REVISIONPower measurement of resistor, inductor and capacitor

W -VI casE

If V * 100 volts and R - 30 ohms, complete

w = 333.3 wejls p IzR= 333.3 un{l s

V=A=

/oovloorffi-a

=3o

S -IY= '#r/oo 3 333.3VA3o

3.134 0= r/s' - P2 = 343,3*G"r"ir'| 3373-

5=C)\Ao

If V - 100 volts and C : 30 ohms, complete

3 g1L xQ: Crt*/h

a,c.supply

P - IzR=

,S -IY =100lo0

^*: :1 S3A3o 1r

'-y l loo r 333.3 VA90

If V : 100 volts and /, - 3A/20o ohms, complete

933.3'* Q-: 333,TVA,

ffi )'x3o Los?-o:313'Wy vtoor 1t?.gVA3o

a-w

[4/ =Y=A=

P - IzR=

,S=IV=/ooVfg:3,bLA7o

1,_ *? ll4-'oV4r

O c,;uhW=t/=A=

313.2- *ut{s

A=.ls'r 333.\ x s,nTreLoyes

REVISIONBalanced resistive star and delta. Two wattmeter power measurement.

Use ABC rotation and Van reference

W.=V*Iocos Xf Wc =V*Ircos 4?

A three phase, three wire, 100 volt, ABC system supplies a balanced delta-connected load with impedances ofZ - 20 /0" ohms. f)etermine the line currents, draw the phasor diagram and find the wattmeter readings when

the two-wattmeter method is applied to A and C phases. Repeat for the load connected in star.

4* t;s

A

loo Wls

Z,un Lal-9,

lfauf , If s, l: lf"ol 'oo/", s f,A

I t*f x lful = lL l='.F rf* B' 66A

InE {*AE flro s' f&o *5m\^& : tOO x B. 6Lx cos 30 e 7f0Wc ={oo x 8,6$r r*sSo 3 7fO

Wu; ff H:r?.1+fl*

ls

I'/A

t{f,

IO0r 2,887 '(t,c g r2.897 ,(

cos 3o ,ZfoLos% = 2{0

&AeA$c,w A/.Ao,ro c4c&E^tf $ cer.sr.o

Itef * Irsl ; lr*x " rcgt,

%o

Sue Loyes

REVISIONBalanced resistive star and delta. Two wattmeter power measurement.

Use ABC rotation and Van reference

Wo =v*I ocos 4f wc =Vrrlrcos 4t:

A three phase, three wire, 100 volt, ABC system supplies a balanced delta-connected load with impedances ofZ - 2A/A" ohms. I)eterrnine the line cuffents, draw the phasor diagram and find the wattmeter readings when

the two-wattmeter method is applied to A and C ph?ses. Repeat for the load connected in star.

F,r b*hn,'& {oo,t:'{ iirl=s.l"t*1"#: "

! v^;j-;G luo.l ohr* Qas t sfANc€. Ldute,tr rrl PHA S €

ufti( Voffi66

{a 3 IAs*

{b : [gc-

{e: ft^F

= 8,6{ N: 8,66/:!*tuo: 8-6 6 ltf ?#"

f"of*efsc

plruse lv e(k 'r1'*g* f77f' line- t/^f lert ry ur

Z.,ggAufA:2ggL

4

fA 3 L'g9 /':W'[c = Z'g9&'o

V*s

Veil

Sue Loyes

vu

a {oo x 8"{#Y*3or 7fO bc,\rt& : loQxZ.g? lcos,30=TfC

\A/O= (oo x $.6{ bsSo = 7fC Lr/6= loo x]*,Wr&)sjo =ZfT

{aa

REVISIONBalanced inductive star and delta. Two wattmeter power measurement.

Use ABC rotation and Van reference

W A = VeuIA cos 4f Wc = Vrulc cos 47

A three phase, three wire, 100 volto ABC system supplies a balanced delta-connected load with impedances ofZ - 2A/90o ohms. Determine the line cuffents, draw the phasor diagram and find the wattmeter readings when

the two-wattmeter method is applied to A and C phases. Repeat for the load connected in star.

t{rtnl,n Wn'r WN 357'74N

6AA4trtEpt*eAeNs w&ngstr tf clas*o

hv

N g-olhp

s f7.Yfzo: p.#WA

h/* slgO lr ILo: r- f 44,s

lc

/ 1l*a!= l{u"|, t'{r*! r roe/zo : 5A

I f* I : tI*lt { f "ls ^ffi *{' P' 6{A

& *J.Es *f** : S/:b * Sfuh/A: IoO r 8.66Y c*s 1203-439

Wc: {CIp ,( 8'66rfCIs 6o : *493

\.\\\\ \{s tra *t Bc*.-

Jtus

I

t

7

.L

,8

lt&

t?Jtt;

2_,

lfA lr f [u

v*

We e. t## x 2. $S f *.dos 6O r el 4*+'3

{*\

'q."t\...^

'\4 \.=..,*\o*.

