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"THE ESTABLISHEilLEADER IN EE REV' JEW" .11
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MUL TIVECTOR Review and Training Center. Rm. 867, Ground Floor, Isabel Bldg. F. Cayco corner Espafia Sts. Sampaloc, Manila Tel. No. 7317423
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MUL TIVECTOR
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~EVIEW
AND TRAINING CENTER
AC Circuits Part 2 Three Phase Circuits/ Systems
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Balanced 3$ Circuits/ Systems:
I.
I
Wye (Star) Connected System
7,\ I I I I I I I
I I
I I I I I
:v,
I
:vi .
I
•I I I
I I
I I I
:: . "'!v,
I 1 = I4>
~-X------~·~>~~--------------~--~ Relationships :
2.
Delta (Mesh) Connected System:
Relationships:
where: V~-phase voltage I~ -phase current v,.- line.voltagc I~_- line current
Power in Balanced 3$ Circuits/Systems
..
(Whether Wyc or. Delta connected) Pr
=
'>[3 Y1 11 (p.f.) = 3V~I~(p:f.)
=
3 1/R~ watts
Or= 13 Y1 It(r.f.) ~ 3 V4>14> (r.f.) = 3 I4> 2X4> vars Sr ·=
YJ
V~_I 1
=
3Y4>14> = 3I/Z4> = ~P/ + Or 2 va
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MUL TIVECTOR
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AND TRAINING CENTER
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Impedance Trian~)c:
Power Triangle:.
tl
r.I
il
i:
Sr
.JPr 2 + o/ va
=
From the above triangles: · p.f. •c
COS ()I ..
r,.
KW . R,
s,~
KV t\
z,
r.f. =sino,=. Or , KVAR =_& Sr KVA Z~ tan 0 1 ""
Or -_ KVAR __ - --
-
Pr
~ R~
KW
where:
r,- total real power drawn by the balanced 3cp load Or- total reactive power drawn by the balanced 3cp load S1 - total apparent power drawn by the balanc.cd 3 load 01 - power. factor angle of the ba'anccd 3cj> load
Phase Sequence-- the order in which the generated voltages in the phase windings of an alternator reach or attain their peak or maximum values. a.
Positive Phase Sequence ABC~
BCA
~CAB
AB- BC- (:A~ BC- CA- t\B AN- BN- CN
~
BN -
CN- AN
~CA--AB-BC
~
CN --AN- BN
Examples of Vector Representations
Vc =/Vel L-240"
V11
=
/Yn/ '
Vn -·/Vn/ .L-120"
Vc = IVc/.c-.120"
Sequence ABC
Sequence BCA
L-240"
I
Sequence CAB
MUL TIVECTOR REVIEW AND TRAINING CENTER b. ·Negative Phase Sequence ACB ,_
~
CBA
~
BAC
AB · CA ~-· BC ~ C!\- BC -1\B ~ i3C- AB-C!\ AN
CN
BN-tCN-BN-AN~BN--1\N-CN
Examples 0f Vecto)· Representations Vn = JVnJ L:-240"
JVnl /0''
Vn SeqtJCnce ACB
~·
JVnl L-120"
Sequence CBA
Sequence BAC
If the phase sequence is not given. assume a positive phase sequence. Three pha~c'·(3$) alternators arc designed to operate with positive phase sequence voltages.
Power Measurements in three Phase (3$) Systems. I.
2.
One-wattmeter Method- used to measure the total real power in a balanced three-phase system with a single wattmeter. Methods ~mployed: a. Potential.., lead shift Method b. Artificial- neutral Method c. T Method d. Current-transformer Method Two-wattmeter Method -·usually used.tomeasure the real power being drawn by a tfu·e~-phase (3$). 3-wire ry~rn. . Current Coil 1 II.
--~
Balanced. 3$ Source
II.:>
Balanced 3$ Load
Potential Coifz Current Coil 2 ,!,
·,1,,
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MUL TIVECTOR REVIEW AND TRAINING CENTER
~e'l'; . ~~~ loao . · -~
,'1
I
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Q 1 =·f3· (W 1 - \V 1 ),
9r""
V(\Vl-\VI),
o--.
' I ,tn.
where:
I
if W 1 > \V 2
·if\~/
YJ(W,-Wz) W I -1·\V 2 .
