TEST 10 Three-Phase AC System: Part
A. 17.41 A B 17.95 A C 16.62 A D 18.46 A Problem 340:EE Board April
Three unequal single-phase loads so connected across the lines of a balanced, 3-phase, 230 volts circuit. The first takes 106 A at 0.78 pf lagging and is connected across lines 1 & 2. The second takes 142 A, at 0.82 pf
lagging and is connected across a lines 2 & 3. And the third takes 28.4 kW at 0.77 pf lagging and is connected across lines 3 & 1. find the three lines currents.
A. 254.40 A, 211.38 A, 252 A B. 231.26 A, 215.20 A, 268 A C. 254.40 A, 215.20 A, 252 A D. 231.26 A, 211.38 A, 268 A Problem 341:EE Board October 1992
A 120-V per phase, three-phase Y connected source deliveres power to the following delta-connected load: Phase 1 = 400 Phase 2 = 20- 60 Phase 3 = 1545
Determine the three line currents.
A. 12.45 A, 9 A, 22.45 A B. 13.49 A, 9 A, 22.45 A C. 13.49 A, 10 A, 20.22 A D. 12.45 A, 10 A, 20.22 A Problem 342:EE Board October 1985
Given:
Vab = 2400 V Zab = 6 + j8 ohms
Vbc = 240240 V Zbc = 5 + j8.66 ohms
Vca =240120 V Zca = 10 + j0 ohms
Solve for the three line currents la, lb and lc.
A. la = 45 a, lb = 43 A, lc =20 A B. la = 48 A, lb = 42 A, lc =24 A
C. la = 45 A, lb = 42 A, lc =20 A D. la = 48 A, lb = 43 A, lc = 24 A
Problem 343:EE Board April 1985
A three-phase 230-V circuit serves two single phase loads, A and B. Load A is an induction motor rated 8 hp, 230 v, 0.70 pf, 0.90 efficiency, which is connected across lines a and b. Load B draws 5 kW at 1.0 pf and is connected across lines b and c. Assume a sequence of a-b-c, solve for the line current on line b.
A. 42.19 A B. 27.74 A C. 41.08 A D. 34.46 A Problem 344:
A four wire 208-V three-phase 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 81 and 71 percent, respectively. Calculate the current in line c. Assume a phase sequence of a-b-c.
A. 71 A B. 75 A C. 64 A D. 69 A
Problem 345:EE Board April 1980
A factory is supplied by a three-phase, 3-wire system with the following characteristics: Vab = 2300 V la = 110 - 36.87 A
Vbc = 230240 V lc = 12553.13 A
Find line current lb.
A. 145.3 A B. 163.3 A C. 184.6 A D. 166.5 A Problem 346:
Given a balanced 3-wire, three-phase system serving an unbalanced wye- connected load. Determine the line current in line a.
Vab = 2100 V Zan = 10
Vbc = 210120 V Zbn =10 = j10
Vca = 210240 V Zcn = 10
A. 15 A B. 12 A C. 14 A D. 16 A
Problem 347:EE Board October 1994
Three resistors 10, 15 and 30 ohmic values are connected in wye-configuration to a balanced 208-volt three-phase supply. Calculate the total power of the system.
Problem 348:EE Board march 1998
Three impedances each 10 + j5 ohms are connected in delta on a balanced three-phase source. If the equation of the phase voltage is Van = 120 sin wt. What is the equation of the current through the impedance
connected across phase A and B?
A. 20.0 sin (wt -22) B. 18.59 sin (wt + 3.44) C. 16.21 sin (wt + 56.56) D. 21.32 sin (wt – 8.15) Problem 349:EE Board June 1990
Two parallel connected loads A and B are supplied by a 440 V, 3-phase, 60 Hz generator. Load A draws an apparent power of 100 kVA at 0.80 pf lagging and load B draws an apparent power of 70 kVA at unity pf.
Determine the feeder current.
A. 208 A B. 212 A C. 214 A D. 202 A
Problem 350:
Two different loads A and B are connected across a balanced 230 V, 3- lines. Load A is a three-phase load that draws 10 kVA at 70% lagging pf. Load B is a single-phase load connected across lines a and b drawing 5 kVA at unity pf. Determine line current in line a. Assume a phase sequence of a-b-c.
