers.
Whenconnectedinserieswiththemeter,theycangive
fourdifferentvoltagerangesasV
1,V
2,V
3andV
4.
•TheselectorswitchSismulti-positionswitchbywhich
werequiredmultipliercanbeselectedinthecircuitThe
mathematicalanalysisofbasicd.c.voltmeterisequally
applicableforsuchmultirangevoltmeter.
P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)
ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

33. P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)
ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

34. Inamultirangevoltmeter,theratioofthetotalresistanceR
Ttothevoltagerangeremainssame.
Thisratioisnothingbutthereciprocalofthefullscaledeflectioncurrentofthemeteri.e.,1/ImThisvalueiscalledsensitivity
ofthevoltmeter.
P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)
ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

35. Amovingcoilinstrumentgivesafullscaledeflectionforacurrentof20mAwithapotentialdifferenceof200mVacrossit.
Calculate1)shuntrequiredtouseitasanammetertogetarangeof0-200mA.2)Multiplierrequiredtouseitasavoltmeterof
range0–1000mV.
P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)
ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

36. Design an Aryton shunt to provide an ammeter with the current ranges 1 A, 5 A and 10 A. A basic meter resistance is 50 and
full scale deflection current is 1 mA.
P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)

37. AbasicD’Arsonvalmovementwithaninternalresistanceof50andafullscaledeflectioncurrentof2mAistobeusedasa
multirangevoltmeter.Designtheseriesstringofmultiplierstoobtainthevoltagerangesof0-10V,0-50V,0–100V&0–
500V.
P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)
ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

38. AbasicD’Arsonvalmovementwithaninternalresistanceof50andafullscaledeflectioncurrentof2mAistobeusedasa
multirangevoltmeter.Designtheseriesstringofmultiplierstoobtainthevoltagerangesof0-10V,0-50V,0–100V&0-
500V.Usethesensitivitymethod.
P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)
ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

39. TwodifferentvoltmetersareusedtomeasurethevoltageacrossRbshowninthefigure.Thetwometersusedare
asfollows:1)Meterwithsensitivity1K/Vandrange5V.2)Meterwithsensitivity20K/Vandrange5V.
Calculate(i)TruevoltageacrossRb(ii)Readingonvoltmeter-1(iii)Readingonvoltmeter-2(iv)%errorinthe
twometers(v)%Accuracyofthetwovoltmeters.
P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)
ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

40. InMovingIronInstruments,aplateorvanofsoftironorofhighpermeabilitysteel
formsthemovingelementofthesystem.Theironvanissosituatedthatitcanmovein
themagneticfieldproducedbyastationarycoil.
ThemovingironInstrumentsareclassifiedintotwotypes:
1.Attractiontype
2.Repulsiontype
P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)
ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

41. Figure: Attraction Type mi Instrument
P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)
Thebasicworkingprincipleoftheseinstrumentsisverysimplethatasoftironpieceifbroughtnearthemagnetgets
attractedbythemagnet.TheconstructionoftheattractiontypeinstrumentisshownintheFigure.
ItconsistsofafixedcoilCandmovingironpieceD.Thecoilisflat
andhasanarrowslotlikeopening.Themovingironisaflatdisc
whichiseccentricallymountedonthespindle.
Thenumberoftumsofthefixedcoilaredependsontherangeofthe
instrumentorpassinglargecurrentthroughthecoilonlyfewturnsare
required.
Thecontrollingtorqueisprovidedbythespringsbutgravitycontrol
mayalsobeusedforverticallymountedpaneltypeinstruments.The
dampingtorqueisprovidedbytheairfriction.
Theoperatingmagneticfieldinmovingironinstrumentsisveryweak.
Henceeddycurrentdampingisnotusedsinceitrequiresapermanent
magnetwhichwouldaffectordistorttheoperatingfield.
ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

42. Figure: Repulsion Type MI Instrument
P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)
Theseinstrumentshavetwovanesinsidethecoil,theoneisfixed
andotherismovable.
Whenthecurrentflowsinthecoil,boththevanesaremagnetized
withlikepolaritiesinducedonthesameside.
Henceduetotherepulsionoflikepolarities,thereisaforceof
repulsionbetweenthetwovanescausingthemovementofthe
movingvane.
ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

