1. A balanced three-phase Y-connected source
has, using a positive sequence Van = 390 Vrms at
30 degrees angle. Find Vab.
2. In a polyphase system, voltages Va =
120∠45oV and Vb = 10∠-15oV with respect to a
reference node o. Find voltage Vba in polar
form.
3. The terminals of a three-phase supply are
labelled a, b, c. Between any pair a voltmeter
measures 115 V. A resistor of 100 ohms and a
capacitor of 100 ohms at the frequency of the
supply are connected in series from a to b with
the resistor connected to a. The point of
connection of the elements to each other is
labelled in n. Determine the voltmeter reading
between c and n if phase sequence is a-c-b.
4. Three impedances of 4-j3 ohms are
connected in Y to a 208 V, three-phase line. Find
the complex power.
5. Three equal star connected circuit
components take 8kW at a power factor of 0.8
lagging when connected across 410V, 3 phase, 3
≤wire, 50 Hz. Find the inductance component
per phase of the load.
6. In a balanced three-phase system the Yconnected impedances are 10≤30 ohms. If Vbc
= 416∠90 volts, solve for Icn.
7. Three identical delta=connected load when
supplied from a 230 volts, 60 Hz, 3-phase, 3
wire supply draws a line current of 10 A at a pf
of 0.8 lagging. Determine the inductance of the
load per phase.
8. A balanced 3-phase load consumes a total
power of 100 kW at a power factor of 0.6
lagging, the line voltage being 1000V.
Determine the value of the reactive component
per phase assuming delta connection with
resistance and reactance in parallel.
9. Three delta connected resistors absorb 60kW
when connected to a 3-phase line. If the
resistors are connected in star, the power
absorbed is.
10. A balanced delta-connected load with
impedance Z= 30∠30 ohms per phase is
connected to a three-phase, three wire 250 V
system by conductors having an impedance of Z
=0.4 + j0.3 ohm per conductor. Obtain the line
to line voltage at the load.
11. A three-phase 120V circuit has a sequence
of abc and delivers power to a group of delta
connected impedances whose values are Zab=
10 + j0; Zbc = 5+j8.66 and Zca=8.66 +j5.
Determine the line current in line a. 12. A
balanced set of three-phase voltages is
connected to an unbalanced set of Y-connected
impedances. The following values are known:
Vab = 212∠90𝑉 ; 𝑉𝑏𝑐 = 212∠ − 150 𝑉; 𝑉𝑐𝑎 =
212∠ − 30 𝑉 ; 𝑍𝑎𝑛 = 10𝛺 ; 𝑍𝑏𝑛 = 10 +
𝑗10𝛺; Zcn = -j20Ω. Find the line current in line a.
13. A 3-phase, 4 wire, ABC system, with Vbc +
294.2∠0 , has the Y-connected impedances ,
Za= 12∠45 Ω, Zb=10∠30𝛺 , Zc= 8∠0 Ω. Obtain
the current in the neutral wire.
14. A balance delta connected load Z = 9∠ − 30
ohms and a balance wye connected load, with Z
= 5∠45 ohms, are supplied by the same ABC
system, with effective line voltage 480V. Solve
line current.
15. A balanced delta load consisting of pure
resistances of 15 ohms per phase is in parallel
with a balanced Y-load having phase
impedances of 8+j6 ohms. Identical impedances
of 2 + j5 ohms are in each of the three lines
connecting the combined loads to a 110-V three
phase supply. Find the line voltage at the
combined loads.
16. A 4-wire 208V, three=phase 60Hz system is
used to supply power to a three-phase 5 hp
induction motor and a single phase 6 kW heater
connected between line c and the neutral line.
The operating efficiency and power factor of
the motor are 82 and 71%, respectively.
Determine the current in line c.
17. Three equal impedances of (8 + j7) ohms are
connected in delta to lines a, b, and c of a 240 V,
3-phase, 3-wire line. What is the reading of a
single-phase wattmeter connected with its
current coil in line a and potential coil across
lines b and c? Assume and abc sequence.
18. A 3-phase, 3 wire load draws the following
line currents: Ia= 60 cis 330 A; Ib = 78.4cis 214
A; Ic = 75 cis 80 A. If the voltages impressed on
the load are balanced 3-phase, having a
magnitude of 4140 volts line to line, solve for
the total power in kW.
19. A balanced 3-phase load draws 75 amperes
line current at 230 volts line to line, and 0.848
lagging power factor. If the two-wattmeter
method is used, solve for the readings of the
wattmeters.
20. Two wattmeters in a three-phase, threewire system with effective line voltage of 120 V
read 1500 W and 500 W. What is the
impedance of the balanced delta connected
load?
21. A wattmeter is used to measure power
drawn by a 230V, 3-phase induction motor. The
current coil is placed in line 1 while the
potential coil is shifted from lines 1 and 2, then
from lines 1 and 3 respectively. If the wattmeter
registers 5760 and 3380 watts respectively,
what is the line current drawn by the motor?
22. A 3-phase, 50hp, 440V, 50 Hz induction
motor operates on full load with an efficiency of
89% and at a power factor of 0.85 lagging.
Calculate the total kVAR rating of a capacitor
bank required to raise the full load pf of 0.95
lagging.
23. Three loads are connected in parallel across
a 12.47 kV three-phase supply.
Load 1: Inductive 60kW and 660 kVAR
Load 2: Capacitive load, 240kW at 0.8pf
Load 3: Resistive load of 60kW
A Y-connected capacitor bank is connected in
parallel with the loads. What is the capacitance
per phase in uF to improve the overall pf to 0.8
lagging?
Constant Practice Makes You Perfect
1. On a 120/208-V four wire Y system, two
lamps are connected from phase A to neutral, 5
lamps from phase B to neutral and four lamps
have the same rating and each draws 2 A, find
the current in the neutral wire.
A. 0 A
B. 8.66 A
C. 6.93 A
D. 5.29 A
2. Two balanced three-phase loads are
connected in parallel. Load 1 draws 20 kW at a
lagging power factor of 0.85; Load 2 draws 15
kW at a lagging power factor of 0.5. The line
voltage at the terminals at the load is 440 V. The
load terminals are connected to the source
teminals by means of cables which have an
impendance of 1 +j3 ohms each. Calculate the
line voltage at the terminals of the source.
A. 795 V
C. 778 V
B. 805 V
D. 788 V
3. A three-phase, 339.4 V, ABC system has a
delta connected load with ZAB = 10∠0 Ω, ZBC
=10∠30Ω, and ZCA=15∠-30 ohms. Find the
current in line A.