A. 37 A B. 42 A C. 31 A D. 46 A
Problem 351:EE Board April 1990
A three-phase motor takes 10 kVA at 0.6 pf lagging from a source of 230 volts. It is in parallel with a balanced delta load having 16 ohms resistance and 12 ohms capacitive reactance in series in each phase. Determine the total power factor.
A. 0.966 lagging B. 0.896 lagging C. 0.917 lagging D. 0.967 lagging Problem 352:
A balanced delta load whose impedance is 4570 ohms per branch, a three-phase motor that draws a total of 10 kVA at 0.65 pf lagging and a wye connected load whose impedance is 10 ohms (resistance) per branch are supplied from a three-phase, three-wire, 208 V, 60 Hz feeder. Determine the overall power factor of the feeder loads.
A. 0.753 B. 0.706 C. 0.826 D. 0.762
Problem 353: EE Board April 1985
A three- phase 230- V circuit serves two single phase loads, A and B. Load A is an induction motor rated 8 hp, 230 V, 0.70 pf, 0.90 efficiency, which is connected across lines a and b. Load B draws 5 kW at 1.0 pf and is connected across lines b and c. Assume a sequence of a-b-c, solve for the total power factor of the load.
A. 0.907 B. 0.704 C. 0.864 D. 0.886
Problem 354:
A 440- V three- phase, 3- wire wire, 60 Hz feeder supplies power to two 30- hp induction motors. One motor is operating at full load, 85% efficiency and has a power factor of 90%. The other motor is operating at one – half of its rated horsepower, 89% efficiency and has a power factor of 78%. What is the overall power factor of the system of motors?
A. 0.862 lagging B. 0.826 lagging C. 0.838 lagging D. 0.801 lagging Problem 355: EE Board April 1988
Three unequal single- phase loads so connected across the lines of a balanced, 3- phase, 230 volts circuit. The first takes 106 A at 0.78 pf lagging and is connected across lines 1 & 2. The second takes 142 A, at 0.82 pf lagging and is connected across lines 2 & 3. And the third takes 28.4 kW at 0.77 pf lagging. Determine the total apparent power.
A. 94 kVA B. 83 kVA
C. 78 kVA D. 101 kVA
Two-balanced Y- connected loads A and B are connected across a three- phase 3- wire balanced system. Load A draws 6 kW at 80% power factor lagging while load B draws 12 kW at 83.5% power factor leading. If the current in the three lines are each equal to 8 A, determine the current drawn by load A.
A. 4.45 A B. 3.58 A C. 4.15 A D. 3.28 A
Problem 357: EE Board March 1998
The phase B line voltage and the phase A line current of a balanced three- phase system are V= 220 sin (wt + 210o) and l = 10 sin (wt – 30o), respectively. What is the power of the system?
A. 1905 W B. 3300 W
C. 5716 W D. 3810 W
Problem 358: EE Board October 1986
The following information is given for a delta- connected load of three numerically equal impedances that differ in power factor: Line voltage = 120 volts; Zab = 1530o; Zbc = 150o; Zca = 15-30 phase sequence of
voltages is a-b-c. Using the phase sequence as a guide, calculate the total power drawn by the load.
A. 2,624 W B. 2,472 W
C. 2,654 W D. 2,731 W
Problem 359: EE Board April 1990
A three- phase motor takes 10 kVA at 0.6 pf lagging from a source of 230 volts. It is in parallel with a balanced delta load having 16 ohms resistance and 12 ohms capacitive reactance in series in each phase. Determine the total line current.
A. 30.05 A B. 34.55 A
C. 32.04 A D. 31.24 A
PROBLEM 360: EE BOARD APRIL 1993
In AC circuits, find the total power in kW in an unbalanced three- phase circuit loaded as follows: Phase l = 120 V, 100 A unity pf. Phase ll = 100 V, 230 A, 80 % pf and phase lll = 110 V, 85 A, 77 % pf.
