Expe imen al Cha ac e iza ion Me hodology o he
Iden i ica ion o Vol age Losses o PEMFC: Applied
o an Open Ca hode S ack
A. Husa *, S. S ahl, J. Rie a
Ins i u de Robò ica i In o mà ica Indus ial (CSIC-UPC)
C/ Llo ens i A igas 4-6 08028 - Ba celona (SPAIN)
(*) co esponding au ho : ahusa @i i.upc.edu
Keywo ds: Ac i a ion losses, Mass anspo losses, Ohmic losses, PEMFC, Open ca hode
Abs ac : The objec i e o his s udy is o desc ibe he me hodology used o
isola e he main ol age loss indica o s h ough a simple and e ec i e ea men o a
cu en in e up and cu en sweep. The ol age loss indica o s a e ac i a ion
pola iza ion, mass anspo , and ohmic losses. The indica o s o hese losses a e
he Ta el slope, mass anspo esis ance and ohmic esis ance espec i ely. The
use o his me hodology o isola e he indi idual ol age losses wo ks qui e well.
E en hough he e may be some inaccu acies, he ends can be clea ly seen. This
me hodology can be used in any PEMFC sys em o moni o he s a e o heal h o he
uel cell. I his me hod we e o be au oma ed and implemen ed on a pe iodic basis,
hen an on-line measu emen o he indi idual ol age losses could be moni o ed.
The da a analysis indica es ha a majo objec i e o he con olle will be o minimize
he mass anspo losses by implemen ing p ope empe a u e con ol.
1 In oduc ion
Rema kable p og ess has been made in polyme elec oly e memb ane uel cell
(PEMFC) ma e ials, componen design, p oduc ion and sys em powe densi y.
Howe e , he e is s ill signi ican wo k o be done in o de o unde s and he di e en
physical phenomena wi hin a wo king uel cell and how hey need o be con olled in
o de o imp o e e iciency, ope a ing ange and s abili y [Li 2008]. This expe imen al
s udy is ocused on iden i ying he majo ol age losses in a PEMFC wi h a simple,
ye e ec i e, me hod using only cu en , ol age, and PEMFC s ack empe a u e
measu emen s. In he li e a u e simple me hodologies ha e been sugges ed as a
way o decompose he i-V pe o mance cu es and he e o e isola e indi idual losses
[Baghalha 2010], [Wu 2008]. The majo losses o be iden i ied a e ac i a ion, mass
anspo and ohmic esis ance. Fo each o hese losses, indica o s ha e been
de e mined. The expe imen al me hodology used o ex ac he indi idual indica o s
is based on wo dynamic es s: cu en in e up and cu en sweep. The ex ac ion
me hods a e explained and he esul s using hese me hods a e p esen ed.
Fi s , he uel cell ol age loss model will be explained in sec ion 2 ollowed by he
expe imen al me hodology o dissec ing he i-V cu e in sec ion 3. Sec ion 4
desc ibes he expe imen al se up and es condi ions ollowed by a discussion o
esul s and he conclusions.
The objec i e is o isola e and iden i y he main ol age loss indica o s wi h a
simple and e ec i e ea men o a cu en in e up and cu en sweep.
2 Fuel Cell Vol age Losses Model
In he widely published [O’Hay e 2009] basic uel cell model used in his wo k, he
uel cell ol age ( ) is equal o he he modynamic e e sible po en ial ( ( )) o a
PEM uel cell minus he h ee majo losses: ac i a ion ( ), mass anspo ( )
and ohmic ( ).
( ) [ ] (1)
The he modynamic e e sible po en ial is ep esen ed by he ollowing equa ion
[O’Hay e 2009]:
( ) (
)
(∏
∏
) (2)
whe e is he change in en halpy and is he change in en opy o he eac ion a
s anda d empe a u e and p essu e, which in his s udy is conside ed o be 25ºC and
1 a m and has a alue o -285826 J/mol and -163 J/mol/K espec i ely. I mo e
accu acy is needed hen equa ions can be in oduced o make he en halpy and
en opy a unc ion o empe a u e. ep esen s he numbe o elec ons ans e ed
pe mole, which in his case is 2 o H2, F is Fa aday’s cons an and R is he uni e sal
gas cons an . is he uel cell ope a ing empe a u e. and a e he
ac i i ies a he inle condi ions, which a e: pa ial p essu e o H2O apou ( he
p oduc ) and H2 and O2 ( he eac an ) di ided by he o al gas p essu e ha en e s
he uel cell. is he co esponding s oichiome ic coe icien o each species
pa icipa ing in he eac ion, which is 1 o all o hem excep o O2, which is
⁄.