A. 49.23 A
B. 64.18 A
C. 23.83 A
D. 54.72 A
4. A 440 V three-phase three-wire system feeds
two balanced Y-connected loads. One load is an
induction motor which maybe represented by
an impedance of 10 = j5 ohms per phase. The
other is a lighting load equivalent to 15 ohms
per phase. Find the total average power
A. 32.11kW
B. 25.52kW
C. 30.28kW
D. 28.37kW
5. A3-phase,50 hp, 440 V, 50 Hz induction
motor operates a full load with an efficiency of
89% and at a power factor of 0.85 lagging. A
capacitor bank is sonnected is parallel to raise
the full load pf to 0.95 lagging. What will bw the
capacitance per phase if the capacitors are
delta-connected?
A. 66.85 uF
B. 9.23 uF
C. 47.65 uF
D. 12.65 uF
6. In a balanced three-phase, 208 V circuit, the
line current is 100 A. The power is measured by
two wattmeter method. If the power factor is
unity, which one is a probable reading on one of
the wattmeters?
A. 20kW
B. 18kW
C.36kW
D. 24kW
7. A three-phase, four-wire 150-V, CBA system
has a Y-connected load, with ZA=6∠0 Ω, ZB=
6∠30Ω and Zc= 5∠45Ω. Solve the current in the
neutral wire.
A. 10.21 A
B. 15.82 A
C. 19.89 A
D. 21.12 A
8. A three-phase, three-wire 500V, 60 Hz source
supplies a three-phase inductor motor, a wye
connected capacitor bank that draws 2 kVAR
per phase, and a balanced three-phase heater
that draws a total of 10 kW. The induction
motor is operating at its rated 75 hp and has an
efficiency and power of 90.5 and 89.5 percent,
respectively. Determine the system complex
power.
A. 75.89 + j24.81
B. 71.82 + j24.81
C. 75.98 – j24.81
D. 71.82 – j24.81
9. Three 50- ohm resistor are connected in star
across 400V, 3-phase supply. If one of the
resistor is disconnected, then the line current
will be ___.
A. 8 A
B. 13.85 A
C. 4 A
D. 0
10. A 400-V, 3-phase, 4-wire service mains
supplies a star connected load. The resistance
of each line is 0.1 ohm and that of the neutral
0.2 ohm. The load impedances are Z1= (6 +j9)
ohms; Z2= 8 OHMS; Z3= (6-j8) ohms. Calculate
the current in the neutral.
A. 56.22 A
B. 50.06 A
C. 45.18 A
D. 49.35 A
11. Three identical loads having an impedance
of (8.66 +j5) ohms are connected in wye across
a balanced three-phase system with
consequence set with Vab =(300 + j0) volts. If a
wattmeter is connected in the circuit with its
current coil on line A and potential coil across
lines A and C, determine the meter reading.
A. 5.196 kW
B. 5.264 kW
C. 5.342 kW
D. 5.428kW
12. A three-phase, 3-wire balanced delta
connected load yields wattmeter readings of
1154 W and 557 W. Obtain the load resistance
per phase if the line voltage is 100 V.
A. 18Ω
B. 12Ω
C. 10Ω
D. 13Ω
13. A factory is supplied at 11 kV, 50 Hz system
and has the following balanced loads: Load A:
1.5 MW at 90% lagging pf; Load B: 600 kW at
100% pf; Load C: 2 MVA at 98% lagging pf; Load
D: 3 MVA at 805 lagging pf. A 3-phase and of
star connected capacitors is connected at the
supply terminals to give power factor
correction. Find the required capacitance per
phase to given an overall power factor of 98%
lagging when factory is operating at maximum
load.
14. Three impedances of 3 + j4, ohms are
connected in delta to a 220-V three-phase line.
Find the complex power
A. 6.92 + j5.19 kVA
B. 6.92 +j5.19 kVA
C. 17.4 + j23.2 kVA
D. 17.4 – j23.2 kVA
15. A three-phase, three-wire system, with a
line voltage Vbc= 339.4∠0 volts, has a balanced
Y-connected load of ZY= 15∠60 ohms. The lines
between the system and the load have
impedances 2.24∠26.57 ohms. Find the line
voltage magnitude at the load.
A. 301.1 V
B. 308.5 V
C. 310.4 V
D. 316.2 V
16. A three-phase 120-V circuit has a sequence
of abc and delivers power to a group of delta
connected impedances whose values are Zab=
10 +j0; Zbc= 5 +j8.66 and Zca= 8.66 +j5.
Determine the line current in line b.
A. 17 A
B. 20 A
C. 24 A
D.12 A
17. Three equal impedances (60 + j30) ohms are
connected in delta at the end of a three-phase
transmission line which has an impedances of (1
+ j2) ohms per conductor. If the line voltage at
the generating station is maintained at 2300 V,
find line to line voltage at the load.
A. 2150 V
B. 2122 V
C. 2142 V
D. 2126 V
18. A delta connected load with 50-Ω
resistance, 209-Mh inductance and 50-Uf
capacitance in series per phase is supplied at
500 rad/sec. With Vcn=390 cis 30 deg as
reference, what is the phase C line current?
A. 13.27 –j5.42 A
B. 12.52 –j5.42 A
C. 13.27 –j 4.28 A
D. 12.52 –j4.28 A
19. The pf of each phase of balanced wyeconnected 5 ohm impedance is 0.6 lagging. This
impedance is connected to a source having a
100-V phase voltage. Determine the apparent
power drawn by the circuit.
A. 6.0 kVA
B. 3.6 kVA
D. 5.4 kVA
A. 42.9 uF
B. 53.6 uF
C. 4.8 kVA
C. 33.7 uF
D. 38.3 uF
20. A 3-phase, 40 Kw, 440 V, 60 Hz induction
motor operates at full load with an efficiency of
90 % at 0.80 lagging pf. It is required to raise the
full load power factor to 0.90 lagging. A threephase bank capacitors are connected across the
load. What will be the capacitance per phase if
the capacitors are delta-connected?
A. 54 uF
B. 39 uF
C. 49 uF
D. 11 uF
21. The phase a line voltage and the phase b
line current of a balanced three-phase system
are: V=220sin (wt-30) volts and I=10 sin (wt150) amps respectively. What is the impedance
per phase?
A. 33- j 19.1 Ω
B. 24- j 10Ω
C. 20 –J 14.5 Ω
D. 34- J 15.2Ω
22. A balanced three phase Y-connected source
has using positive phase sequence,
Van=390∠30 V. Determine Vac.
A. 675∠0 V
B. 675∠120 V
C. 675∠-60 V
D. 675∠180 V
23. A balanced delta connected load of 15 + j18
ohms per phase is connected at the end of a
three phase line. The line impedance is 1 +j2
ohms per phase. The line is supplied from a
three-phase source with a line to line voltage of
207.85 V rms. Taking Van as reference,
determine the magnitude of the line to line
voltage at the load terminals.