43. Letcurrentflowinginthecoil=Iandtheenergystoredinthecoil=(1/2)LI
2
WhenthereisachangeofcurrentfromIto(I+dI),mustbeaccompaniedbychangeinemfofcoil.
e=d(LI)/dt=IdL/dt+LdI/dt
Theelectricalenergysuppliedbythesource=eIdt=I
2
dL+LIdI……………… ..(1)
Asthecurrentchangesto(I+dI),deflectioninthepointerbecomesdƟresultingintochangeininductanceofcoilfrom
Lto(L+dL).LetthisdeflectioninpointerisduetodeflectiontorqueTd.
Thusmechanicalworkdone=TdXdƟ ……………… ..(2)
EnergystoredinCoil=(1/2)(L+dL)(I+dI)
2
Changeinstoredenergyofcoil=FinalStoredEnergy–InitialStoredEnergy
=(1/2)(L+dL)(I+dI)
2
–(1/2)LI
2
Neglectingsecondorderandhighertermsofdifferentialquantitiesi.e.L(dI)
2
,2IdIxdLanddL(dI)
2
=(1/2)[2LIdI+I
2
dL]
Changeinstoredenergyofcoil=LIdI+(1/2)I
2
dL …………………… (3)
P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)
ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

44. Accordingtolawofconservationofenergy,thiselectricalenergysuppliedbythesourceisconvertedintostoredenergyinthecoil
andmechanicalworkdonefordeflectionofneedleofMovingIronInstruments.
Electricalenergysupplied=Changeinstoredenergy+Workdone
⇒I
2
dL+LIdI=LIdI+(1/2)I
2
dL+TdXd….[from(1),(2)&(3)]
⇒TdxdƟ=(1/2)dLI
2
Deflectingtorque,Td=(1/2)I
2
(dL/dƟ)
Inmovingironinstruments,thecontrollingtorqueisprovidedbyspring.ControllingtorqueduetospringisgivenasTc=KƟ
Inequilibriumstate,deflectingandcontrollingtorqueareequal.
⇒(1/2)I
2
(dL/dƟ)=KƟ
Ɵ=(1/2)(I
2
/K)(dL/dƟ)
Fromtheabovetorqueequation,weobservethattheangulardeflectionofneedleofmovingironinstrumentsissquareofrms
currentflowingthroughthecoil.Therefore,thedeflectionofmovingironinstrumentsisindependentofdirectionofcurrent.
P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)
ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

45. P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)
•Hysteresiserror
Duetohysteresiseffect,thefluxdensityforthesamecurrentwhileascendinganddescendingvaluesİsdifferentWhiledescending,the
fluxdensityishigherandwhileascendingitislesser.So,meterreadshigherfordescendingvalueofcurrentorvoltage.So,remedyfor
thisistousesmallerironpartswhichcandemagnetizequicklyortoworkwithlowerfluxdensities.
•Temperatureerror
Thetemperatureerrorarisesduetotheeffectoftemperatureonthetemperaturecoefficientofthespring,thiserrorisoftheorderof0-02%
per
o
Cchangeintemperature.Errorscancauseduetoself-heatingofthecoilandduetowhichchangeinresistanceofthecoil.So,coiland
seriesresistancemuchhavelowtemperaturecoefficientHencemanganinisgenerallyusedfortheseriesresistances.
•Straymagneticfielderror
Theoperatingmagneticfieldincaseofmovingironinstrumentsİsverylow.HenceeffectofexternaltoStraymagneticfieldcancause
errorThiseffectdependsonthedirectionofthestraymagneticfieldwithrespecttotheoperatingfieldoftheinstrument.
•Frequencyerror
ThesearerelatedtoA.C.operationoftheinstrument.Thechangeinfrequencyaffectsthereactanceoftheworkingcoilandalsoaffectsthe
magnitudeoftheeddycurrents,thiscauseserrorsintheinstrument.
•Eddycurrenterror
wheninstrumentisusedfora.c.measurementstheeddycurrentsareproducedintheironpartsoftheinstrument.Theeddycurrentaffects
theinstrumentcurrentcausingthechangeinthedeflectingtorqueThis-producestheerrorinthemeterreading.Aseddycurrentsare
frequencydependent,frequencychangescauseeddycurrenterror,
ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