'\oo

zec fu&o

%*

foa

Sue Loyes

REVISIONBalanced inductive star and delta. Two waffmeter power measurement.

Use ABC rotation and Van reference

W A = VosIA cos 4f W, = VruI ,cos 4?

A three phase, three wire, 100 volt, ABC systern supplies a balanced delta-connected load with impedances ofZ - 2A/90o ohms. Determine the line currents, draw the phasor diagram and find the wattmeter readings when

the two-wattmeter method is applied to A and C phases, Repeat for the load connected in star.

Prre in/;{xs}an(e

A

loa"{ r* no pow(r tilf:Le^IT C-'44 S9y %oo

,/e ^t

lni

lc

ln

TA

16

-f-{G? LAq J-A+ -

F Tgt'f*0:B.6t *:2s8"66ffi

p A ? tt h M*,kJ, %,re, ff,Zv

l,'n, c.o(rfta/ ry, z.gg[n s 2-.89bY

] //

[o 3 2,ggffi; G2 gqL?o

-L C". eIL?Tcn*facs 8'{6m-

{s

t*a

f

U/A €

woz

*+t3+73

h/4

l,rt

l7a

6o

{r,rop x 8.t6 LoS lL? :

loo v g ${ cos 6o 5

Ysu

: tCIo>.L.89LotSue Loyes

4

: *{4-b.'{

: l- /+4.f

li,.e- c.ttr(€nf '#-$ s g.tiA

: {og *L.99 u5

REVISIONBalanced capacitive star and delta. Two wattmeter power measurement.

Use ABC rotation and Van reference

WA =VenIA cos 4f Wc =Vrulc cos 4':

A three phase, three wire, 100 volt, ABC system supplies a balanced delta-connected load with impedances ofZ * 2A/.- 90o ohms. Determine the line cuffents, draw the phasor diagram and find the wattmeter readings

when the two-wattmeter method is applied to A and C phases. Repeat for the load connected in star.

U- Etooffi ra

I {**tr 'l Lr*l'lL*{s 'oo/u = 5A

lf*l = lt6 l.lf. t= "ffi '(5 * 8'66A

IA: {.ag - f&i, = 5/&o *fb!74

)/* s toar S' 6fi.*'col 63 3 +4gg

Wc * i; "g:i{.*t t7'' 5 * +ag

&

W,nr W&" '57'74N

It*i"i[a] :/t. !a57,WA r to0 r2.98/ t cPs

Wg .,* too x7'e*y' x c.''5

6*t*NffioNo a$&.fi,E$r

hv

N

LEAPF euSEp

zA 2'o l;Pa

2.o [Po

s I.8874& l+4.3G !+4.3

lc

7hfzo

6o:t?_o x

'2o!;.9o

t-

REVISIONBalanced capacttive star and delta. Two wattmeter power measurement.

Use ABC rotation and Van reference

W A = Venlr cos 4f Wc = Vrulc cos 4':

A three phase, three wire, 100 volt, ABC system supplies a balanced delta-connected load with impedances ofZ - 20 /.- 90" ohms. Deterrnine the line cuffents, draw the phasor diagram and find the wattmeter readings

when the two-wattmeter method is applied to A and C phases. Repeat for the load connected in star.

pure Weoda,*\r*e_ a.v *fou'RJ LoP'||t qr*^pj

t r'l

t\-n

lc

lioe (,ocrs,.f XG i flo-t L ln rutu1/*Jv%5774g,6iA

T* = Iogt --f 6a,e-g

T =f"o"L

€' Ta^

* Tag

g.{ { [!a8.{( Eo

* rsr: 8'{6 ffo

If'.' u)rce,J y- g'I,a: Z-g,. m, ; = z'93

is = 2'ghnotL : L'99ffi

Vns

W^t

vro

{th

\A/A = toT t< 8.{6. US 6O: +33

vs

1^,h : t,O O x L.p/vdol 60 :

WL r {CIp x L-t?^ tu-I f?e:

Sue trynt,,*.