A. 162.32 V
B. 166.18 V
C. 168.56 V
D. 164.75 V
24. Three similar resistors are connected in star
across a 400-V, 3-phase lines. The line current is
10 A. To what value should the line voltage be
changed to obtain the same line current with
the resistors delta-connected?
A. 230.94 V
B.133.36 V
C. 115.22 V
D. 76.98 V
25. A balanced delta connected load contains 8+
j4 ohms per phase, while a balanced wye
connected load consist of 2-j1 ohms per phase.
Both loads are connected in parallel to a threephase three-wire system in which the line
voltage is 120 V rms at the loads. The three line
extending from the loads to the source each
have a resistance of 0.2 ohm. Determine the
power lost in the wires.
A. 1.42kW
B. 1.38 kW
C. 1.24kW
D.1.83kW
26. The power input to a 2000 V,50 Hz, 3-phase
motor running on full load at an efficiency of
90% is measured by two wattmeters which
indicates 300 kw and 100kw respectively.
Calculate the line current of the motor.
A. 137.4 A
B. 169.6 A
C. 152.7 A
D. 115.5 A
27. The phase c voltage and phase a current of a
balanced three-phase system are: V=200 sin
(wt+90) volts and I=10 sin wt-45). Dtermine the
total reactive power of the system.
A. 1553 VARS
B. 1672 VARS
C. 1245 VARS
D. 1842 VARS
28. A 500 kVA transformer is at full load and
0.60 lagging pf. A capacitor bank is added
improving the power factor to 0.90 lagging.
After improvement, what percent of rated kVA
is the transformer carrying?
A. 66.7%
B. 57.7%
C.86.6%
D.63.6%
29. A wye-connected-load and a delta
connected load are supplied by a four-wire 400
V three-phase, 50 Hz system. The connection
for the wye loads are 2/20Ω at line a, 30∠50Ω
to line c and 6∠75Ω to line b. The connections
for the delta load are 50∠30Ω between lines a
and b, 25∠-60Ω between lines b and c, and
17.3∠90Ω betweenlines a and c. Find the
current on line b.
A. 41.64 A
B.26.26 A
C. 38.53 A
D. 31.38 A
30. A wattmeter reads 5,540 W when the
current coil is connected in phase a and the
voltage coil is connected between the neutral
and phase a of a balanced 3-phase system
supplying a balanced load of 30 A at 400 V.
What will be the reading of the instrument if
the connections to the current coil remain
unchanged and the voltage coil is connected
between phase b and c? Take a-b-c phase
sequence.
A. 7200 W
B. 8600 W
C. 6800 W
D. 4500 W
31. Three condensers each having a capacity of
75 uF are connected in star to a 400 volts,
three-phase, 50 cycle supply. Calculate the
capacitance of each of the three condensers so
that when they are connected in delta to the
same supply, the line current will remain the
same.
A. 25uf uF
C. 100 uF
B. 150 uF
D. 225 uF
32. At what power factor will the reading on
one of the wattmeters in a two-wattmeter
method be zero?
A. 0.866
C. 0.707
B. 0.5
D. unity
33. Three identical resistors are connected in
wye across a balanced 3-phase source. If one of
the resistors is open, the total power drawn by
the remaining two resistors is?
A. increased by 50%
B. increased by 25%
C. reduced by 50%
D. reduced by 25%
34. The two-wattmeter method is used in
measuring power taken by a balanced delta
connected load. The wattmeters read 1500 W
and 500 W, respectively. If the line voltage is
120V, determine the magnitude of the
impedance per phase.
A. 24.25 ohms
B. 16.33 ohms
C. 28.20 ohms
D. 9.76 ohms
35. A balanced delta connected load consisting
of a pure resistance of 18 ohms per phase is in
parallel with a purely resistive balanced Yconnected load of 12 ohms per phase. The
combination is connected to a 3-phase balanced
supply of 346.41 V (line to line) via 3-phase line
having an inductive reactance of j3 ohms per
phase. Determine the total complex power
drawn from the supply.
A. 19.2 –j14.4 KVA
B. 19.2 +j14.4 KVA
C. 24.2-j12.8KVA
D. 24.2 –j12.8 KVA
36. A balanced three-phase three wire system
supplies two balanced Y-connected loads. The
first draws 6kW at 0.08 pf lagging while the
second requires 12kW at 0.833 pf leading. If the
current in each line is 8A, find the current in
second load.
A. 3.27 A
B. 4.12 A
C. 6.29 A
D. 5.58 A
37. A 2300 V, three phase system supplies a
120-kW, 0.6 pf lagging 3-phase balanced load.
Determine the capacitance in each phase of a Yconnected capacitor bank to adjust the power
factor to 0.90 lagging.
A. 45 uF
B. 51 uF
C. 58 uF
D. 54 uF
38. A star-connected balanced load is supplied
from a 416 V 50Hz, three phase balanced
system. Each phase of load consists of a
resistance and a capacitor joined in series. The
readings of two wattmeters connected to
measure the total power supplied are 782 W
and 1980 W, both positive. Calculate the
capacitance of each capacitor.
A. 98.42 uF
B. 106.10uF
C. 79.57 uF
D. 88.42 uF
39. Two wattmeters are used to measure the
total power drawn by a balanced delta
connected load. If the wattmeters read 1200 W
and 800 W respectively, and the line to line
voltage is 208 V, solve for the resistance per
phase of the load.
A. 51.31 ohms
B. 31.72 ohms
C. 57.94 ohms
D. 20.07 ohms
40. The load on a three phase wye connected
220 V system consist of three 6 ohms
resistances connected in wye and in parallel
with three 9 ohm resistances connected in
delta. Determine the magnitude of the line
current.
A. 62. 8 A
B. 68.7 A
C. 70.2 A
D. 63.5 A
41. A 3-phase, 30wire balanced Y-load takes a
line current of of 30 A at 0.7 pf lagging. Line
voltage is 400 V. A single phase wattmeter is
connected in the circuit with its current coil in
line 1 while its potential coil in lines 2 and 3.
Determine the reading of the wattmeter.
A. 8400 W
B. 9699W
C. 8569 W
None of these
42. A balanced delta load consisting of pure
resistances of 15 ohms per phase is in parallel
with a balanced Y-load having phase
impedances of 8 +j6 ohms. Identical
impedances of 2 + j5 ohms are in each of the
three lines connecting the combined loads to a
110-V three phase supply. Find the current
drawn from the supply.
48. Three 40 Ω non-inductive resistances are
connected in star across a 200-V, 3 phase lines.
Calculate the power taken from the mains.
A. 4000 W
B. 2000 W
C. 1000 W
D. 3000 W
A. 10.52 A
B. 8.05 A
49. Three impedances 3 + j4 , ohms are
connected in delta to a 220V three phase line.
Find the complex power.