2.1 Ac i a ion pola iza ion losses:
A ce ain p opo ion o ene gy is needed o s a he chemical eac ion. This
phenomenon p oduces a non-linea ol age d op called ac i a ion pola iza ion. These
losses occu on bo h anode and ca hode ca alys s. Howe e , he oxygen educ ion
eac ion kine ics is much slowe han hyd ogen oxida ion eac ion, and he educ ion
eac ion p oduces a much la ge magni ude o ac i a ion pola iza ion loss. The
oxida ion eac ion on he anode is much as e and p ac ically cons an h ough ou
he cu en ange. I only a single eac ion is conside ed hen he ol age loss due o
ac i a ion pola iza ion can be desc ibed by he Ta el equa ion [Ba bi 2005]:
(
)
(
) [ ] (3)
The pa ame e is he cha ge ans e coe icien and exp esses how he change
in he elec ical po en ial ac oss he eac ion in e ace changes he eac ion a e. I
depends on he ype o eac ion and he elec ode ma e ial. I s alue is heo e ically
be ween 0 and 1 depending on he ca alys ma e ial [La minie 2003]. I physically
ep esen s he ac ion o addi ional ene gy ha goes owa d he ca hodic educ ion
eac ion a an elec ode. The cha ge ans e coe icien can also be hough o as a
symme y coe icien o he elec ode eac ion and i is ypically conside ed o be
a ound 0.5 wi h hyd ogen and oxygen eac ing on a pla inum ca alys [Mench 2008].
The exchange cu en densi y [ ] is he a e a which he eac ion p oceeds
(simul aneously in bo h di ec ions) a equilib ium po en ial ( ( )) when he ne
cu en equals ze o [Ba bi 2005]. The exchange cu en densi y is a measu e o he
e ec i eness o he elec ode in p omo ing he elec ochemical eac ion whe e he
highe he exchange cu en densi y, he lowe he o e all ac i a ion losses. The uel
cell cu en densi y is deno ed by [ ]. The ac i a ion losses a e gene ally he
dominan e ec on he uel cell ol age, as is shown in igu e 1.
When he uel cell is no connec ed o an ex e nal ci cui (open ci cui ol age), he
uel cell ol age would be expec ed o be close o he he modynamic po en ial,
ela i e o he ambien condi ions and eac an pa ial p essu e. Howe e , he
measu ed uel cell ol age is much lowe , usually less han 1 V/cell, which can be
a ibu ed o hyd ogen c osso e and in e nal cu en s. These losses a ise because
he memb ane in a PEMFC is sligh ly elec onically conduc i e and pe meable o
gasses. These losses can be conside ed as an in e nal cu en . The amoun o
cu en ha hese losses ep esen is a he small compa ed o no mal ope a ing
cu en s. Howe e , hese in e nal cu en losses ha e a la ge e ec on he ol age
when he ex e nal cu en is e y small. In his s udy hese losses a e conside ed
pa o he ac i a ion losses [Ba bi 2005] and should no a ec he esul s.
The Ta el slope is he main indica o o ac i a ion losses and will be explained in
mo e de ail in sec ion 3.3.
2.2 Ohmic losses:
The esis ance o he low o elec ons h ough he elec ically conduc i e uel cell
componen s and o he low o ions h ough he memb ane causes a ol age d op,
which can be exp essed by Ohm’s law:
[ ] (4)
The in e nal cell esis ance is in [ ]. The elec ic and con ac
esis ance can be conside ed cons an wi h espec o cu en and empe a u e. Thus
any change in he esis ance is only dependen on memb ane wa e concen a ion
and memb ane empe a u e. [Sp inge , 1991]
is he indica o o memb ane ionic esis ance.
2.3 Mass anspo losses:
The consump ion o eac an gases a he ca alys laye s leads o concen a ion
g adien s and hus changes he pa ial p essu e o he eac an s, which a ec s he
uel cell ol age as seen p e iously in equa ion (2). Re e ing o Fa aday's law o
elec olysis, he ans e ed cha ge and he mola lux o a eac an a e p opo ional
o he cu en densi y [Ba bi 2005]:
[ ] (5)
The highe he cu en densi y, he lowe he eac an concen a ion is a he
ca alys laye .
