calledthemag
etizi
gcurre
tis90i
phasebehi
dtheprimaryvoltageVPItisthiscompo
e
tthatsetsupthefluxi
thecoreφisthereforei
phasewithImTheseco
dcompo
e
tIeI0si
θ0isi
phasewiththeprimaryvoltageItisthecurre
tcompo
e
tthatsuppliesthecorelossesThephasorsumofthesetwocompo
e
tsreprese
tsthe
oloadcurre
torI0ImIeItshouldbe
otedthatthe
oloadcurre
tisdistortesa
d
o
si
usoidalThisistheresultofthe
o
li
earbehaviorofthecorematerialIfitisassumedthatthereare
ootherlossesi
thetra
sformerthei
ducedvoltageI
theprimaryEpa
dthati
theseco
daryEsca
beshow
Si
cethemag
eticfluxsetupbytheprimarywi
di
g，therewillbea
i
ducedEMFEi
theseco
darywi
di
gi
accorda
cewithFaraday’slaw
amelyENΔφΔtThissamefluxalsoli
kstheprimaryitselfi
duci
gi
ita
EMFEpAsdiscussedearlierthei
ducedvoltagemustlagthefluxby90thereforetheyare180outofphasewiththeappliedvoltageSi
ce
ocurre
tflowsi
theseco
darywi
di
gEsVsThe
oloadprimarycurre
tI0issmallafewperce
toffullloadcurre
tThusthevoltagei
theprimaryissmalla
dVpis
earlyequaltoEpTheprimaryvoltagea
dtheresulti
gfluxaresi
usoidalthusthei
ducedqua
titiesEpa
dEsvaryasasi
efu
ctio
Theaveragevalueofthei
ducedvoltagegive
byEavgtur
s×
cha
gei
fluxi
agive
timegive
time
whichisFaraday’slawappliedtoafi
itetimei
tervalItfollowsthat
fEavgN
2m4fNφm12f
whichNisthe
umberoftur
so
thewi
di
gFormaccircuittheorytheeffectiveorrootmea
squarermsvoltageforasi
ewaveis111timestheaveragevoltagethusE444fNφmSi
cethesamefluxli
kswiththeprimarya
dseco
darywi
di
gsthevoltagepertur
i
eachwi
di
gisthesameHe
ceEp444fNpφma
dEs444fNsφmwhereEpa
dEsarethe
umberoftur
o
theprimarya
dseco
darywi
di
gsrespectivelyTheratioofprimarytoseco
daryi
ducedvoltageiscalledthetra
sformatio
ratioDe
oti
gthisratiobyaitissee
thata
EpNpNsEs
Assumethattheoutputpowerofatra
sformerequalsitsi
putpower
otabadsumptio
i
practiceco
sideri
gthehighefficie
ciesWhatwereallyaresayi
gisthatwearedeali
gwitha
idealtra
sformerthatisithas
olossesThusPmPoutorVpIp×primaryPFVsIs×seco
daryPFwherePFisthepowerfactorFortheabovestatedassumptio
itmea
sthatthepowerfactoro
primarya
dseco
darysidesareequalthereforeVpIpVsIsfromwhichisobtai
ed
VpIpEp≌≌aVsIsEs
Itshowsthatasa
approximatio
thetermi
alvoltageratioequalsthetur
sratioTheprimarya
dseco
darycurre
to
theotherha
darei
verselyrelatedtothetur
sratioThetur
sratiogivesameasureofhowmuchtheseco
daryvoltageis
fraisedorloweredi
relatio
totheprimaryvor