C. 9.62 A
D. 11.18 A
A. 6.92 + j5.19 kVA
B. 6.92 - j5.19 kVA
C. 17.4 + j23.2 kVA
D. 17.4 - j23.2 kVA
43. A three-phase, 4 wire star connected system
with 230-V between each phase and neutral has
resistances of 4, 5 and 6 ohms respectively in
the three phases, Estimate the current in the
neutral.
A. 16.7 A
B. 19.3 A
50. A 440 V, three phase source supplies a wye
connected 10 kVA load at 0.8 lagging power
factor and a delta connected 10 kVA unity pf
load. Calculate the total apparent power input
to the two loads.
C. 12.5 A
D. None of these
A. 18.97 kVA
B. 22.84 kVA
C. 20.56 kVA
D. 26.19 kVA
44. A three phase ABC system, with Vbc =
294.2∠0 , has the delta connected load,
Zab=5∠0 ohms, Zbc = 4∠30 ohms, Zca= 6∠15ohms. Obtain the current in line A.
A. 127.9∠-43.3 A
B. 103.2∠56.4 A
C. 77.1∠-172.1 A
D. 99.7∠99.7 A
45. Solve the total power factor of the following
parallel connected loads; Load 1, 5 kW, pf=0.8
lagging; load 2, 4 kVA, 2 kVAR(capacitive); load
3, 6kVA, Pf = 0.9lagging.
A. 0.954 lagging
B. 0.977 leading
C. 0.954 leading
D. 0.977 lagging
46. The following load impedances are
connected delta across a 220 V balanced abc
system: Zab= 10∠36.87 ohms; Zbc =10∠0 ohms,
Zca= 10∠45 ohms. Find the reading of a kW
meter connected with its current coil connected
in line b while the potential coil connected
across lines b and c.
A. 5.12 kW
B. 4.08kW
C. 4.26 kW
D. 5.45 kW
47. The total power absorbed by a certain 3phase balanced load is 60kW, the reactive
power being 10kVAR. Determine the reading on
one of the two wattmeters properly connected
to measure the total power.
A. 1642.3 W
B. 1573.2 W
C. 1132.5 W
D. 1262.8 W
51. A balanced wye connected load and a
balanced delta connected load are supplies by a
3 phase 480 V, 50 Hz generator. The branch
impedances of the wye and delta loads are
10<30 ohms and 20<-50 ohms respectively.
Determine the complex equivalent of the total
power drawn.
A. 42.16- j14.95 kVA
B. 22.21 –j11.52 kVA
C. 42. 16-j11.52 kVA
D. 22.21 –j14.95 kVA
52. Three loads are connected in parallel across
a 12.47 kV three-phase supply
Load 1: Inductive load, 60kW and 660 kVAR
Load 2. Capacitive load, 240 kW at 0.8 pf
Load 3: Resistive load of 60kW
Find the total power factor.
A. 0.866
C. 0.77
B. 0.60
D. 0.65
53. A three-phase, 60 Hz, 2200 volts induction
motor delivers 500 hp, 0.8 lagging pf and
efficient of 94%. The power factor is raised to
0.90 lagging by connecting a bank of condensers
in delta across the lines. If each of the
capacitance unit is built up of four similar 550 V,
solve the required capacitance of each
condenser.
A. 56 uF
C. 81 uF
B. 77 uF
D. 60 uF
54. Three identical impedances are connected
in delta to a three-phase supply to 400 V. The
line current is 34.65 A and the total power
taken from the supply is 14.4 kW. Calculate the
reactance of each impedance.
A. 12Ω
B. 10Ω
C. 16Ω
D. 14Ω
55. A balanced wye connected source, Van =
200∠0 volts rms is connected by four perfect
conductors to an unbalanced Y-connected load,
Zan = 8 + j6 ohms, Zbn = j20 and Zcn = 10Ω. Find
the neutral current.
A. 2.66 – j10.32 A
C. 2.42 – j12.20 A
B. 3.01 – j11.22 A
D. -1.53 – j5.96 A
56. Given the magnitude of the line to line
voltages of a 3-phase system, Vab = 200V; Vbc =
346 V; Vca= 400 V. If the phase sequence is abbc-ca, with Vab= 200∠0 volts, Vbc is equal to
____.
A. 346<-60
C. 346<-90
B. 346<-150
D. 346<-120
57. A resistor of 300 ohms and a capacitor of 8
uF are connected in series across the lines A and
B of a voltage between the junction of the
resistor and capacitor and line C. Assume: VAB =
400∠0 V; VBC = 40∠-120 V; VCA = 400∠120 V.
A. 548 V
C. 542 V
B. 536 V
D. 539 V
58. A three phase Y connected system with 20 V
per phase is connected to three loads: 10 ohms,
20∠20 ohms, and 12∠-35 to phase 1, 2 and 3,
respectively. Find the current in the neutral line.
A. 19.2 A
C. 18.8 A
B. 22.9 A
D. 24.1 A
59. A 400-V 3-phase motor having full load
output of 20hp at 0.88 efficiency and 0.80
power factor. Find the readings of the two
wattmeters connected to measure the input.
A. 14.25kW, 2.704kW
C. 12.15kW, 4.806kW
B. 10.50kW, 6.454 kW
D. 8.75kW, 8.204 kW
60. Three delta-connected impedances, Z2 =
15∠38.9 ohms are connected across a 230-volts
3-phase balanced system through a line
impedance of ZL = 1∠60 ohms. Determine the
line to line voltage at load terminals.
A. 194 V
C. 202 V
B. 197 V
D. 209 V
61. A 230-V, three-phase, three-wire feeder is
serving two different loads; The first is a threephase motor load drawing 10kVA at 0.70 pf. The
second load is a 5kW heater load connected
across lines 2 and 3. Determine the current in
line 3.
A. 21.7 A
C. 46.4 A
B. 50.6 A
D. 25.1 A
62. A three-phase induction motor is drawing
10 A when a single-phasing takes place. The
current drawn by the motor is ___
A. 5(sq rt of 2)
C. 10( sq rt of 2)
B. 10(sq rt of 3)
D. 5 (sq rt of 3)
63. The power to a balanced three-phase
system is measured by the two wattmeter
method. One wattmeter reads 1986 watts, and
the reading of the other is 2517 watts.
Determine the line current if the line voltage is
208 volts.
A. 11.34 A
C. 12.76 A
B. 10.45 A
D. 15.22 A
64. Each phase of a star-connected load consist
of a non-reactive resistance of 100 ohms in
parallel with a capacitor of capacitance 31.8 uF.
Determine the total kVA when connected to a
416-V 3-phase, 50 Hz supply.
A. 2.45
C. 1.73
B.3.39
D. 2.67
65. A balanced three phase wye connected load
150 kW takes a leading current of 100 A, when
the line is 2400 V, 60 Hz. What is the
capacitance per phase?