0 power factor of the balanced 3~ load P 1 total real ot' true power drawn by the balanced 3$ load <) 1 total reactive power drawn by the balanced 3~ load
Notes; I. '")
1\t 1\t /\t /\t
unity p. r.. the t\Vo wattmeters have equal reading. That is W 1 "' W2 0.866 p. f .. one wattmeter reading is f,wice the other. 0.5 p.f.. one wattmeter reads zero while the other registers tlie total circuit ppwer. less than 0.5 p.f, one wattmeter give~ a negative reading and the other positive. 1
Symmctl'ical Compcmcnts Fortescue's Theorem:!\ set ofnunbalanced related phasors may be resolved into n systcnjs of balanced phasors called the symmetrical components. · For thrcc-plidSC systen\s. a. b. c.
\v~
have:
positive sequel1ce component negative sequence component zero sequence component
For Voltages:
v, = v, 0 + v" 1 + v" 2 .
I
YAo
=J(v,,
. . VAl
=3 v,
Y,u
==-~{v,
J(
. .
+ Vu + Yc) +aVn +ll
2
') I
v(:
,I
where:
2
+:a V11 +aVe),
a I L 120° = -0.5 + j0.866. 2 a .' I L2400 "' .-O.S --j0.866 VA. Y11 , Yc =·unbalanced voltages Yo. V 1• Vi"" zero. positive and negative symmetrical components of voltage respectively
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MULTIVECTOR REVIEW AND TRAINING CENTER
For Currents: I I .\II = J
;,.._
•
2
lc ~' 1_, 11 .+ ai" +a f,u.
'
where:
(I \
1 (1 3
I
I B + I{ ) .
I ,1
:::
,
1
a I 11 + a 2 1c )
1. \2
= -~ (1 ,
t
a I 11
.
2
1
al < )
'-
I 1 , Ill. I< • unbalanced currents
· i., .. IJ. '-~
zero. posit_1ve and negative sym1netrical components of current respectively I:-; •· neutral current
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MUL TIVECTOR REVI'EW AND TRAINING CENTER AC CIRCUITS .
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PART 2- POLYPHASE SYSTEM . EXERCISES:
'1. In a balanced three-phase Y-connected system, the line voltage and the cJrresponding phase voltage are displaced from each other by i A oo . B. 30° C. 90° D. 120°
con~ected
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2. In balanced star (wye) system) the line voltage is . . ·: A 0. 707 times the phase voltage 1 B. 1.414 times the phase v~ltage C. phasor sum of two phase voltages D. phasor difference of two :phase vol-tages
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REE - May 2008 3. A three- phase system has line to line voltage Vab = 1,500 V rms with 30 ;deg angle with a wye load. Determine the phase voltage. · · A -433 + j750 V rms B. 750 + j433 V rms C. j866 V rms 0 866 V rms REE - Sept. 2007
4. The wye connected three-phase voltage source has V sub c = 115 v rms with -240 degrees angle. Find tt1e line to line voltage V sup be. A -99- j173 v rms . C. 0- j199 v rrns ·
B. 199 + jO v rms D. 99- j173 v rms
REE -April 2002 , 5. Three ·1 0-ohm resistors connected in wye are supplied from a balanced three phase source where phase ~·line voltage is given by 230 sin377t. What is the phase~ line current? A 13.28sin377t · B. 13.28 sin(377t- 30°) C. 23 sin (377t- 30°) D. 40 sin(377t + 30°) REE- May 2010 . 6. An ABC sequence set of voltages feeds ·a balanced three-phase, wye-wye system. The line and the load impedances are 1 + j1 0 and 10 + j 10 0, respectively. If the load voltage on phase A is Van = 110. v rms with 30 degrees. angle, determine the line voltage of the input for phases A and C. A.-j210vrms B. 105+j60.5vrms C. -105 + j60.5 v rms D. -210 v rms ; REE - April 2002 7. In a balanced three phase system, the phase A voltage is 132.8 cis 0°, what is the line to line voltage VcA? ·· A 230 cis 30°
B. 230 cis(- 30°)
C. 23o'cis(-60~)
D. 132.8 cis120°