* l++. 5!* lq-+.r

\d1 z tos )r g -6tr ro! lb

REVISIONUnbalanced capacitive star and delta (f'wice capacitanqe in one leg)

Use ABC rotation and Van reference

W A = VesIA cos 4f Wc = Vrul rcos 47

A three phase, three wire, 100 volt, ABC system supplies an unbalanced delta-connected load with impedances

of Z = 20/.- 90" , Z - 20/.- 90o and /, r I0/.- 90o ohms. Determine the line culrents, draw the phasor

diagram and find the wattmeter readings when the two-wattmeter rnethod is applied to A and C phases. Repeat

for the load connected in star.

Wr z{oo#oln

dIL&c 'b

V+*, = ffre": tTT&&o

Al* %sfVu

zA &o AL9**o Eho

ZnsJ-.OA,Q

eLoSeo

N

zsc Lol;!o

= 5&oo

tool;Po: 5ehA a fO' , fe* Co$ f 3 f CIo x t3,2x co$ +9,f :8{+

r,n*r*g *f*h= f &e*rCIw: t3 'z &f, r?In

4tI oxaAravtEa

l+r.r,;za.wr iF

lc

,r_-I*QA -

m///

'ilLg *fg cn*{ag=€&'

'rb ? ttr *, s ' &'

T* = I-w*f*6g'; {0* s 58 * '3.

L t,z?J*

trr.F-*r.#r.tl

Lo/*o{oot*-a-<Pto lso

3lc

-7: 86+* 8{[

&'{Qor

$l.o,,l d b*

rtS{,3

&wu

r:&e

*Lg

*{bu

%'Sue Loyes

REVISIONUnbalanced capacitive star and delta (t'wice capacitance in one leg)

Use ABC rotation and Van reference

W A = Veull cos 4f Wc = VruI ,cos l?t

A three phase, three wire, 100 volt, ABC system supplies an unbalanced delta-connected load with impedances

of Z =20/.- 90" , Z -2A/.- 90" and Z =l0Z- 90o ohms. Determine the line cwrents, draw the phasor

diagram and find the waffmeter readings when the two-waffmeter method is applied to A and C phases..kp*ut

roritre loadconnectedin star' pvrL c4 ptud*of\re-,^.. t\a D a

NgEv ,\ ? A *'o^,Frn-(V(L \

f v-vv. . r\4(twq

lnAl*

&a flo2qo zobo

lru

{ea: Vas

d- f

7ae

.fsa = b ?

toc-$* A \/r"a !.Lca - fr;

3.3c9

.fJ-A *s S.i/*n*fi8"

dcA

6o *8

Sue Loyes

lc

le

=wrw=5&&e0 u&a,+

f4. tag -&dt rA6 ffi'*tu' &

,ro,* : Z.f Uffiotoo& 6 2 c- /z.a-e'-t-4"/LFkd,c

\t/*: (00 xRtr W : toa 'Jf"jc,cs {zy-}o} c 2{6,{

ioe Loftlo

/

Ut : lo0 x 13x LoSF5, * b); - u& WL,2 (00'{ Lfilrr${go+}^r}; -Zl {.{

REVISION' TWo wattmeter measurement of unbalanced resistor, inductor and capacitor delta load

Use ABC rotation and Van reference

W A = Venll cos 4f Wc = Vrul rcos 47

A three phase, three wire, 100 volt, ABC system supplies an unbalanced delta*connected load with impedances

of Z -20/0o, Z-2A/gA" and Z*20/.-90oohms. Determine the linecuffents, drawthephasordiagram

and find the wattmeter readings when the two-wattmeter method is applied to A aqd C phases.

f , !,y-?kz:, ; s&r* A Ag Lo*r {o,cry e Sl,!ryL6c= ffir :l lsotg = 5Neuh - ffio

B [a: IM* f cA 3 fiEo*5/*z+<tt80 - sEon)ka

b€

:. ftJLo a- r$c

Cl. ecbf,L-LA F

+-L&-tf-

J-g e

VUA g

l't/r *g.7 /I€g.7&.fl€ /3ooJ {,,+

efL6f

J-9"

{00 x 9.7* cos

loO xf x C{ts

: frg4.* r*a

= Iro -fo*

/5 r 93{.9

/5o a s l-33.eV{A + lnig

Ia

s 5o3.9UY/

'TfY'c;"l fr o rqr'$ f,n

7 -frA !he 6Ae*L fokterp=

!,

= 5Oo **&!