46. SI. No Moving Coil (MC)
Instrument
Moving Iron (MI)
Instrument
1 Coil is moving & connected
to pointer
Coil is fixed & iron vane is
moving
2 Suitable for only DC
measurements
Suitable for both AC & DC
measurements
3 Scale is uniform Scale is non-uniform
4 Accuracy is High Accuracy is Low
5 Free from hysteresis & stray
magnetic field errors
Serious errors exist due to
hysteresis, frequency
changes and stray magnetic
fields.
6 Power consumption is lowPower consumption is high
P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

47. Advantages
1.ItisauniversalinstrumentwhichcanbeusedforthemeasurementofACandDCquantities.
2.Theyhavehighvalueoftorquetoweightratio,hencefrictionalerrorisquitelow.
3.Theseinstrumentsarequiterobustduetoitssimpleconstructionasthereisnomovingpartintheinstrumentwhich
carriescurrent.
4.Theseinstrumentscanbedesignedtoprovideprecisionandindustrialgradeaccuracy.Awelldesignedmovingiron
instrumentshaveaerroroflessthan2%orlessforDC.ForAC,theaccuracyoftheinstrumentmaybeoftheorderof
0.2to0.3%at50Hz.
Disadvantages
1.These instruments suffer from error due to hysteresis, frequency change and stray losses.
2.Thescale is non-uniform and cramped at lower end. So the accurate readings are not possible at lower range.
P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)
ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

48. TheinductanceofamovingironinstrumentisgivenbyL=(10+5-^2)µHwhereis
thedeflectionintheradiansfromzeroposition.Thespringconstantis12X10^-6Nm/rad.
Estimatethedeflectionforacurrentof5A.
P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)
ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

49. Anelectrodynamometertypeinstrumentisamovingcoilinstrumentinwhichtheoperatingfieldisproducedbyanothercoil
whichisfixed.Thistypeofinstrumentcanbeusedeitherasanammeterorasavoltmeter,butisgenerallyusedasawattmeter.
Anelectrodynamictypeinstrumentconsistsoftwofixedcoils,amovingcoil,controlspring,dampingdeviceandmagnetic
shieldingarrangement.
Electrodynamicinstrumentsarealsocapableoffunctioningastransferinstruments.Besides,theiruseasan
ammeter,voltmeter,andwattmeter;theyarealsousedtotransfercalibrationofworkinginstruments.
P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)
Theinstrumentconsistsofafixedcoilandamovingcoil.Thefixedcoilisusuallyair-
coredtoavoidhysteresiseffectswhenusedonACcircuits.Fixedcoilsarewoundwith
finewireforuseasavoltmeter.But,iftheinstrumentistobeusedasanammeteror
wattmeter,thenthefixedcoilsarewoundwithheavywirecarryingthemaincurrent.
ThemovingcoilismountedonanAluminiumspindle.Itiswoundeitherasself
sustainingcoilorelseonanon-metallicformersoastopreventeddycurrents.Moving
coilsarealsoair-cored.Controllingtorqueisprovidedbytwocontrolsprings.These
springsactasleadstothemovingcoil.
AirfrictiondampingisprovidedbyAluminiumvanesattachedtothespindleatthe
bottom.ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

50. P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)
ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

51. Letthe current in fixed coil be I
1and that in moving coil be I
2
L
1=Self-inductanceoffixedcoil
L
2=Self-inductanceofmovingcoil
M=Mutualinductancebetweenfixedandmovingcoils
ThefluxlinkageoffixedcoilØ
1=L
1i
1+Mi
2
ThefluxlinkageofmovingcoilØ
2=L
2i
2+Mi
1
Theelectricalenergyinputtotheinstrument=e
1i
1dt+e
2i
2dt
ButaccordingtoFaraday’sLaw,e
1=dØ
1/dtande
2=dØ
2/dt
Therefore,energyinputtotheinstrument=i
1dØ
1+i
2dØ
2
=i
1d(L
1i
1+Mi
2)+i
2d(L
2i
2+Mi
1)
=i
1L
1di
1+i
1
2
dL
1+i
1i
2dM+i
1Mdi
2+i
2L
2di
2+i
2
2
dL
2+i
1i
2dM+i
2Mdi
1
SinceL
1andL
2areconstant,thereforedL
1=0anddL
2=0
=i
1L
1di
1+i
1i
2dM+i
1Mdi
2+i
2L
2di
2+i
1i
2dM+i
2Mdi
1…………(1)
Someoftheaboveinputenergytoelectrodynamometerinstrumentsarestoredintheformofmagneticenergyinthecoilwhile
restisconvertedintomechanicalenergyofmovingcoil.Thus,EnergyInput=MechanicalEnergy+StoredEnergy
P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