A. 100 uF
C. 150 uF
B. 303 uF
D. 205 uF
66. A balanced delta connected load of 15 + j18
ohms per phase is connected at the end of a
three phase line. The line impedance is 1 + j2
ohms per phase. The line is supplied from a
three phase source with a line to line voltage of
207.85 V. Determine the line current
A. 16 A
C. 12 A
B. 14 A
D. 18 A
67. A balanced delta connected load with
impedance 10∠-36.9 ohms , and a balanced Y-
connected load are supplied by the same three
phase ABC system having Vca= 141.4∠240 V. If
the current in line B is 40.44∠13.41 A, what are
the impedance of the Y connected load?
A. 5∠-60 ohms
B. 5∠-53.3 ohms
C. 4∠-30 ohms
D. 4∠-66.7 ohms
68. A 3-phase, induction motor is connected
across a 220-V, 3-phase source. A wattmeter
reads 600 W when its current coil is connected
in line 1 and its potential coil across line 1 and 2.
If the potential coil of the wattmeter is
transferred to lines 2 and 3, the reading of the
wattmeter is the same. Calculate the current
drawn by motor.
A. 5.45 A
C. 3.56 A
B. 4.32 A
D. 6.81 A
69. A 230-V balanced three-phase source is
supplying a parallel combination of Y-connected
load and a delta connected load. if the Y and
delta loads are balanced with phase
impedances of 8 – j8 ohms and 24 + j24 ohms
respectively, find the total line current.
A. 16.6 A
C. 17.5 A
B. 15.8 A
D. 18.5 A
70. A balanced, 3-phase, star connected load of
150 kW takes a lagging current of 100 A with a
line voltage of 1100 V, 60 Hz. Find the reactance
of the load per phase.
A. 5.1 ohms
C, 3.3 ohms
B. 3.9 ohms
D. 2.8 ohms
71.A 3-phase, 2200 V, wye connected power
system with grounded neutral supplies energy
to a 3-phase Y connected impedances, Zao =
10∠0 ohms, Zbo = 10∠0 ohms, and Zco = 10 + j10
ohms, with point O as common point of the Y
connected impedances. Calculate the potential
difference between point O and the system
ground. Assume point O is not grounded and an
a-b-c phase sequence, with Vab as reference.
A. 1100 V
C. 439 V
B. 220 V
D. 352 V
72. The load connected to a e-phase supply
comprises three similar coils connected in star.
The line currents are 25 A and the kVA and kW
are 20 and 11 respectively. Determine the
reactance of the coil.
A. 10.67 ohms B. 9.12 ohms
C. 8.91 ohms D. 5.87 ohms
73. The terminals of a three phase supply are
labelled a, b and c. Between any pair a
voltmeter measures 115 V. A resistor of 100
ohms and a capacitor of 100 ohms at the
frequency of the supply are connected in series
from a to b with the resistor connected to a.
The point of connection of the elements to each
other is labelled n. Determine the voltmeter
reading between c and n if phase sequence is
abc.
A. 148.4 V
C. 161.2 V
B. 153.3 V
D. 157.1 V
74. Three parallel three-phase loads are
supplied from a 207.85 V rms, 60 Hz threephase supply. The loads are as follows: Load 1;
A 15 hp motor operating at full load, 93.25%
efficiency and 0.6 lagging power factor; Load 2:
A balanced resistive load that draws a total of 6
kW; Load 3: A Y-connected capacitor bank with
a total rating of 16kVAR. What is the total
supply current?
A. 50 A
C. 46 A
B. 54 A
D. 60 A
75. A balanced three-phase, three wire abc
system has delta-connected load with a 50
ohms resistor, a 5 uF capacitor, and a 0.56 H
inductor in series in each phase. Using positive
phase sequence with Van = 390∠30 V rms and
w= 500 rad/s, find the current in line b.
A. 9∠97.4 A
B.9∠-22.6 A
C. 9∠-142.6 A D. 9∠127.4 A
76. A certain load takes 40 kVA at 50% lagging
pf while another load connected to the same
source takes 80 kVA at 86.7% lagging pf. Find
the total kVA
A. 89.36
C. 120
B. 116.5
D. 74.68
77. Three identical loads having an impedance
of 10 cis 30 ohms are connected in wye across a
balanced three phase system with sequence set
with Vab = 300 cis 0 volts. If a wattmeter is
connected in the circuit with its current coil on
line B and potential coil across lines B and C,
determine the meter reading
A. 2.946 kW
C. 2.248 kW
B. 2.204 kW
D. 2.598 kW
78. A three-phase line has an impedance of 0.4
+ j2.7 ohms per phase. The line feeds two
balanced three-phase loads that are connected
in parallel. The first load is absorbing 560.1 kVA
at 0.707 pf lagging. The second load absorbs
123 kW at unity pf. The line to line voltage at
the load end of the line is 3810.5 V. Determine
the magnitude of the line voltage at the source
end of the line.
A. 4160 V
C. 6600 V
B. 4670 V
D. 5440 V
79. Three wye-connected impedance of ( 3 + j5 )
ohms per phase are connected across a
balanced three-phase source of 100V per phase
through a line impedance of ( 1 + j1 )ohm.
Determine the magnitude of the line current.
A. 16.31 A
C. 13.86 A
B. 12.45 A
D. 17.15 A
80. Three 100 uF capacitors are connected in
mesh to a 500 V three phase 50 cps supply.
What will be the values of each of three
capacitors such that when connected in star
across the same supply, the line current will be
the same?
A. 300 uF
C. 33.33 uF
B. 150 uF
D. 173.2 uF
81. In a balanced three-phase circuit, two loads
are connected in parallel. Load 1 draws 80 kW
and 60 leading kVAR. Load 2 draws 120 kW and
160 lagging kVAR. The line voltage of the system
is 1000 volts. Find the line current at the
generator terminals.
A. 115 A
C. 129 A
B. 156 A
D. 172 A
82. Determine the operating power factor of a
three phase balanced load if the reading of the
two wattmeters properly connected to measure
power is 3:1.
A. 0.756
C. 0.671
B. 0.863
D. 0.707
83. A balanced wye connected source, Van = 200
cis 0 V is connected by four perfect conductors
to and unbalanced Y-connected load, Zan =
10ohms, Zbn = 10 cis(-30) ohms and Zcn = 28.28
cis 75 ohms. Determine the power absorbed by
the load.
A. 7.42 kW
C. 6.34 kW
B. 8.04 kW
D. 7.83 kW
84. Three identical star connected resistors are
connected across a three-phase, 400 V mains.
The circuit draws a total power of 690 W,
determine the resistance of each resistor.