The cu en densi y a which he eac an concen a ion eaches ze o is called he
limi ing cu en densi y ( ). Conside ing his ela ionship be ween eac an mass
anspo and cu en densi y, he mass anspo losses can be exp essed as [Ba bi
2005]:
(
) (6)
Howe e his exp ession o mass anspo losses does no ep esen he
expe imen al alues well [O’Hay e 2009]. In a o ced low open ca hode uel cell
whe e he ai eac an s oichiome y is always o e 10 and he maximum cu en
d awn om he s ack is ela i ely low (0.27 A/cm2) i is assumed ha he mass
anspo losses a e neglec ed o cu en densi ies o less han 0.04A/cm2 and a e
conside ed linea beyond ha cu en densi y. High cu en densi ies a e no possible
wi h open ca hode s ack due o he lack o humidi ica ion and he s anda d ope a ing
condi ions, hence he mass anspo losses seem linea .
( ) (7)
3 Expe imen al Me hodology Applied o Open Ca hode PEMFC
The ollowing expe imen al app oach is used o isola e he indi idual losses in he
uel cell s ack. The da a p esen ed in he ollowing sec ion is an example o eal da a
ea ed using his me hod. The main di icul y is o isola e mass anspo om
ac i a ion losses.
As he Nyquis plo s om Elec ical Impedance Spec oscopy (EIS) only gi e
linea in o ma ion a he measu ed poin o ope a ion, ano he me hod o de e mine
he nonlinea losses caused by he ac i a ion a e desc ibed.
Al hough he da a used in his explana ion co esponds o an open ca hode uel
cell, he me hodology is alid o all PEMFC.
3.1 Cu en in e up
The pu pose o he cu en in e up (CI) is o ob ain he ohmic esis ance ( )
o he uel cell in a as and accu a e manne . The p incipal concep is o isola e he
esis ance ha is ou side o he RC ci cui , which should be seen as an
ins an aneous jump in ol age when he load is emo ed, because i has no
capaci i e componen . The de eloped algo i hm de ec s he jump in ol age when
he load is disconnec ed and sepa a es he cu e in wo s aigh lines o gene a e he
poin whe e he ins an aneous ol age inc ease s ops, as illus a ed in igu e 2. The
algo i hm de ec s he jump by looking o 3 consecu i e poin s o ising ol age and
hen uses he i s poin as he e ical line. Then looks o he poin a e he jump
whe e he di e ence be ween he poin s is less han 0.002V and hen c ea es a line
using he ollowing 10 poin s.
EIS da a has been compa ed o he ohmic esis ance measu emen ia he
cu en in e up me hod in o de o calib a e he de ec ion algo i hm o he EIS
esul s, shown in igu e 3.
3.2 Cu en sweep
The pu pose o he cu en sweep is o ob ain an i-V cu e o he uel cell wi h
minimal changes o he in e nal condi ions. This is done by quickly passing h ough
speci ically selec ed cu en se poin s.
In his s udy cu en sweeps we e pe o med when he uel cell eached s eady
s a e condi ions, howe e i is no necessa y. The ime cons an o he sys em was
de e mined om he EIS bode diag am and is de e mined o be in he o de o
. I is in e es ing o no e ha he ime cons an o he uel cell inc eases as
he cu en dec eases. The ime needed o he ol age o s able ou a a cu en se
poin o 0 A/cm2 is much longe han a he o he cu en s, which can be clea ly seen
in igu e 4.
In his s udy he uel cell is le a each cu en se poin o only 300ms, which
p o ided enough ime o he uel cell o s able ou .
As can be seen in igu e 4 he e a e 10 cu en es poin s, 4 poin s wi h a
di e ence o he ope a ing cu en o 5% o he ope a ing cu en and 6 poin s in he
nonlinea egion a lowe cu en densi ies. The 4 poin s a ound he ope a ing
condi ion gi e a good eading o he linea slope o he uel cell. The 6 poin s a he
low cu en densi ies gi e a good eading on he nonlinea egion o he uel cell. The
black line in igu e 1 shows he plo o he ex ac ed cu en sweep (i-V) om igu e 4.