52. MechanicalEnergy=ElectricalInput–StoredEnergy………… (2)
Thus,tofindthemechanicalenergy,weneedtofindthechangeinstoredenergyinthemagneticfieldofthecoil.
Letusassumeaninfinitesimallysmalltimedtforthesakeofcalculationofchangeinstoredenergy.
Changeinstoredenergy=d(1/2L
1i
1
2
+1/2L
2i
2
2
+Mi
1i
2)
=i
1L
1di
1+i
2L
2di
2+i
1Mdi
2+i
2Mdi
1+i
1i
2dM+(i
1
2
/2)dL
1+(i
2
2
/2)dL
2
ButL
1andL
2areconstant,thereforedL
1=0anddL
2=0
=i
1L
1di
1+i
2L
2di
2+i
1Mdi
2+i
2Mdi
1+i
1i
2dM……(3)
Fromequation(1),(2)and(3),MechanicalEnergy=i
1i
2dM
LetT
dbethedeflectingtorqueanddƟbethechangeindeflection,thenmechanicalenergy=T
ddƟ
T
ddƟ=i
1i
2dM⇒T
d=i
1i
2dM/dƟ
Theaboveequationgivesthedeflectingtorqueinelectrodynamicsorelectrodynamometerinstruments.Itcanbeseenthat
deflectingtorquedependsuponthemultiplicationofinstantaneousvalueofcurrentandrateofchangeofmutualinductance
betweenthefixedandmovingcoil.
P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)
ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

53. Case-1:WhenDCquantityisbeingmeasured.
Let I
1and I
2be the current in fixed and moving coil respectively. Therefore deflecting torque T
d= I
1I
2dM/dƟ
Butthisdeflectingtorqueiscontrolledbythespring.Springprovidesthecontrollingtorque.Thecontrollingtorquedueto
springforadeflectionofƟ;Tc=KƟwhereKisspringconstant.Atequilibriumthecontrollingtorqueanddeflectingtorques
areequal,henceTc=T
d
⇒KƟ=I
1I
2dM/dƟ
⇒Ɵ=(I
1I
2dM/dƟ)/K
Case-2:WhenACquantityisbeingmeasured.
Let i
1and i
2are sinusoidal current having a phase displacement of Ø. i
1= Im
1Sinwtandi
2= Im
2Sin(wt-Ø)
Theinstantaneousdeflectingtorqueisgivenas;Td=(Im
1Sinwt)[Im
2Sin(wt-Ø)]dM/dƟ
TheaveragetorqueforonetimeperiodofthecurrentsaregivenbyTd=(I
1I
2CosØ)dM/dƟ
WhereI
1=RMSValueofi
1andI
2=RMSvalueofi
2
Forsinusoidalalternatingcurrent,thedeflectingtorqueisdeterminedbytheproductofRMSvalueofcoilcurrentsandthe
cosineofphaseanglebetweenthem.WhentheinstrumentisusedforAC,theinstantaneoustorqueisproportionaltoi
2
.Thus,
thetorquevariesasthecurrentvariesbutthedirectionoftorqueremainsthesame.Becauseoftheinertiaoftheinstrument,the
needledoesnotfollowthechangeintorqueratherittakesapositionwheretheaveragetorquebecomesequaltothecontrolling
torque.
P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)
ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

54. ADVANTAGES:
1.These instruments are free from hysteresis and eddy current losses.
2.They can be used on both AC and DC.
3.They are used as transfer instruments.
DISADVANTAGES:
1.Low torque/weight ratio and hence low sensitivity.
2.Costlier than PMMC and moving iron type.
3.Non-uniform scale.
P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)
ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