8. Line B of a 230 V ungrounded-wye system touches the ground: What is the voltage between line A and the ground? A 230V B. 115V C. OV D. 132.79V 9. A system consist of three equal resistors connected in delta and is fed from a balanced three-phase supply. How much power is reduced if one of the resistors is disconnected? A 33% B. 50% C. 25% D. 0%
AC Circuits 2 Page 1 of 5
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MULTIVECTOR REVIEW AND TRAINING CENTER . ' AC CIRCUITS . . I
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REE - April 2005 . . . .·. ". ,1 0. Three heater !Jnits each taking 1,500 watts a11e connected delta to a 120 volt three phase line. What is " · ·the resistance of each unit in ohms? A 9.6 . B. 5.4 \ C. 8.6 D. 7.5
~ 1. The resistance ·
between i:my. two 'teamnals of a balanced delta-connected load is· 12 ohms. The · resistance of each phase is , A 12 ohms ·B. 18 ohms D. 36iohms C. 6 ohms i
REE- Sept. 2006 12. A three-phase balanced load has 10 ohms resistance in each of its. phases. The load is supplied by a 220 v, three-phase source. The load is connected in wye. What is the poweri absorbed by the load? A. 19.36 KW.:. B. 14.52 KW C. 9.68 KW D. 4.~4 KW . \ REE - March 1998 13. Three impedances,- j10, j10 and 100 are 'wye connected. Determine the' impedance of an equivalent delta. · A 12.5, j12.5, - 12.5 0 B. 10, j10,- j10 0 C. j8.5, j12.5, 8 0 D. 5, 5j, - j5 0 REE -Sept. 2005 ., . 14: A balanced wye-connected load has a ph.ase impedance of 15 + j10 ohms.·.What is the impedance per phase of the equivalent delta connected load? A 5 + j3.33 0 B. 26 + j17.32 0 ' C. 45 + j30 0 D. f.3.~6 + j5.77 0 J•:
. REE .,- Sept. 2009 . :~ 15. A balanced delta connected load of 15 + j 18 ohms per phase is connected ~t the end of a three-phase · line. The line impedance is 1 + j2 ohms per phase. The line is supplied fro~ a three-p~ase source with a line to line voltage of 207.~85 v mis. Using Van as reference, what is the current in pha~e A? ·.A -7.2- j9.6 A B. 7.2 + j9.6 A C. -7.2 + j9.6 A D. 7.2- j9.6 A I
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16. Three identical capacitances, each of 150 IJF are connected in star. The v~lue of capacitance in each ! ; phase of the equivalent delta connected load would be A 150 IJF B. 450 IJF C, 50 IJF D. 300 IJF 17. Three identical wye-connected resistances consume 1 ,000 watts. If the resistances are connected in delta across the same supply, the power consumed will be _ __ A 3,000 W B. 6,000 W C. 1,000 W D. 33~ W REE - Sept. 2004 • 18. A 480-volt three-phase system supplies 85 A 60° . B. 45°. REE - Sept. 2007 19. A balanced wye connected load of 8 Find the real power in KW? A 23 ·B. 13.8 ·~
. , power factor of 0.8. What is the power factor angle? C. 3r D. 15°
A at a
+j6 ohms per phase is connected to a three-phase 480-v system. C. 18.4
D. 10.6
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REE - Sept. 2007 20. A balanced three-phase, .wye-connected l.oad of 150 kw takes a le'ading current of 100 A, when the line 1 is 2,400 v, 60 HZ. What is the capacitance per phase? . A 21 mF :. B. 21 IJF . . C. 205 mF ., D. 205 IJF AC Circuits.2 Page 2 of 5
MUL TIVECTOR' REVIEW AND TRAINING CENTER
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AC CIRCUITS
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21. A 50-HP, three phase induction motor with full load efficiency of 85% ·and power factor of 0.80 is < connected to a three phase; 480 V system: The equivalent star connected impedance that can replace this motor is - - - - - '
B. 7.3L36.87° 0 D. 4.2L36.87° 0
A. 7.3L- 36.87° 0
C. 4.2L:... 36.87° 0