The es ime a each se poin has o be kep o a minimum due o he na u e o
he open ca hode sys em whe e he wa e con en and he empe a u e in he uel
cell a e d i en by he cu en . The o al ime o he cu en sweep could be educed
o less han 1s i necessa y. Howe e i can be no ed in his es ha e en a a o al
o 3s, he ol age be o e and a e he es a e he same.
3.3 B eakdown o he cu en sweep
Using he esis ance da a om he CI and assuming ha mass anspo losses
a e negligible ( ) a cu en densi ies o less hen 0.04A/cm2 ( he nonlinea
pa o he sweep), equa ion (1) was sol ed o .
(8)
A loga i hmic unc ion is i ed o he da a om 0.00 o 0.04 A/cm2 as shown in
igu e 5. The slope o his line in he loga i hmic scale is he Ta el slope, and he
in e cep on he x axis is he exchange cu en densi y.
(9)
Using he i ed Ta el slope and exchange cu en densi y he line was
ex apola ed ou o he s eady s a e cu en se poin . Thus he di e ence be ween
he he modynamic e e sible po en ial ( ) and he ex apola ed cu e gi es
ac i a ion losses ( ) seen in igu e 1.
Now looking back a equa ion (1) all he a iables a e known excep o ( ),
which now can be sol ed. Wi h his, he b eakdown o he indi idual losses can be
plo ed, as shown in Figu e 6.
The x-axis in e cep o he mass anspo losses a e a i icially se o 0.04 A/cm2
due o he assump ion ha he e a e no mass anspo losses a he lowe cu en
densi ies. This can be seen in igu e 5 whe e he do ed end line sepa a es om he
solid line.
Take no e ha he losses calcula ed using his me hod is only alid o he cu en
and empe a u e a which he sweep and CI we e aken, which in his case is he
middle poin a 4 Amps and 32.2ºC.
I his me hod is au oma ed and implemen ed on a pe iodic basis hen an on-line
measu emen o he indi idual ol age losses could be moni o ed.
4 Expe imen al se up & ope a ing condi ions
A Ho izon® H-100 open ca hode, 20 cell, 22cm2 ac i e a ea uel cell s ack in an
en i onmen al chambe was es ed. The only ac i e con ol mechanism employed is
a single an ha bo h cools and p o ides he oxygen needed o he eac ion. All he
o he con ol mechanisms a e disconnec ed and a cons an pu e, d y hyd ogen low
is supplied o he s ack.
The ambien condi ions se in he en i onmen al chambe we e 25ºC wi h 90%RH.
The s eady s a e cu en densi ies o 0.09, 0.18, and 0.27A/cm2 co espond o 2, 4
and 6A. The combined ca hode and cooling an was se o con ol a cons an uel cell
empe a u e. The uel cell empe a u e se poin s a e: om a minimum empe a u e,
30, 35, 40, 45, 50, 55ºC. Pu e d y hyd ogen was supplied o he anode a 0.36, 0.71
and 1.07 SLPM as he s eady s a e cu en was inc eased om 2, o 4 and 6A
espec i ely.
LabVIEW da a acquisi ion so wa e was used in conjunc ion wi h analog o digi al
con e e (ADC) o he NI da a acquisi ion sys em combined wi h he HCPL-788J
isola ion ampli ie om Agilen Technologies o measu e he s ack ol age. The hall-
e ec -based cu en senso ACS713 om Alleg o Mic oSys ems measu es he
cu en in he load ci cui . The swi ch used o pe o m he cu en was an in elligen
powe highside swi ch IPS6021 om In e na ional Rec i ie . Finally, he da a

acquisi ion ca d used o he high equency es was a PCI-DAS 4020/12 om
Measu emen Compu ing, whe e he sampling a e can be se om 1kHz o 20MHz.
5 Resul s and Discussion
In his sec ion se e al esul s a e discussed, wi h espec o cu en and ambien
empe a u e.
The load on he s ack ob iously has he la ges in luence on he uel cell ol age
loss as seen in igu e 7. I is in e es ing o no e ha a all h ee cu en s he ol age
losses dec ease wi h an inc ease in empe a u e bu i is only he 6A cu e ha has a
nonlinea dec ease. The sou ce o he nonlinea i y will be discussed in sec ion 5.2
and 5.3 and shows he p ac icali y o his me hodology as a diagnos ic ool.