55. P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)
Theoperationofalltheelectrostaticinstrumentsisbasedontheprinciplethatthereexistsaforcebetweenthetwoplates
withoppositecharges.Thisforcecanbeobtainedusingtheprinciplethatthemechanicalworkdoneisequaltothestored
energyifthereisarelativemotionofplates.
ConsidertwoplatesAandBwhereplateAisfixedwhileBismovable.Two
platesareoppositelychargedandplateBisrestrainedbyaspringconnectedto
fixedpoint.LettheforceofattractionbetweenthetwoplatesbeFnewton.Let
thecapacitancebetweenthetwoplatesbeCfarad.TheenergystoredEisthe
givenby,
When applied voltage increases by dV, the current flowing through capacitance
also changes and it is given by,
ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

56. AlsoduetochangeinappliedvoltagebyvaluedV,the
capacitanceincreasesbyDCbecauseplateBmoves
towardsafixedplateAwhichdecreasesthedistanceof
separationbetweentwoplatesincreasingnetcapacitance.
Thus,thenetenergystoredisgivenby,
P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)
Accordingtolawofconservationofenergy,
Electricalenergysupplied=Changeinstoredenergy+Work
done
⇒V
2
dC+CVdV=CVdV+(1/2)V
2
dC+TdXd
Deflectingtorque,Td=(1/2)V
2
(dC/dƟ)
Controllingtorqueisprovidedbyspring.Controllingtorquedue
tospringisgivenasTc=KƟ
Inequilibriumstate,deflectingandcontrollingtorqueareequal.
⇒(1/2)V
2
(dC/dƟ)=KƟ
⇒Ɵ=(1/2)(V
2
/K)(dC/dƟ)
ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

57. The two types of electrostatic voltmeter are
1.Quadrant typeelectrostatic voltmeter which is used to measure voltages up to 10 kV to 20 kV.
2.Attracted disc typeelectrostatic voltmeter which is used to measure voltages above 20 kV.
Quadrant Type Electrostatic Voltmeter
Theinstrumentconsistsoffourfixedmetaldoublequadrantsarrangedsuchthatthereisasmallairgapbetweenthe
quadrantsandthetotalassemblyformsshallowcircularbox.Insidethisboxadoublesectoredneedleissuspendedby
meansofaphosphorbronzethread.Theneedleissuspendedsuchthatitisplacedequidistantfromaboveandbelow
quadrantplatesasshownintheFigure.
Asshownintheabovefigurethefixedquadrantsareconnectedtogether.
Thevoltagetobemeasuredeithera.c.ord.c.isconnectedbetweenthe
fixedquadrantsandthemovingneedle.Thisneedlerotatesduetothe
electrostaticforcesetupduetothechargeaccumulationonthequadrant
plates.Thenthesuspensionexertsacontrollingtorqueandtheneedle
settlesatthepositionwhereboththetorques,controllinganddeflection,
areequal.
P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)
ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

58. There are two types of the electrical connections in the quadrant electrometer,
1.Heterostatic connection
2.Idiostatic connection.
Heterostatic Connection
Inthistypeofconnection,ahighvoltagebatteryisusedtochargetheneedletoavoltageconsiderablyhigherthanthe
voltagetobemeasured.TheconnectiondiagramisasshownintheFigure.Inthisconnection,thequadrantsareconnected
togetherindiagonallyoppositepairs.Themovingvanei.e.,needleispositivelychargedduetobattery.Thedeflectingforce
duetotopandbottomquadrantsonmovableneedlecancelseachotheronbothsides.Theonlydeflectingforceresponsible
isforceofattractionbetweenleftquadrantsandrightmovingsectorandforceofrepulsionbetweenrightquadrantandleft
movingsector.
P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

59. Idiostatic Connection
Thisisconnectiongenerallyusedincommercialinstruments.Inthistypeofconnection,needleisconnectedtoanyoneof
thepairsofquadrantsasshownintheFigure,directlywithoutexternalvoltage.
Themovingneedleisnegativelycharged,theleft-handquadrant
isnegativelychargedandtheright-handquadrantispositively
charged.Theforceofattractiononneedleduetotopandbottom
partsofright-handquadrantcanceleachother.
Sothereisnomotionofneedleduetorighthandquadrant
Similarlytheforceofrepulsiononneedleduetotopandbottom
partsofleft-handquadrantalsocanceleachother.
Thus,therighthandpositivelychargedquadrantattractthepartoftheneedleneartolefthandquadrantwhiletheleft
handnegativelychargedquadrantrepelsthepartoftheneedletorighthandquadrant.Thisrotatestheneedleandhence
thepointer.
P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