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REE - April 2004 . ( · 22.'1t is required tq increase th~ power factor of a 750 KW: three-phase balanced load from 70% lagging to 90% lagging. The line voltage is 6,900 volts, 60 Hz. Specify the capacitor required to increase the .power factor of this wye-connected load in microfarad per phase. A. 20.45 . . B. 22.39 C. 18.58 D. 17.22 REE - Sept. 2007 i 23. A balanced wye-connected load of 30 + j10 ohms per phase is connected to a 3-phase 60 HZ ?-08 volts supply. Determine th~ value of each capacitor in ~1F whicH will yield unity power factor. · A. 9.63 . B. 8.39 C. 9.28 . b. 8.84 24. Find the average power absorbed by a balanced three-phase load in arJ ~CB circuit in which one line
=
voltage is Vac 480L30,0 and one line current to the load is lb A.1337.W.. B. 1122W C. 1719W
=2.1L80° A. D. 1122W
REE - Sept. 2001 . <: 25. The phase B line voltage .and the phase A line current of a balanced three< phase systems are V =: 220 sin( rot + 21 0°) volts· and I 10 sin ((I) t + 180°) amperes, respectively. What is the power of the system? · A. 1,905W B. 3,300W C. 5,716W D. 3,810W
=
REE - May 2010 26. A balanced three-phase source serves three loads: Load 1: '24 KW, 0.6 lagging p.f. Load 2: 10 KW, unity p.f. Load 3: 14 KVA, 0.81eading p.f. If .the line voltage of the load is 208 rms at 60 Hz, find the line current. A. 143 A B. 139 A C. 141 A D. 137. A
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27. Two balanced loads are connected ln parallel to a three phase 460-volt sou~ce. Load A is 90 kVA at a power factor of 0.6 lagging and loadS is 25 ,kVAat unity power factor. What 1is the new power factor of the system? < . ; A. 0.741agging . 8. 0.74 leading : C. 0.80 lagging D. 0.80 leading i
Hz
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28. A three-phase, 440 V, 60 supply ·is con'nected to a three-phase, wye-cbnnected induction motor and synchronous motor. The impedance per phase of the induction motor is (1 .5 + j2.5)0. The synchronous motor is over-excited and draws 100 A at 0.8 power factor. What is the combined power factor ofthe load? · ; A. 0.99 lagging . 8: 0.991eading ,. C. 0.51 lagging D. 0.51 leading . REE - Sept. 2009 .· . · . ,1'l . 29. In two-wattmeter methbdofpower measurement, the readings of the two wattmeters were 6, 717 watts and 2,658 watts,· respeG,tively. Find the powerfactor. ·.' A o.9o · B. o.?o : c. 0.60 D. o.aq 1 ,\
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MULTIVECTOR REVIEW AND TRAINING. CENTER
AC CIRCUITS REE .:... April 2005 30. The total power consumed by a balanced 3 load is 3,000 watts at 80% pd,Wer factor. Two wattmeters WA a~W8 are connected to the line. What is the reading of W A? : A 2,150 watts B. 2,000 watts. C. 1,500 watts D. 2,500 watts
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REE- Sept:2004 . . . , : 31. The power drawn by a balanced 30 load is 3,000 watts at 80% power factot. If two wattmeters WA and We are used, what is the reading of We? · · ' t A 800 B. 950 C. 900 D. 850 REE - Sept. 2008 I 1 32. In a balanced three ..... phase 230 V circuit, the line current is 90 A The power is measured by two -wattmeter method. If the power factor is 100% and the line current is the same, what is the reading on each wattmeter? A 25.6 kW . B. 30.4 kW C. 17.9 kW D. 20.7 kW
33. The two-wattmeter.method ·is applied to a three phase, three-wire, 100 V, ABC system with the meters in lines B and C, W 8 ::::: 836 watts and We ::::: 224 watts. What is the impedance of the balanced delta connected load?· A 10L45° 0 B. 10L -45° 0 C. 20L -45° 0 D. 20 ...::::45° 0 {34. Two wattmeters are connected for the two,.:wattmeter method with current coils in lines A and B of a · 208 V, ABC circuit that has a balanced delta load. If the meter readings are 6 kW and - 3 kW,· respectively, find the load impedance per phase. A 18.8L -.35.2°0/phase B. 18.8L79.1°0/p.hase !