A. 230 ohms
C. 696 ohms
B. 120 ohms
D. 76.66 ohms
85. Two wattmeters in a three phase, three wire
system with effective line voltage of 120 V reads
1500 W and 500 W. What is the impedance of
the balanced delta-connected load?
A. 18.7∠30
C. 17.8∠30
B. 13.6∠40.9
D. 16.3∠40.9
86. A three-phase delta connected load consists
of 10∠45 ohms impedance. The load is
connected across a 200-V three-phase source. If
the power input to the load is measured by two
wattmeters, find the reading of each
wattmeter.
A. 6425.6 W; 2058.4 W B. 6691.2 W, 1792.8 W
C. 5925.2 W; 2558.8 W D. 6188 .6 W, 2295.4 W
87. A 3-phase motor takes 10 kVA at 0.6 pf
lagging from a source of 220 V. It is parallel with
a balanced delta connected having a 16 ohms
resistance and –j12 reactance in series in each
phase. Find the line current of the combination.
A. 32.43 A
C. 36.78 A
B. 42.11 A
D. 47.21 A
88. A balanced 3-phase star connected load of
150 kW takes a leading current of 100 A with a
line voltage of 1100 V, 50 Hz. Find the circuit
resistance of the load per phase.
A. 10 ohms
C. 12 ohms
B. 5 ohms
D. 8 ohms
89.In an unbalanced 3-phase wye system, the
phase voltages are Vna = 132 cis 0; Vnb = 130
cis 235; and Vnc = 133 cis 117. Determine the
line to line voltage Vac?
A. 225.95 cis 148.37
C. 228.32 cis 125.46
B. 220.15 cis 134.42
D. 292.18 cis 130.85
90. Determine the total complex power of the
following parallel connected loads; Load 1, 200
VA, pf =o.7 lagging; Load 2, 350 VA, pf = 0.5
lagging; Load 3, 275 VA, pf = 1.
A. 590 +j444, VA
C. 560 + j450 VA
B. 550 + j480 VA
D. 580 + j500 VA
91. It is required to raise the power factor of a
750 kW balanced three phase load from 70 %
lagging to 90 % lagging. The line voltage is 6900
volts, 60 cycles. Specify the capacitor require for
wye-connected bank in microfarads per phase.
A. 22.4 uF
C. 20.6 uF
B. 28.3 uF
D. 23.7 uF
92.A wattmeter has its current coil connected in
line 1 while its potential coils is connected
across line 2 and 3. If the wattmeter reads 1000
W, the total reactive power of the load is ___
A. 1000 VAR
C. 1732 VAR
B. 2000 VAR
D. 0 VAR
93. A three-phase line has an impedance of 2 +
j4 ohms. The line feeds two balanced threephase loads that are connected in parallel. The
first load is Y- connected and has an impedance
of 30 + j40 ohms per phase. The second load is
delta connected and has an impedance of 60 –
j45 ohms per phase. The line is energized at the
sending end from a three phase balanced
supply of line voltage 207.85 V. Determine the