60. Attracted Disc Type Electrostatic Voltmeter
Attracted Disc Electrostatic Voltmeter
Theattracteddisctypeinstrumentsaregenerallyusedforthemeasurementofvoltagesabove20kV.
Thesystemconsistsoftwoplatessuchthatoneplatecanmovefreelywhileotherisfixed,Boththeplatesareperfectly
insulatedfromeachotherThevoltagetobemeasuredisappliedacrosstheplatesasasupplyvoltageasshownintheFigure.
Duetothesupplyvoltage,electrostaticfieldgetsproducedwhichdevelopsaforceofattractionbetweenthetwoplates.Due
totheforceofattraction,themovableplategetsdeflected.Inthismechanismthecontrollingtorqueisprovidedbyaspring.
P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

61. P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)
Atransformerthatisusedtomeasureelectricalquantitieslikecurrent,voltage,power,frequencyandpowerfactoris
knownasaninstrumenttransformer.Thesetransformersaremainlyusedwithrelaystoprotectthepowersystem.
ThePurposeoftheinstrumenttransformeristostepdownthevoltage&currentoftheACsystembecausethelevelof
voltage&currentinapowersystemisextremelyhigh.Sodesigningthemeasuringinstrumentswithhighvoltage&
currentisdifficultaswellasexpensive.Ingeneral,theseinstrumentsaremainlydesignedfor5A&110V.
Themeasurementofhigh-levelelectricalquantitiescanbedoneusingadevicenamelyinstrumenttransformer.These
transformersplayanessentialroleincurrentpowersystems.
TypesofInstrumentTransformers
Instrumenttransformersareclassifiedintotwotypessuchas
1.CurrentTransformer
2.PotentialTransformer
instrument Transformers
ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

62. Thistypeoftransformercanbeusedinpowersystemstostepdownthevoltagefromahighleveltoalowlevelwiththe
helpofa5Aammeter.Thistransformerincludestwowindingslikeprimaryandsecondary.Thecurrentinthesecondary
windingisproportionaltothecurrentintheprimarywindingasitgeneratescurrentinthesecondarywinding.Thecircuit
diagramofatypicalcurrenttransformerisdemonstratedinthefollowingfigure.
currentTransformers
Inthistransformer,theprimarywindingconsistsoffewturnsanditis
connectedwiththepowercircuitinseries.Soitiscalledaseriestransformer.
Likewise,thesecondarywindingincludesanumberofturnsanditisconnected
toanammeterdirectlybecausetheammeterincludessmallresistance.
Thus,thesecondarywindingofthistransformerworksalmostinthecondition
ofashortcircuit.Thiswindingincludestwoterminalswhereoneofits
terminalsisconnectedtogroundtoevadethehugecurrent.Soinsulation
breakdownchanceswillbereducedtoguardtheoperatorfromhugevoltage.
Thesecondarywindingofthistransformerintheabovecircuitisshort-circuited
beforedisconnectingtheammeterwiththehelpofaswitchtoavoidthehigh
voltageacrossthewinding.
P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

63. Thistypeoftransformercanbeusedinpowersystemstostepdownthevoltagefromahighleveltoalowerlevelwith
thehelpofasmallratingvoltmeterwhichrangesfrom110Voltsto120Volts.Apotentialtransformertypicalcircuit
diagramisillustratedbelow.
Thistransformerincludestwowindingslikeanormaltransformerlikeprimary&secondary.Theprimarywindingof
thetransformerincludesanumberofturnsanditisconnectedinparallelwiththecircuit.Soitiscalledaparallel
transformer.
potential Transformers
Similartotheprimarywinding,thesecondarywindingincludes
fewerturnsandthatisconnectedtoavoltmeterdirectlybecause
itincludeshugeresistance.Thereforethesecondarywinding
worksapproximatelyinopencircuitcondition.
Oneterminalofthiswindingisconnectedtotheearthtomaintain
thevoltagewithrespecttotheearthtoprotecttheoperatorfroma
hugevoltage.
P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