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D. 32.2L36.2° 0/phase REE - Sept. 2009. 35. A three-phase, W,e-connected system with 240-v per 'phase is connected to three loads: 10 ohms, 18.79 + j6.84 ohms, 9.83- j6.88 ohms to phases A,B, and C, respectively. Find the current in phase C. A 1.74 + j19.92A B. -1.74 + j19.92 A C. --1.74- j19.92 A D. 1.74- j19.92 A
4:_
36. Three impedances Zab ::::: j3 ohms, Zbc::::: 3 + j4 ohms and Zca ::::: 10 + jO ohms are connected in delta across a 220 volts, three phase balanced source. The total power qf the circuit is · A 1,839 8, 18,392 C. 1,936 D. 1,849
w
w
w
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37. A 480 V, three~phase, three-wire source supplies· to a combination of industrial loads. The line currents drawn from the source are: Ia =55.78L-59.4°A,Ib =43.85L176.7°A,Ic ~48.0L71.3°A. Determine the total power drawn from the source. A 17:31 kW B. 36.24 kW C. 3.1 kW D. 38.29 kW 38. A three-phase, four--wire system has the following, unbalanced loads: ·Za =i 10 + j1 00
I
Zb
=13--: j20;
Zc = 7.5 + j1 00. Determine the total power delivered to the load if the line voltage is 208 V. A 4.48 kW
8.1.48 kW
C. 2.49 kW
D. 2.90 kW
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MULTIVECTOR REVIEW AND TRAINING CENTER AC CIRCUITS '
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REE - April 2005 39. A 3-phase 4-wire system has the following unbalanced loads: Z 1 = 10.+ j5 0, Z 2 Z3
= 8 + j4 0, and
= 20 + jO 0. The line" to neutral voltage of the system is 120 volts. What is the reading of the
wattmeter in watts in Z3 ?; ..~
C. 1,000
8.720
D. 1,050
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REE - March 1998 40. The three unbalanced currents are: Ia 10 cis(- 30°), lb seque·nce of phase A current. A 8.66 cis 3oo'A B. 5.77 cis (-60") A C.- 5.77 A
=
=0,
lc ·= 10 cis 150°. Find the negative '
J
D. 5·.77 A
REE- Oct. 1998 41. The load of a wye connected transformer are: fa 10 cis( -30°), tb = 12 cis 215°. lc = 15 cis 82°. What is the neutral current? A. 1.04 cis 72.8° B. 0.92 cis 62.5° C. 2.21 cis (-30°) D. 3.11 cis 72.8°
=
REE - Sept. 2007 42. For the following phase currents Ia = 34.64, lb = -10- j17.32, lc = -10 + j17.32. What is the positive sequence for phase c? A. 12.44- j21.55 B. 12.44 + j21.55 C . .,-12.44 + j21.55 D. -12.44- j21.55 43. A wye-connected, three phase system has the following sequence components of current: i Zero sequence current= 12.5 cis 30° Positive sequence current= 28 cis(- 45°) Negative sequence current = 20 cis (-32°) Determine the current flowing in the neutral wire. D. 22.5 cis 1oo A. 4.17 cis 30° · B. 37.5 cis 30° C. 35.7 cis (-60°) I
REE -April 2007 : 44. Given the following sets of symmetrical components, determine the phase 'current for phase B. lao 1 at 75 deg 1a1 = 1 at 15 deg 1a 2 = 1 at -45 deg i A. 0.259 + j0.966 B. 0.516 -i- j1.931' C. 1.932 + j0.518 . D. 1.4'14 + j1.414
=
REE- Sept. 2002 45. 'The phase currents of a three-phase system are: lA= 100 Cis OoA. Is= 80 cis 240° A lc= 91.8 cis 130.9° A What is the zero sequence current? . A.OA B. 270.7 cis 3.68° A C. 34.68 cis(-30.2~ )A D. 90.23 cis 3.68° A l;i . 0
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. REE - Sept. 2010 · :i 46. One conductor of a three-phase line is open. The current flowing to the de)lta connected load through line A is 20 A. With the current flowing in line A as reference and assuming :that line C is open, what is the zero-sequence current of phase B? . A.j11.5A B.10+j5.78A C.O D.10l-j5.78A '
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MUL TIVECTOR REVIEW AND TRAINING CENTER AC CIRCUITS- PAHT II ; SUPPLEMENTARY PROBLEMS THREE PHASE SYSTEMS .