The nex sec ions will discuss he e olu ion o he indi idual ol age losses a he
di e en cu en s and uel cell ope a ing empe a u e.
5.1 Ac i a ion losses e alua ion
The ac i a ion losses a e shown in igu e 8. They dec ease linea ly wi h uel cell
empe a u e in hese anges o cu en s and empe a u es. The eason o he linea
dec ease in ac i a ion losses is due o he dec ease in he modynamic e e sible
po en ial (Eo) which dec eases wi h uel cell empe a u e, hus causing he ac i a ion
losses o dec ease. Howe e , he o iginal cu en sweep da a does no show his
dec ease. The low cu en densi y cu en sweep da a o he same cu en a
di e en empe a u es a e iden ical o each o he a less han 0.04 A/cm2. Thus his is
only a heo e ical dec ease in ac i a ion losses due o he o de in which he da a
was decomposed.
The Ta el slope, being he indica o o ac i a ion losses, e lec s he linea i y as i
seems o emain ela i ely cons an wi h espec o empe a u e a each cu en
es ed, as shown in igu e 9.
5.2 Mass anspo losses e alua ion
The mass anspo losses inc ease g ea ly wi h he inc ease in cu en (see igu e
10), which is expec ed acco ding o equa ion 5 and 6. All he measu emen e o s a e
inco po a ed in o his indica o due o he o de in which he ol age loss
decomposi ion was done. Howe e , an in e es ing end is seen wi h ega d o
empe a u e. The e is a gene al linea dec ease in mass anspo losses wi h he
inc ease in uel cell empe a u e and seems o be linea o empe a u es lowe han
50ºC. Howe e , when empe a u es go beyond 50ºC, he e seems o be s abling ou
o he losses. This can be seen d ama ically in he mass anspo indica o shown in
igu e 11.
This elbow in he 6A da a sugges s ha he e is a change in s a e o he di usion
and/o ca alys laye s. This could possibly be due o he e apo a ion o mos o he
liquid wa e in hese laye s allowing o maximum di usion lux. The e is a possible
ade-o o maximizing di usion wi h inc eased memb ane esis ance, as will be
shown in he ohmic losses sec ion.
5.3 Ohmic esis ance losses e alua ion
Ohmic losses inc ease wi h an inc ease in cu en and empe a u e. The e seems
o be a dis inc upwa d end as he uel cell eaches 45ºC. This may indica e ha
beyond his empe a u e and inle ela i e humidi y he memb ane is no ully
sa u a ed, which ein o ces he hypo hesis ha he e is no mo e liquid wa e in he
laye s.
E en hough he ohmic losses a e ela i ely small compa ed o he o he losses in
he uel cell, he e may be some undesi able long- e m deg ada ion caused by a d y
memb ane.
The Ohmic esis ance anges om 0.115 o 0.140 (Ohm-cm2). This is compa able
o s udies in he li e a u e which indica e anges om 0.100 o 0.182 (Ohm-cm2) o
Na ion 212 and 117 espec i ely [Hou 2011], [Büchi 1996]. Fuel cell esis ance Rohm
is ela i ely cons an a each cu en o empe a u es below 45ºC.
6 Conclusions
The p oposed me hodology in his wo k o isola e he indi idual ol age losses
unc ions qui e well. E en hough he e may be some inaccu acies, he ends a e
clea ly seen. This me hodology can be used o moni o any PEMFC s a e o heal h
wi h espec o ac i a ion, mass anspo , and ohmic losses.
I mus be no ed ha all he powe gene a ed du ing he sweep would be los .
Thus i will a ec he in ended pe o mance o he sys em. Capaci o s could be
placed in pa allel wi h he uel cell o supply he needed powe du ing he sweep. The
e iciency loss due o he sweep will be dependen on he equency and he du a ion
o he sweeps. This analysis has no been done bu i is s ongly dependen on he
uel cells design and i s sensibili y o he ope a ing condi ions. An op imiza ion
analysis o he sweep, in o de o minimize he equency and he du a ion o he
sweeps, would also need o be done.
I his me hod is au oma ed and implemen ed on a pe iodic base, hen an on-line
measu emen o he indi idual ol age losses could be moni o ed.
Th ough analysis o he open ca hode uel cell da a i is clea ha a majo
objec i e o he con olle will be o minimize he losses h ough p ope con ol o he
empe a u e by means o he an.
