SINGLE PHASE SYSTEM - SUPPLEMENTARY PROBLEMS
1. A voltage wave is given by v = 100 sin314t. How long does it take this wave form
to complete one- fourth cycle?
A. 20 ms
B. 10 ms
C. 5 ms
D. 1 ms
2. When a 15 V square wave is connected across a 50-volt AC voltmeter, it will read
________.
A. 21.21 V
B. 10.61 V
C. 15 V
D. 9.55 V
3. Calculate the effective value of v(t) = 100 sin400t+ 50 sin800t+ 10 cos 1200t V.
A. 79.5 V
B. 57.9 V
C. 112.25 V
D. 121.52 V
9. Using Problem 7, what is the equivalent power factor of the circuit?
A. 0.924
B. 0.866
C. 0.707
D. 0.876
10. Using Problem 7, what element should be connected across the circuit so that
the current would be in phase with the source?
A. 54 mH
B. 25.4 mH
C. 13 mH
D. 31 mH
11. An impedance has a lagging power factor and takes 250 W when connected
across 100 V, 60 Hz source. What power will it absorb when connected across 100
V, 50 Hz source?
A. 325 W
B. 352 W
C. 322 W
D. 235 W
4. A circuit draws a current of (3-j8) A from a source of (100+ j37) V. Find the true
power of the circuit.
A. 4W
B. 596 W
C. 300 W
D. 296 W
12. A telephone circuit makes power available at a pair of terminals. The open circuit
voltage across the terminals is 1 volt and the impedance looking into the terminals is
500 - j500. What is the maximum power that can be drawn from the circuit?
A. 0.002 W
B. 0.0005 W
C. 0.001 W
D. 0.0014 W
5. Across a 230 V, 60 Hz power supply is a 15-ohm non-inductive resistor. What is
the equation of the voltage and resulting current?
A. e =398.4 sin60t, i = 21.6 sin60t B. e = 325.5 sin377t, i = 21.6 sin377t
C. e=230 sin377t, i= 15.3 sin377t
D. e = 230 sin120t, i = 15.3 sin120t
13. The ohmic resistance of a large magnetic contactor is measured to be 20𝛺. A
230 V is impressed on the contactor and the current is taken as 3.2 A. Neglecting
core loss, determine the inductance of the contactor.
A. 201 mH
B. 183 mH
C. 315 mH
D. 251 mH
6. A resistor and a coil are connected in series with a voltage source. If the voltage
across the coil is 10sin(866t+70°) V and the current flowing thru the resistor is
2cos(866t-80°) A, what is the resistance of the coil?
A 4.92
B. 2.5
C. 5
D. 4.33
14. A coil has a resistance of 6 ohms and an inductance of 0.02 H. When a noninductive resistor is connected in series with the coil, the current drawn when
connected to a 220 V DC source is equal to the current drawn by the coil alone
across a 220 V, 60 Hz source. Determine the resistance of the non-inductive resistor.
A. 363 𝛺
B. 6.39 𝛺
C. 369 𝛺
D. 396 𝛺
7. Ten impedances connected in parallel draws the following individual current, 5∠0°,
5∠5°, 5∠10°, 5∠15°, 5∠20°, 5∠25°, 5∠30°, 5∠35, 5∠40°, 5∠45°. What is the effective
value of the total current? (Shortcut solution will be discussed on refresher)
A. 48.444 A
B. 34.255 A
C. 25.345 A
D. 84.389 A
8. Using Problem 7, what is the equivalent impedance that could replace the
impedances if the source voltage is 100 sin150t V?
A. 1.325∠30°
B 6.026∠2.5°
C 32.51∠50°
D. 1.46 ∠22.5°
15. A series RL circuit has L = 0.02 H and an impedance of 17.85 𝛺. When a
sinusoidal voltage is applied, the current lags the voltage by 63.5°. What is the value
of the angular frequency?