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1. When phase sequence of a three -phase sytem is reversed.----"--., A. phase currents change in anglenot in magnitude B. phase currents are changed C.~al power consumed is changed D. ph\e power are changed . •
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2. Determine the line voltage Vca if Vbn = 277.::80° and the phase sequence is 8AC:
A. 480L-10°V'·
8. 480L:10°V
C. 480/'170°V
D: 480;~-170°V
3. A balanced three-phase load Is· connected to 240 V. , three-phase source. Determine the
of
, impedance the wye-connected load if one phase current~~= 3.2L75° A. A 30.6- j30.6 n . 8. 30.6 + j 30.6 n c. 11.2 + j 41.8 n D. 111.2- j41.8
n
4. Three equal· impedances of (25 + j30)0 are connected in wye to 240i V, 60 Hz, three-pha?,e · source. Determine the value of the capacitor to be connected in parallel with the load so that the . total current drawn by the load is 3 amperes. · · A. 90 ~tF , B. 80 ~tF C. 70 pF D. 60 ~tF '
5. A delta-connected load draws 17.28 kW from 240 V, balanced three-phc;tse supply. What is th.e resistance of the load if the reactance Js equal to 5 ohms? . 1 A. 5 n 8. 7.5 n C. 10 n D .. 4.5 n 6. Three identical impedances of 15L60° ohms are connected in star to a Vhree-phase, three-wire, 240 V system. The lines between the supply and the load have an impedance 2 + j1 ohms. Find· the magnitude of the line voltage at the load. A. 123V 8. 240V · C. 416V D. 213Y '
. 7. A delta connected loadNwing an impedance of (300 + j210).n per phase is supplied from 480 V, three-phase supply through a line having an impedance of (4 + j8) 0 per~ wire. What is the total power supplied to th~ load? ' · '\ A. 1418 W B. 473 W C. 454 W D. ·J:\363 W 'J
REE- Oct. 1996 . j\ 8. A 132 kV line, three-phase system delivers 70.7 MVA of a balanced delta load of power factor · 70.7%. Determine the reactance necessary in order to attain unity power factor. A. 1,092 B. 965 1,142 D. 1,045
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9. A. certain lo~d takes 300 kW at 400 V. A three-phase capad'J.:tor bank·rate8 15 kVA per phase is connected in parallel with the load to raise the power factor of the load to 90% lagging. What is the power factor of the load before correction? A. 99% B. 92% .. C. 85% D. 88%
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MULTIVECTOR REVIEW AND TRAINING CENTER AC CIRCUITS- J>ART H .I 10. A factory load draws 100 kW at 75% lagging power factor from a 480 V source. To increase the power factor to 90% lagging, a synchronous motor operating at 80% leading power factor is connected to the load. What is the rating of the motor if it has an efficiency of 80%? . B. 43 HP C. 33 HP { D. 35 HP A 54 HP
~otor
11 ..A three-phase, wye-connected induction is cohnected.:to a 480 V, ithree-phase supply. It draws ~urrent of 15 amperes at 80% power factor. A delta connected reactance is connected in , parallel · ith the motor and the combination draws 15 amperes. ~hat is the ~alue of the element?
. . A.)
A ~tF . .
B. 122.5 ~\F
.
C. 28.7 ~tF
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.·
0. 245.0 ~tF.
12. A three-phase balanced load is connected across 220 V, three-phase, ACB source. A wattmeter · with its current coil in line A and voltt)ge coif across lines A and B reads 8QO W. The potential coil is then connected across lines A and C )Nith the current coil in the same line. What is the power .· . , factor of the load if the meter reads -800 W? A. 0.5 lagging B. 0.5 leading C. 0.87 lagging D.0:~'7 leading '
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13. In two-wattmeter method, the readings of the wattmeter will be identical wh¢n _ _ __ A. load in one of the two phases is zero: B. power factor is unity 1 C. power factor is 0.5 D. neutral is e~rthed ~ ' ~ '
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14. A wye-connected balanced three-phase load draws 75 A from:'~30 V, 60Hz, source. To measure the total power, two wattmeters are connected in lines A and e:·and reads S,625 Wand 17,250 W, respectively. Determine the impedance of the balanced .load. : ·t A. 3.07 .<-::30°0 .
B. 3.77 L-30°
n .
c.
1,77 L:30°
n
D.
!1 ;77 L:-30°
n
. 15. Two wattmeters are used to measure the power drawn by a balanced three·:·phase load from a440 V, three-phase source. The wattmeters are connected in lines A and Band reads 10 kW and -2.5 kW. When a capacitor is connected in parallel with thE;! load ahd the· wattmeters reconnected in lines B and C, the wattmeter in line B reads 7.5 kW. What is the power factor of the combined · ': load? A 33% B. 50% C . .28% D. 72% 16. The ra~io of the readings of wattmeters connected to measure the power delivered to an inductive load is 0.75. If the load draws 75 kVA from 440 V supply, determine·the impedance per phase of the delta-connected load.