-f "1

,bC,

Sue Loyes

REVISIONTWo wattmeter measurement of unb aLanced resistor, inductor and capacitor delta load

Use ABC rotation and Van reference ^n o,"t poy* ot;sty*I& L€&,W o = V*I ocos 4f Wc = VrJ rcos 4'uc P: VTe- 3 ioo-/u =foD%*

A three phase, three wire, 100 volt, ABC system supplies an unbalanced delta*connected load with impedances

of Z=2020o, Z-2A/90" and Z-2AZ-90"ohms. Determinethe linecuffents, drawthephasordiagram

and find the wattmeter readings when the two-wattmeter method is applied to A and C phases.

fas * Tr-k : 5&O -* ; k-fu : {.83 -ii'.fi}'_9,t6ffi' /rr. f f /'

T&a r '.933 *JiJ.il 9'6{re-

{oe-fu r '2,:#^o ? ffr'Eaa Zo&'

fq*= Wg : tLrq', {&"hor* w ff2'

fu4: fu 7,M,g&Ve* 40H

{No=Lt1sS;f$.o

IA W : loo r 9.ttr tuS /{.AO)33

Zcn

T GJ-'gL

*,n*6#

.fGTL€

;NO It

5&w el

LoHo',

lT,T:-L$L J4+8

tro *tBL=

oZnc Zo&0

&

INC," Io o x

433

h-r lfU

tfrfu

F +33ft7?lJa,/

5coWe * V(LF

Sue Loyes

REVISIONTwo wattmeter rneasurement of unbalanced resistor, inductor and capacitor star load

Use ABC rotation and Van referense

t\lryt@:=venll cos 4r wc =v'ulc cos *r*n

n r{, A lwor$ ft...,..

Athreephase,@00vo1t,ABCsystemsupp1ieSanunba1ancedstar.connected1oadwithimpedanceSof Z = 2O/0o , /, - 20/90" and Z - 20/.- 90o ohms. Determine the line currents, draw the phasor diagram

and find the wattmeter readings when the two-wattmeter rnethod is applied to A and C phases.

&4g4**,*u&an

t?e*74W

f(*"-

I

Q:{M*r&o3 z.ffrc{

,+J-A&

fa*

loo ffiffia{do *a

SMQ< /*9oJ u'dd

?*s/,q"

WA * {col { ros: 433

lh{L: !oox2.{g:61

fyyLrc - {&kZ.e ffio

{s"1

t*s thCI -/E)

7r

7o/:?oo

trt G ffu" -f&a: tM

&ac-&eEn&q*r+t 3*

&ad i-o o &, + toatg +*ffir ?,effiO

4*sa j0- #1!2*fu&-'

e2-

he +W : 1E3 +67

: 5Oo wq/*(

Sue Loyes

Balnrro{ &//o /oor(

ABC rotationVan as reference

f , eV"LJab : dn-d' =

*

Tt a Vu*,J.OC ------q- -

&

.frn: WT

llo&, F o., /-6: /*a t--*.*#' ' 'z;i-i +zLL//0 /-2o p zL #fffi - cfzLffi

,

7 llogfo = zL reW ra.t ttgs.f zLM

vab = tro fro

f"A: 22HS

df-' *Ara,

= -f^t * [ra--: zl,zf j f, tv* - (5, 6%52 t,z)

= 26,9++ *j 2[-94+

r ZB.(oS Ufcf 39) &{ sue f-opes

fcocn '\

?LL

4.:lLM"'

Vbc rro't-ho

-[o

tI

Co ^f 6(c Yob tro & wi.l,t llo & ("lA 9O')

8a,/a,w(o(. s+er /oao(

2o Eo prr f i,ose BA|8;C rotation

Van as reference

tt

bd-vF =logp'&f

6&"6 t:6o

( rev'6lfu6&"6 gt*o

willL lt" l9o (sob 9o')

,W ,2oe &o

*e,

a

aa

at

: 2o8*a

Is* 6w

'bil

cn

cbvw4

."fI=J*h"

fb:

tLo / !,or-_r - n-,- rr.,,d

?s Eo" ,f Slrovo -f n+ fb* f c3 O = f,,

?.o /*" "fr ? lLo l,*lh" r*c ffi.{Gupc'.(e- U^ lk N

Sue f,opes