A 400 rad/sec
B. 500 rad/sec
C. 600 rad/sec
D. 800 rad/sec
REE- April 1997
16. A current of 2.5 A flows through a series circuit consisting of a 100 𝛺 resistor and
an unknown capacitor across a source of 460 V, 50 Hz. What is the value of the
capacitive reactance?
A 𝑋𝐶 =91.86 𝛺
B. 𝑋𝐶 =39.19 𝛺
C 𝑋𝐶=154.45 𝛺
D. 𝑋𝐶 =184.0 𝛺
REE- April 1996
17. A circuit consists of a 4 𝛺 resistor and 300 uF capacitor in series. It is connected
across a 60 Hz voltage source with a 500 V peak voltage. What is the phasor form of
the current?
A. I=19.7∠57.5 °
B. I=8.84∠73.2°
C. I=36.5∠65.7°
D I=10.5∠65.7°
18. A small single phase, 240 V induction motor is tested in parallel with 160 𝛺
resistor. The motor takes 2 amperes and the total current is 3 amperes. What is the
power of the whole circuit?
A. 800 W
B. 360 W
C. 220 W
D. 580 W
19. A capacitor is placed in parallel with two inductive loads, one of 20 A at 30°
lagging and another of 40 A at 60° lagging. What current in amperes should flow in
the capacitor so that the circuit will have a unity power factor?
A. 35.8 A
B. 44.6 A
C. 28.8 A
D. 50.2 A
20. A single-phase AC generator is supplying power to a load of 3,200 W at 230 V
and a power factor of 60%. If the total loss is 10% of the load, what would be the
savings in watts if the power factor is raised to 80%?
A. 64
B. 240
C. 427
D. 140
21. When a 240 V, 50 Hz supply is applied to a parallel combination of 15 𝛺 resistor
and inductor, the total current is 22.1 amperes What must be the value of the
frequency for a total current of 34 amperes?
A. 25 Hz
B. 60 Hz
C. 75 Hz
D. 100 Hz
22. A coil of 10 𝛺 resistance and 0.1 H inductance is connected in parallel with a
capacitor of unknown capacitance. If the total impedance of the combination is 100
𝛺, determine the value of the capacitance.
A. 50 𝜇F
B. 100 𝜇F
C. 150 𝜇F
D. 200 𝜇F
23. A coil of 50 𝛺 resistance and 150 mH, inductance is connected in parallel with a
50 𝜇F capacitor. The source voltage is 100 sin (𝜔t + 30°) V. What is the equation of
the line current?
A 1.91 sin (𝜔t + 52.5°)
B. 1.25 sin (𝜔t + 75.5°)
C. 1.25 sin (𝜔t - 62°)
D. 1.32 sin (𝜔t - 75.5°)
24. An impedance equal to 4.4∠60° 0 is connected across a 220 V source. What
should be the value of the second impedance in parallel with the first, if the total
power delivered to the circuit is to be 16.5 kW and the overall power factor is to be
unity?
A. 2.21∠30.1° 𝛺
B. 3.33∠ −40.9° 𝛺
C. 5.63∠30° 𝛺
D. 6.53∠ −45° 𝛺
25. An inductive reactance of 8 ohms is connected in parallel with a capacitive
reactance of 18 ohms. This combination is then connected in series with a variable
resistance. For what value of resistance will the power factor be 0.5?
A. 8.314 𝛺
B. 3.138 𝛺
C. 13.81 𝛺
D. 1.381 𝛺
26. What size of condenser must be placed across an inductance having a
resistance of 10 ohms and reactance of 20 ohms to draw minimum current from the
line when the combination is connected across a 60-cycle line?(Assume a condenser
of negligible resistance).
A. 20 𝜇f
B. 106 𝜇f
C 10 𝜇f
D. 6.33 𝜇f
27. A circuit draws 25 A when connected across a source of frequency f. Determine
the current drawn by the same circuit at resonance if 𝑓1 is half the resonant
frequency.