line to line voltage at combined loads.
A, 193. 64 A
C. 172.42 A
B. 120.42 A
D. 168.25 A
94. A 3-phase power supply to a factory has the
following voltages and current measurements:
Vab = 240 cis 0 V; Vbc = 240 cis 240 V; Vca= 240
c9s 120 V; Ia=120 cis 330 A; Ib= 157 cis 214 A; Ic =
150 cis 80 A. Solve for the total power.
A. 50.5 kW
C. 55.3 kW
B. 52.7 kW
D. 58.8 kW
SOLUTIONS:
𝐼𝑐𝑛
1.
𝐼𝑐𝑛
416
(
) ∠ − 60
√3
=
10∠30
= −𝑗24 𝐴
7. 𝐼𝑝 =
10
= 5.77 𝐴
√3
−1 (0.8)
𝜃 = 𝑐𝑜𝑠
𝜃 = 36.87 𝑍𝑝 =
𝑉𝑎𝑏 = √3(390)∠60
𝑉𝑎𝑏 = 675.5∠60
3. KVL at Loop x:
𝑉𝑏𝑐 + 𝑉𝑐𝑛 + 𝑉𝑛𝑏 = 0
𝑉𝑐𝑛 = −𝑉𝑏𝑐 − 𝑉𝑛𝑏
𝑉𝑐𝑛 = 𝑉𝑐𝑏 − 𝑉𝑛𝑏
𝑉𝑛𝑏 = 𝐼𝑎𝑏 𝑋𝑐
𝑉𝑎𝑏
115∠0
𝐼𝑎𝑏 =
=
𝑍
100 − 𝑗100
𝐼𝑎𝑏 = 0.813∠ 45
4. 𝑆𝑇 = 3𝑉𝑝 𝐼𝑝
208
𝑉𝑝 =
= 120 𝑉
√3
𝑉𝑝 120∠0
𝐼𝑝 =
=
= 19.2 + 𝑗14.4 𝐴
𝑍𝑝 4 − 𝑗3
𝑆𝑇 = 3(120)(19.2 − 𝑗14.4)
= 6912 − 𝑗5184 𝑘𝑉𝐴
5. Y-connection
𝑃𝑡 = 3𝑉𝑝 𝐼𝑝 (𝑝𝑓)
𝜃 = 𝑐𝑜𝑠 −1 (0.8)
𝐼𝑝 = 14.08 𝐴
410
𝑉𝑝
√3
𝑍𝑝 = =
𝐼𝑝 (14.08∠ − 36.87)
𝑍𝑝 = 13.45 + 𝑗10.09Ω
𝑋 = 2𝜋𝑓𝐿
10.09 = 2𝜋(50)𝐿
𝐿 = 32.11 𝑚𝐻
6. 𝑉𝑎𝑛 = 𝑉𝑏𝑛 = 𝑉𝑐𝑛
𝑉𝑐𝑛
𝐼𝑐𝑛 =
𝑍𝑛
=
230∠0
5.77∠−36.87
= 31.89 +
𝑋 = 2𝜋𝑓𝐿 = 63.43 𝑚𝐻
𝑉𝑝
230∠0
=
= 31.89 + 𝑗23.92 Ω
𝐼𝑝 5.77∠ − 36.87
𝑋 = 2𝜋𝑓𝐿 = 63.43 𝑚𝐻
𝑍𝑝 =
8. 𝑃 = 3𝑉𝑝 𝐼𝑝 𝑐𝑜𝑠𝜃
100000 = 3(1000)𝐼𝑝 (0.6)
𝐼𝑝 = 50.55 𝐴
𝐼𝑝 = 55.55∠ − 𝑐𝑜𝑠 −1 (𝑜. 6)
𝐼𝑝 = 33.33 − 𝑗44.44 𝐴
𝑉𝑝 1000
𝑋= =
= 22.5Ω
𝐼𝑥 44.44
9. Δ − 3𝑌
𝑍Δ = 3𝑍𝑦
𝐼Δ = 3𝐼𝑦
𝑃Δ = 3𝑃𝑦
A – C – B sequence
𝑉𝑐𝑛 = 115∠ − 60 (0.813∠45)(−𝑗100)
𝑉𝑐𝑛 = 42.105∠ − 89.983
𝑉𝑐𝑛 = 42.1 𝑉 𝑖𝑓 (𝑎 − 𝑐 − 𝑏)
𝑉𝑐𝑛 = 157.1 𝑖𝑓 (𝑎 − 𝑏 − 𝑐)
410
) 1𝑝(0.8)
√3
𝐼𝑝
𝑗23.92 Ω
2. Reference at node O
Va = Vao
Vb = Vbo
loop: Vao + Vab + Vba = 0
Vba = -Vao – Vob
Vba = -Vao + Vbo
𝑉𝑏𝑎 = −(120∠45) + (100∠ − 45)
𝑉𝑏𝑎 = 111.35 ∠ − 83.95
5000 = 3 (
𝑉𝑝
𝜃 = 36.87
60 = 3𝑃𝑦
𝑃𝑦 = 20𝑘𝑊
10. Δ − 𝑦
𝑍Δ
𝑍𝑦 =
3
30∠30
𝑍𝑦 =
3
𝑍𝑦 = 10∠30 Ω
𝑉𝑝 =
250
= 144.337 𝑣𝑜𝑙𝑡𝑠
√3
𝑢𝑠𝑖𝑛𝑔 𝑉𝐷𝑇:
(144.337)(10∠30)
𝑉𝑅𝑃 =
(0.4 + 𝑗0.3) + (10∠30)
= 137.57∠ − 0.3265
𝑉𝑅𝐿𝐶 = √3(𝑉𝑅𝑃 )
𝑉𝑅−𝐿𝐿 = 238.174𝑉
11. @ 𝑋: (𝐾𝐶𝐿)
𝐼𝑎 + 𝐼𝑐𝑎 = 𝐼𝑎𝑏
𝐼𝑎 = 𝐼𝑎𝑏 − 𝐼𝑐𝑎
𝑉𝑎𝑏 𝑉𝑐𝑎
𝐼𝑎 =
−
𝑍𝑎𝑏 𝑍𝑐𝑎
120∠0 120∠120
𝐼𝑎 =
−
10
8.66 + 𝑗5
𝐼𝑎 = 16.97∠ − 45
|𝐼𝑎 | = 17 𝐴
12.
𝑉𝑎𝑏 = 212∠90 𝑉
𝑍𝑎𝑛 = 10Ω
𝑉𝑏𝑐 = 212∠ − 150 𝑉 𝑍𝑏𝑛 = 10 + 𝑗10Ω
𝑉𝑐𝑎 = 212∠ − 30𝑉
𝑍𝑐𝑛 = −𝑗120 Ω
𝑍𝑎𝑏 =
𝑍𝑎 𝑍𝑏 + 𝑍𝑏 𝑍𝑐 + 𝑍𝑐 𝑍𝑎
𝑍𝑐
𝑍𝑎𝑏
10(10 + 𝑗10) + (10 + 𝑗10)(−𝑗20) + (−𝑗20)(10)
=
−𝑗20
300 − 𝑗300
𝑍𝑎𝑏 =
−𝑗20
𝑍𝑎𝑏 = 15 + 𝑗15 Ω
300 − 𝑗300
𝑍𝑐𝑎 =
10 + 𝑗10
𝑍𝑐𝑎 = −𝑗30Ω
𝐼𝑎𝑏 = 𝐼𝑎𝑏 − 𝐼𝑐𝑎
𝑉𝑎𝑏 𝑉𝑎𝑐
𝐼𝑎 =
−
𝑍𝑎𝑏 𝑍𝑐𝑎
212∠90 𝑉 212∠ − 30𝑉
𝐼𝑎 =
−
15 + 𝑗15Ω
−𝑗30Ω
𝐼𝑎 = 3.658∠15
|𝐼𝑎 | = 3.66 𝐴
13. 𝑉𝑏𝑐 = 294.2∠0
𝑍𝑎 = 12∠45𝛺
𝑍𝑏 = 10∠30𝛺
𝑍𝑐 = 8∠0𝛺
𝐼𝑛 = 𝐼𝑎 + 𝐼𝑏 + 𝐼𝑐
𝑉𝑎𝑛 𝑉𝑏𝑛 𝑉𝑐𝑛
+
+
𝑍𝑎𝑛 𝑍𝑏𝑛 𝑍𝑐𝑛
169.85∠90 169.85∠ − 30
+
12∠45
10∠30
169.85∠ − 30
+
8∠0
𝐼𝑛 = 15.317 𝐴
𝐼𝑛 =
14. ∆ = 𝑌
𝑍∆
𝑍𝑦 =
3
9∠ − 30
𝑍𝑦 =
3
𝑍𝑦 = 3∠ − 30
(3∠ − 30)(5∠45)