64. Theadvantagesofinstrumenttransformersare
1.Thesetransformersuseammeter&voltmetertomeasurehighcurrents&voltages.
2.Byusingthesetransformers,severalprotectingdevicescanbeoperatedlikerelaysotherwisepilotlights.
3.Instrumenttransformerbasedtransformersarelesscost.
4.Damagedpartscanbeeasilyreplaced.
5.Thesetransformersofferelectricalisolationamongmeasuringinstruments&highvoltagepowercircuits.Sothat
electricalinsulationrequirementscanbereducedinprotectivecircuits&measuringinstruments.
6.Byusingthistransformer,variousmeasuringinstrumentscanbeconnectedtoapowersystem.
7.Lowpowerconsumptionwillbethereinprotective&measuringcircuitsbecauseofthelowlevelofvoltage&
current.
Theonlydisadvantageofinstrumenttransformeris,thesecanbeusedsimplyforACcircuitsbutnotforDCcircuits
Advantages & disadvantages of instrument Transformers
P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

65. Ratio’s of instRument tRansfoRmeRs
1.Actualratio[R]
Theactualtransformationratioisdefinedastheratioofthemagnitudeofactualprimaryphasortothecorresponding
magnitudeofactualsecondaryphasor.Theactualratioisalsocalledtransformationratio.
R=
Magnitudeofactualprimarycurrent
Magnitudeofactualsecondarycurrent
…..forCT
R=
Magnitudeofactualprimaryvolatge
Magnitudeofactualsecondaryvoltage
…..forPT
2. Nominal ratio [Kn]
The nominal ratio is defined as the ratio of rated primary quantity to the rated secondary quantity, cither current or voltage.
K
n=
Ratedprimarycurrent
Ratedsecondarycurrent
…..forCT
K
n=
Ratedprimaryvolatge
Ratedsecondaryvoltage
…..forPT
P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

66. 3. Turns ratio [n]
n=
Numberofturnsofsecondarywinding
Numberofturnsofprimarywinding
…..forCT
n=
Numberofturnsofprimarywinding
Numberofturnsofsecondarywinding
…..forPT
4. Ratio Correction Factor (RCF)
It is the ratio of transformation i.e., actual ratio to the nominal ratio.
TheratiowhichisindicatedonthenameplateofatransformerisalwaysItsnominalratio.
Ratio’s of instRument tRansfoRmeRs
P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

67. Thenominalratioofaninstrumenttransformerdoesnotremainconstantinpracticeastheloadonthesecondarychanges,it
changesbecauseofeffectofsecondarycurrent,powerfactorandmagnetizingaswellascorelosscomponentsofcurrent
andthiscauseserrorsinthemeasurements.
Fortheparticularclassoftransformersthespecificloadingatratedsecondarywindingvoltageisspecifiedsuchthatthe
errorsdonotexceedthelimit.Suchapermissibleloadiscalledburdenofaninstrumenttransformerthusthepermissible
loadacrossthesecondarywindingexpressedinvolt-amperesattheratedsecondarywindingvoltageorcurrent,suchthat
errorsdonotexceedthelimitiscalledburdenofaninstrumenttransformer.
Burden of an Instrument Transformer
If only the impedance of the load is considered then burden due to only load can be obtained
P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

68. Figure: equivalent circuit of a current transformer along with load
P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)
Theory of Current Transformers
ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

69. Figure: phasor diagram of the Transformer with a lagging P.F. load
P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)
C . T. -Derivation of Actual Ratio
ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

70. P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

71. This is approximated value of actual ratio but practically very close to actual result, the equation (3) can be further
expanded as,
P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)
ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

72. Thephaseangleθisdefinedastheanglebetweenreversedsecondarycurrentphasori.e.,reflectedsecondary
currentphasorandtheprimarycurrent.
Signconvention:θispositiveifreflectedsecondarycurrentleadsprimarycurrent.θisnegativeifsecondarycurrent
lagsprimarycurrent.
P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)
C . T . -Derivation of Phase Angle (θ) of Transformer
ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

73. P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)
ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

74. TheloadingofpotentialTransformerisverysmallinpracticehenceexcitingcurrentI
0isoftheorderofis,i.e.,secondary
windingcurrent.WhileinanormalpowerTransformerI
o.isverysmallcomparedtoI
s.Theequivalentcircuitofpotential
TransformerisshownintheFigure.
Theory of potential Transformers
P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)
ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS

75. Differences between Instrument and Power Transformers
P.Naresh(Ph.D.),Asst.Prof.,EEEREC(A)ElectricalMeasurements:UNIT-IMEASURINGINSTRUMENTS