Fu u e wo k will be dedica ed o de e mining how he hyd ogen pu ge a e, inle
empe a u es and ela i e humidi y a ec he indi idual losses.
7 Acknowledgemen s
All he expe imen al es s we e pe o med a he Fuel Cells Labo a o y o he
Ins i u de Robó ica i In o má ica Indus ial (CSIC-UPC, Ba celona) and a e only
possible due o i s ad anced equipmen and p o icien echnical s a . This wo k is
pa ially unded by he p ojec o CICYT DPI2010-15274 MICINN and CICYT
DPI2011-25649 MICINN
8 Re e ences
[Baghalha 2010] M. Baghalha, J. S umpe and M. Eike ling, Model-based
decon olu ion o po en ial losses in a PEM uel cell, ECS T ans. 28, pg. 159-167,
2010
[Ba bi 2005] F. Ba bi , PEM Fuel Cells: Theo y and P ac ice, Else ie Academic
P ess, 2005
[Büchi 1996] F.N. Büchi, G. G. Sche e , In-si u esis ance measu emen s o Na ion
117 memb anes in polyme elec oly e uel cells, J. Elec oanaly ical Chemis y,
Vol 404, pg 37-43, 1996
[Hou 2011] A s udy on pola iza ion hys e esis in PEM uel cells by gal anos a ic s ep
sweep, In e na ional Jou nal o Hyd ogen Ene gy, ol 36, Is. 12, pg. 7199-7206,
2011
[La minie 2003] J. La minie, Fuel Cell Sys ems Explained 2nd Edi ion, John Wiley &
Sons L d, 2003
[Li 2008] H. Li, Y. Tang, Z. Wang, Z. Shi, S. Wu, D. Song, J. Zhang, K. Fa ih, J.
Zhang, H. Wang, Z. Liu, R. Aboua allah, A. Mazza, A e iew o wa e looding
issues in he p o on exchange memb ane uel cell, J. Powe Sou ces, Vol 178 pg.
103-117, 2008
[Mench 2008] M. M. Mench, Fuel Cell Engines, John Wiley & Sons, Inc. 2008
[O'Hay e 2009] R. O'Hay e, Fuel Cell Fundamen als, John Wiley & Sons L d, 2009
[Sp inge 1991] T. E. Sp inge , T. A. Zawodzinski, and S. Go es eld, Polyme
elec oly e uel cell model, J. Elec ochem. Soc., Vol 138, No 8, 1991
[Wu 2008] J. Wu, X. Z. Yuan, H. Wang, M. Blanco, J. J. Ma in, and J. Zhang,
In e na ional Jou nal o Hyd ogen Ene gy, Vol 33, Is. 6 1735-1746, 2008
9 Figu e Legend
Fig. 1. G aphical ep esen a ion o equa ion (1) depic ing he h ee main losses a a gi en cu en
(g aph based on eal da a 4A a 32.2ºC)
Fig. 2. CI da a o 3 es s a he same ope a ing condi ion o show epea abili y. Ohmic esis ance using
CI is 0.121-cm2
Fig. 3. Nyquis plo a he same condi ions (4A) as he CI da a. Ohmic esis ance using EIS is 0.119-
cm2
Fig. 4. A e age cell ol age and cu en densi y dynamic o a cu en sweep wi h 300ms a each poin .
No e ha he ol age be o e and a e he es is he same.
Fig. 5. The solid line ep esen s he eal da a (ETP – V c - iRohm). The linea ex apola ion o he lowe
cu en densi y poin s is ep esen ed by he do ed line. No e ha i is in a loga i hmic scale.
Fig. 6. The g aph depic s he b eakdown o he ol age losses om expe imen al da a.
Fig. 7. The g aph shows he e olu ion o o al ol age loss a h ee di e en cu en s 2, 4, 6A as a
unc ion o uel cell empe a u e wi h cons an en i onmen al condi ions
Fig. 8. Ac i a ion losses o he uel cell s ack
Fig. 9. Ta el slope as ac i a ion indica o
Fig. 10. Mass anspo losses
Fig. 11. Linea mass anspo indica o ep esen ed as a esis ance o 2, 4 and 6A.
Fig. 12. Ohmic losses wi h espec o cu en and empe a u e
Fig. 13. Ohmic esis ance as he ohmic indica o