(3∠ − 30) + (5∠45)
𝑍𝑇 = 2317 − 𝑗0.136Ω
𝑉𝑝
𝐼𝐿 = 𝐼𝑃 =
𝑍𝑝
480
(
)
√3
2.317 − 𝑗0.136
𝐼𝐿 = 𝐼𝑝 = 119.34∠3.36
|𝐼𝐶 | = |𝐼𝑝 | = 119.34 𝐴
𝑍𝑇 =
15. 𝑍𝑦 =
𝑍∆
3
=
15
3
= 5𝛺
5(8 + 𝑗6)
𝑍𝑝 = (2 + 𝑗5) + [
]
5(8 + 𝑗6)
𝑍𝑝 = 5.414 + 𝑗5.73 Ω
110
𝑉𝑝
√3
𝐼𝑝 =
=
= 8.055 ∠ − 46.63 𝐴
𝑍𝑝 5.414 + 𝑗5.73
𝑉𝑝 − 𝐼𝑝 𝑍𝐿 − 𝑉𝐿 = 0
110
𝑉𝑙𝑜𝑎𝑑 =
− (8.055∠ − 46.63(2 + 𝑗5))
√3
𝑉𝑙𝑜𝑎𝑑 = 28.285∠ − 34.05
𝑉𝑙𝑜𝑎𝑑 𝐿−𝐿 = √3(28.285)
𝑉𝑙𝑜𝑎𝑑 = 49 𝑉
16. 𝐼𝑐 = 𝐼ℎ + 𝐼𝑐𝑛
𝑃𝑜𝑢𝑡
𝐼𝑚 =
√3𝑉𝐿 𝑝𝑓𝑛
5(746)
𝐼𝑚 =
√3(208)(0.71)(81%)
𝐼𝑚 = 𝐼𝑐𝑛 = 18 𝐴
𝜃 = 𝑐𝑜𝑠 −1 (0.71)
𝜃=44.765
𝑃𝑛
6000
𝐼𝑛 =
=
= 49.96 𝐴
𝑉𝑝 (208
⁄ )
√3
𝐼𝑐 = 49.96∠120 + 18∠(120 − 44.77)
𝐼𝑐 = 64∠108.57
|𝐼𝑐 |= 64 A
17. 𝐼𝑎 = 𝐼𝑎𝑏 − 𝐼𝑐𝑎
𝑉𝑎𝑏 𝑉𝑐𝑎 240∠0 240∠120
𝐼𝑎 =
−
=
−
𝑍𝑎𝑏 𝑍𝑐𝑎 8 + 𝑗7
8 + 𝑗7
𝐼𝑎 = 39.105 ∠ − 71.186 𝐴
𝑊 = 𝑉𝑏𝑐 𝐼𝑎 𝑐𝑜𝑠𝜃
𝑊 = 240(39.105[cos 120 − 71.86])
𝑊 = 6180 𝑤𝑎𝑡𝑡𝑠
18. 𝑊1 = 𝑉𝑎𝑐 𝐼𝑎 𝑐𝑜𝑠𝜃
𝑊1 = (4140)(60)[(cos(30))]
𝑊1 = 215.12 𝑘𝑊
𝑊2 = 𝑉𝑏𝑐 𝐼𝑏 𝑐𝑜𝑠𝜃
𝑊2 = (4140)(78.4)[cos[(240) − (214)]]
𝑊2 = 291.73 𝑘𝑊
𝑊𝑇 = 𝑊1 + 𝑊2 = 215.12 + 291.73
𝑊𝑇 = 506.85 𝑘𝑊
19. 3∅
𝐼 = 75 𝐴 @ 230 𝑉
𝜃 = 𝑐𝑜𝑠 −1 (0.848)
𝜃 = 32
0. .848 𝑙𝑎𝑔
𝑊1 = 𝑉𝐿 𝐼𝐿 cos(30 − 𝜃)
𝑊1 = (230)(75) cos(30 − 32)
𝑊1 = 17239 𝑘𝑊
1500−500
20.𝜃 = 𝑡𝑎𝑛−1 √3 [1500+500]
𝜃 = 40.893
𝑝𝑓 = cos(40.843)
𝑝𝑓 = 0.866
𝑃𝑧 = 3𝑉𝑝 𝐼𝑝 (𝑝𝑓)
1500 + 500 = 3(180)𝐼𝑝 (0.866)
𝐼𝑝 = 7.35 𝐴
𝑉𝑝
120∠0
𝑍𝑝 = =
𝐼𝑝 7.35∠40.893
𝑍𝑝 = 12.341 + 𝑗10.688 𝛺
1
2𝜋(60)(740.48)
C = 3.58uF
C=
1.
21.
𝐼𝑛 = 𝐼𝑎𝑛 + 𝐼𝑏𝑛 + 𝐼𝑐𝑛
𝑊1𝑠𝑡 = 5760 𝑤
𝑊2𝑛𝑑 = 3380 𝑤
𝑊1 𝑊2
]
𝑊1 + 𝑊2
5760 − 3380
𝜃 = tan−1 √3 [
]
5760 + 3380
𝜃 = 24.276
𝑝𝑓 = cos 𝜃
𝑝𝑓 = 0.912
𝑃
3780 + 3380
𝐼=
=
√3𝑉𝐿 𝑝𝑓 √3(230)(0.912)
𝐼 = 25.168 𝐴𝑚𝑝
𝜃 = tan−1 √3 [
= 4∠0 + 10∠ − 120 + 8∠120
𝐼𝑛 = 5.291∠ − 160.89°
|𝐼𝑛 | = 5.29 A
2.
𝑆𝑡 = 𝑆1 + 𝑆2
20
15
=(
) ∠ cos −1 0.85 + ( ) ∠ cos−1 0.5
0.85
0.5
𝑆𝑡 = 51.94∠47.634°, kVA → lagging
𝑆𝑡
51,940
𝐼𝑡 =
=
= 68.153 A
√3𝑉𝐿 √3(440)
𝑉𝑆 = 𝑉𝑃 + 𝐼𝑡 𝑍𝑙𝑖𝑛𝑒
22.
𝑆𝑇 = 𝑆1 + 𝑄𝐶
𝑄𝐶 = 𝑆𝑇 − 𝑆1
𝑃𝑜𝑢𝑡𝑝𝑢𝑡 50(0.746)
𝑃𝑖𝑛 =
=
= 41.91 kw
𝜂
0.89
41.91
𝑄𝐶 = (
∠ cos−1 0.95)
0.95
−(
∠ cos −1 0.85)
𝑄𝐶 = j12.198 Kvar
=
440
∠0 +
√3𝑉𝐿
(68.153∠ − 47.634)(1 + j3)
V
phase
𝑉𝑆 = √3(459.42) = 795.738 V, line to line
𝑉𝑆 = 459.42∠10.97°,
3.
𝐼𝑎 = 𝐼𝑎𝑏 − 𝐼𝑐𝑎
𝑉𝑎𝑏 𝑉𝑐𝑎 339.4∠0 339.4∠120
=
−
=
−
𝑍𝑎𝑏 𝑍𝑐𝑎
10∠0
15∠ − 30
𝐼𝑎 = 54.72∠ − 11.93°
|𝐼𝑎 | = 54.72 A
23.
𝑆𝐿 = 𝑆1 + 𝑆2 + 𝑆3
240
𝑆𝐿 = (60 + 𝐽660) + (
∠ − cos−1 0.8) + 60
0.8
𝑆𝐿 = 360 + j480 kVA
𝑄𝐶 = 𝑆𝑇 − 𝑆𝐿
360
𝑄𝐶 = [
∠36.87] − [360 + 𝑗480]
0.8
𝑄𝐶 = −j210 kVAR
210 70KVAR
𝑄𝐶 =
=
3
PHASE
𝑉𝑃2
𝑋𝐶 =
𝑄𝐶
12470
(
)
√3
𝑋𝐶 =
70 𝐾𝑉𝐴𝑅
𝑋𝐶 = 740.48
1
C=
2𝜋𝑓𝑋𝐶
4.
𝑉𝑃 =
440
= 254 V
√3
𝐼𝐿 = 𝐼1 + 𝐼 2
254∠0 254∠0
+
= 38.619∠ − 15.255 A
10 + 𝑗5
15
𝑆𝑡 = √3𝑉𝐿 𝐼𝐿 ∗= √3(440∠0)(38.619∠15.255)
𝑆𝑡 = 28.394 + j7.744, kVA
|𝑃𝑡| = 28.394 kW
𝐼𝐿 =