A. 37.6 kW B. 35.3 kW
C. 32.8 kW D. 31.24 kW
Problem 361: EE Board April 1983
Two single- phase transformers are connected in V (open delta) and serving a delta connected impedance load, each impedance is equal to 1636.87o ohms. If the transformer voltages impressed on the impedances are:
Vab = 2400 o, Vab = 240240o, Vab = 240120o volts
Solve for the total kVA drawn by the load.
A. 6.23 B. 8.31 C. 10.8 D. 11.3
Problem 361: EE Board October 1980, EE Board October 1982
Three impedances, Zan = 20 + j0, Zbn = 16 + j12, Zcn = 5 – j15 ohms are connected in wye across a 230 V
(line to line), 3- phase, 4- wire source. The phase sequence is a-b-c, counterclockwise. Determine the current passing thru the neutral.
A. 7.54 A B. 9.12 A C. 8.81 A D. 8.02 A
Problem 363: EE Board April 1981
A wye- connected transformer with neutral connection has balanced voltages of 265 V between lines and neutral. The transformer is serving two single- phase motors. Motor A (rated 4 hp, 0.90 efficiency, 0.80 power factor lagging) is connected across line a and neutral. Motor B (rated 3 hp, 0.85 efficiency, 0.85 power factor, lagging) is connected across line b and neutral. Solve for the neutral current, using Van as reference vector.
A. 20.42 A B. 25.37 A
C. 22.45 A D. 23.14 A
Two single- phase motors are connected between the lines and neutral terminals of a 3- phase, 4- wire, 230 V secondary side of a three- phase transformer. Load A is connected across line a and neutral while B is across line b and neutral. The currents la and lb are 40 A, 0.707 pf lagging, and 25 A, unity pf, respectively. Determine the
neutral current , ln.
A. 54.25 A B. 50.34 A
C. 51.86 A D. 52.37 A
Problem 365:
Two single- phase motors are connected to a 3- phase, 4- wire wye feeder having 220 V between phase and the neutral. One motor rated 5 HP, 0.866 pf lagging and 90% eff is connected across phase A and neutral. The second motor is connected across phase C and neutral, and rated 3 HP, 0.707 pf lagging and 90% eff. Solve for current through the neutral.
A. 20.56 A B. 29.54 A C. 21.67 A D. 23.43 A
Problem 366:
A 230- V, three- phase, 4- wire balanced system supplies power to group of lamp loads. If the line currents are respectively 60 A, 86 A and 40 A respectively, solve for the current in the neutral wire. Assume the power factor of lamps to be unity.
A. 40 A B. 14 A C. 66 A D. 36 A
Problem 367: EE Board October 1998
The loads of a wye- connected transformer are: Ia = 10 cis (-30o)
Ib = 12 cis 215o
Ic = 15 cis 82o
What is the neutral current?
A. 1.04 cis 72.8o B. 2.21 cis (-30o)
C. 0.92 cis 62.5o D. 3.11 cis 72.8o
TEST 11 - Three-Phase AC System: Part II
Problem 368: EE Board April 1980
A factory is supplied by a three- phase, 3- wire system with the following characteristics:
Vab = 2300o V Ia = 110- 36.87 A
Vbc = 230240 V Ic =12553.13 A
Determine the total power consumed by the load.
A. 42.76 kW B. 48.78 kW C. 40.23 kW D. 45.12 kW Problem 369:
A 3-phase, 3 wire feeder has the following line currents and line voltages: Vab =2200 V Iaa = 30-j30 A
Vbc =220240 v Icc =29+j39.8 A
Determine the reactive power supplied by the feeder.
A. 7.75 kVAR B. 7.34 kVAR C. 8.32 kVAR D. 8.45 kVAR Problem 370:
Given a balanced three-phase system with the following loads: Vab =2300 V Zab = 60
Vbc =230120 V Zbc = 30+j50
Vca =230240 V Zca = -j80
Determine the reading of the two wattmeters properly connected using line c as the common point. A. 440.9 W, 907.5 W B. 394.1 W, 951.2 W
C. 440.9 W, 951.2 W D. 394.1 W, 907.5 W