A 7.74L:13~9°0
B. 7.74L:-13.9°
n
C. 2.58L:41.4°0
D. 2.58L-41.4°.0
'17. A balanc.ed three-phase, three-wire, 480 V supply has two loads. The first load is delta connected :' and takes 30 kW at 80% lagging power factor. The second load is delta connected and uses 24 kVA at 90% leading power factor. Find the readings of the two wattmeters connected in lines A ·· and C. . A. 28,940 & 22,660 W B. 20,400 & 31,:200 W C. 30,000 & 21;600 W D. 32,680 & 113,920W 18. A 25 HP induction motor is operating at rated load from. a thre~~phase 450 V, 60 Hz system. The efficiency and power factor of the motor are 87% and. 90% respectively. The apparent power in KVA drawn by the motor is _ __ A. 23.82 B. 27.78 C. 21.44 D. 19.30 )
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· 19. A three-phase, three-wire, 240 V CBA system supplies power to a w{e-connected load with impedances of: Za A. 1,553W
=Zb =25.c::90° n, Zc = 20,:~0° n. Find the total power. B. 2,589W
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C. 1,883W
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:' D. ~.·104W
20. A 100 \J, balanced three-phase source has two single phas'e loads; !The first load has an ip:1pedance of (5.+ jX) ohms and connected across lines A and B. The se:::qnd load is connected , Iacross 8 and C and ~as an impedance of (R - j2) ohms. Determine the v~lues of R and X, if the current in line 8 is 25.93L'-102.37° A and the ratio of X toR is 1.5. A. 2 n, 3 n B. 3 n. 4.5 n c. 4 n. 6 n
' · D. 5· n, 7.5
n
· 21. A 480 V, three-phase, three-wire, ACB :sequence source supplies power to a combination of single phase industrial loads. The line currents drawn from the source are: Ia = 35L' -42.5° A, lb = 60L' 165° A, lc = 48L'38° A. However.' it was found out that the instrument used in measuring the current in line 8 is defective: Whpt is the total power drawn from the source? A. 15,593 W B.· 9,180 W C. 16,728 W D. 24,000 W 22. Three- single phase loads are connected between lines of a 280 V, balanced three-phase source. The currents measured in lines 8 and Care: lb = 85.22 /-72 5° A, lc = 60.71./170° A. What is the negative sequence component of the currents? ·
A. 39.21L'105.2° A
8 .. 33:93L'161.6° A
C. 37.64,(-1045° A D. 41.82L'72.8° A
23. A balanced three-pha~e source with positive phase sequence has two single phase loads. Load 1 is a capacitive reactance of 10 ohms connected between lines A and C. Load 2 is an inductive resistor connected between lines 8 and C. Determine the impedance of the resistor so that the current in line js zero. A. 17.32 + j10 n a. 8.66 + j5 n C.10+j300 D.5+j150
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24. Three identical resistances connected in star carry a li,ne current of 12 A. If the same resistances are connected in delta across the same supply, what is the new value of the line current? A.12A . As. 4A C. 8A D. 36A 25. A three-phase induction motor delivers150 HP while, operating ·at 80% efficiency and a power factor of 0.8 lagging from 480 V lines. A wye connected power. factor correction capacitor is to be installed to improve the overall power factor to 0.9 lagging. deter11_1ine the:capacitance required per phase. ' I A. 428 1-JF B. 142.6 1-JF C. 1283 1-JF D. 3850 1-1F 26. A balanced star connected load is supplied from .a symmetrical three phase, 400 volts ABC system. The curre.nt in each phase is 30 amperes and lags 30°. behind the line voltage. What is the total power? A.18,000W. 8.10,393W C.20,785W D.31,177W 1
27. A balanced delta load with impedances of 15 - j9 ohms is connected to a three-phase source by ' three wires each of which has 2 + j5 ohms impedance. The load phase voltage is 120 V. Find the line voltage of the source. A. 69 V B. 208 V C. 150 V D. 87V
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28. Three equal impedances, each represented by a series RL circuit are connected to a three-phase source.- A total power of 7630 watts is measured by the two-wattmeter method. If one wattmeter gives zero deflection, determine the values of Rand XL for a line: voltage of 230 V. A. 3.2, 10 0 B. 5.2, 10 0 C. 3.2, 9 0 D. 5.2, 9 0 29. Floating neutral in a three-phase sum)ly; is undesirable because it will cause _ _ __ A. high voltage across the load B. unequal line voltage across the load C. lowvoltage across the load D. it h,as no effeCt on the load . REE- Oct. 1997 30. The sequence currents of a three phase current are: Zero sequence curr~nt 14.13 cis 17.34° Positive seq.· uence current= 708.26 ci.~ (- 31°) Negative sequence current= 2.98 cis.10.06° etermine the phase A current. A. 720 cis (-30°) B. 730 cis (-15.2 6 ) C. 710 cis 88°:
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31. A three-phase load is balanced if all the three phases have the same A. impedance · B. powerfactor C. impedance and power factor D. power
D. 695 cis 15.2° --,--r--
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32. A balanced delta COn~ected loads. draws 10 A of line current and 3 kW af 220 V. The reactance of each phase of the load is -----:---,-A. 38.1 0 . . B. 30 0 C. 23.5 0 D. 22 0 . REE- March 1998 33. The sequence com.ponents of phase A current are: Zero sequence current= 0.47 + j1.49 Positive sequence current = 18.4 cis (-31. 6°) Negative seql'lence current= 3.23 cis 168.2° Determine the phase C current. A.17.5cis91° B.18cis215° C. 22.5cis82o
D. 15 cis 100° I
REE - April 200.1 . 34. The three unbalanced currents are: 18 = 10 cis (-30°) 1 lb = 0, lc = 10 cis ~ 50°. Find the phase B positive sequence current. A. 8.66 A B. 5:77 cis 240° 'A · C. 5.77 A D. 8.'66 cis 120° . I
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35. Find the line voltage V0 b if vbn = 265.6L37° and the sequence is BCA. · A. 460L:-203°V · B. 460L:-;173°V . C. 460L:-83°V D. 4BOL:-53°V 36. The power flowing in a three-phase, three~wire balanced load system is measured by the twowattmeter method. The reading or, wattmeter A is 5 kW and on wattmeter B is -1 kW. If the voltage of the circuit is 440 V, 60 Hz, what ,is the value of the capacitance :that must be introduced into each phase to cause the whole power measured to appear on wattmeter A? A. 74:64 1-JF .B. 47.46 J..IF C. 64.47 1-JF D. 42.44~-JF .
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37. The phase sequence of a three-phase system is BCA.. The other possible phase sequence A. CBA
. 8 CAB
C.ACB
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c;i~n
be
D. none of these
38. Two-wattmeter r:nethod is applied to a three-phase motor running at full load. The two wattmeters indicate 85.5 kW and 34.7 kW, respectively. What is the operating power fa'ctor of the motor? A. 87.45% B. 80.69% ' C. 89.49% D. 94.76% 39. Three iri1pedances Za == 6,/20°0,Zb 8,.40°0.andZc 10/0°0 are con,nected in wye and are supplied by a 480 V balanced three phase source. The current in line b is _:_ __ . '\A. 46.19.!-50°A B. 33.11,~169.45''A C. 27.71.'90°A D: 43.2/~ ·90°A '
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RE~ - Sept. 2006 . 40. On~ conductor ofa three-phase line is ope'n. The current flowing to the /\~connected load through line·£ is 20 A. With the current in line£ as reference and assuming that lin;e g is open, what .is ~t;Je negative sequence qment of phase£? •\ ~ A. 10 + j5.78 B. 10- j5,78 C. j11.55 D. '".';i10 + j5.78 ·:1 .. .
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REE - Sept. 2008 it · 41 .. In a balanced three - phase wye - wye system; the source is an abc sequence set of;.voltages . · The load voltage on the phase A is Van= 110 V rms with 80 degrees ang:le. Znne = 1 + j1 (6hms · and Z1oad = 10 + j13 ohms. Determine the input sequence of the line tq neutral voltage V rms between phase B and neutral. · · · · ! · ··· A.-78.1-j41.9 B.93.4-j77.8 C.120.2-j20.7· D-i114.1-j41.9 REE - April 2005 42. The loads on a 230-volt three-phase generator consist of (a) three groupsi of incandescent lamps, each group containing twenty 100 watts lamps and (b) a 9 hp motor operating at 82 percent P.Ower . factor and 87 percent efficiency. Find the total load current in amperes. ' · A. 30 B. 37 C. 40 D. 45 REE - May 2009 .· 43. One conductor of a three-phase line is open. The current flowing to the delta conn~cted~ load through line A is 20 A. With the current in line A as reference and assuming that line C is.:'open, what is the positive sequence current of phase C? · ·· · A.10+j5.78 B.10-j5.78 C.-10-j11.56 D.j11.56
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