A. 12.5 A
B. 17.68 A
C. 35.35 A
D. 50 A
28. A series RLC circuit is connected across a 120 V, 60 Hz source and draws a
leading current of 5 A. Determine the voltage across the capacitor at resonance if R
= 50 and L = 25 mH.
A. 47.12 V
B. 164.5 V
C. 236.6 V
D. 422.6 V
29. The Q-factor of a coil is given by ________.
A. the ratio of its maximum energy stored to its energy dissipated per cycle
B. its power factor
C. the reciprocal of its power factor
D. the ratio of its resistance to its inductive reactance
REE-April 1997
36. Determine the power factor angle 𝜃 in the series circuit which consists of R = 25
𝛺, L = 0.2 H, across a power supply of 200 V, 30 Hz.
A. 36.4°
B. 46.4°
C. 52.4°
D. 56.4°
30. A coil takes apparent power and reactive power of 100 VA and 80 VAR,
respectively. What is the Q factor of the coil?
A. 1.33
B. 10
C. 8
D. 6
37. A load of 20+ j135 𝛺 is connected across a 220 V source. Determine the power
factor and the VARS.
A. 49.6%, 1042 VARS
B. 85.3%, 975 VARS
C. 52.2%, 1023 VARS
D. 42.3%, 1087 VARS
31. A coil is to be wound with Q-factor of 8. A lamp rated 120 V, 480 W is connected
in series with the coil and connected across 230 V, 60 Hz source. What is the
impedance of the coil if the voltage across the lamp is maintained at 120 V.
A. 35.2∠82.9° 𝛺
B. 27.5 ∠72.4° 𝛺
C. 45.5∠82.9° 𝛺
D. 40.5∠72.4° 𝛺
38. An incandescent lamp load, generally considered to be made up of resistors,
take 4.8 kW from a 120-volt AC source. The instantaneous maximum value of power
is _________.
A. 4,800 watts
B. 9,600 watts
C. 2,400 watts
D. 480 watts
32. An inductive coil having a resistance of 25 ohms and inductance of 0.2 H is
connected in parallel with a 100 𝜇F capacitor. Find the frequency at which the total
current taken is in phase with the supply voltage.
A. 35.6 Hz
B. 46.5 Hz
C. 29.5 Hz
D. 52.9 Hz
39. A factory takes 50 kW at 0.75 lagging power factor from a 480 V source. In order
to raise the power factor to 0.9 lagging, a synchronous motor rated 10 HP with an
efficiency of 87.5% is used. Find the power factor of the motor.
A. 0.476 lagging
B. 0.825 lagging
C. 0.476 leading
D. 0.825 leading
33. The series circuit of R = 30 & X = 40 and a parallel circuit of R' and X' have the
same impedance and power factor. Calculate the value of R' and X'.
A. 8.33 𝛺, 6.25 𝛺
B.2.56 𝛺, 3.83 𝛺
C. 7.47 𝛺,7.51 𝛺
D. 5.62 𝛺,9.84 𝛺
34. A parallel circuit with one branch of R = 50 and a single unknown element in the
other branch has the following applied voltage and total current e=10 cos (50t + 60°)
V and i= 5.38cos (50t-8.23°) A. The unknown element is __________.
A. L=0.04 H
B. L = 0.02 H
C. C = 10 𝜇f
D. C = 5 𝜇f
35. The voltage across the resistor, inductor and capacitor connected in series is 60
V, 90 V, 10 V respectively. What is the voltage across this circuit?
A. 160 V
B. 140 V
C. 100 V
D. 50 V
ELECTRICAL TRANSIENT - SUPPLEMENTARY PROBLEMS
1. A coil has a time constant of 1 second and an inductance of 10 H. What is the
value of the current 0.1 second after switching on to a steady voltage of 100 volts?
A. 1.52 A
B. 0.952 A
C. 0.64 A
D. 1.96 A
2. A circuit having R = 25 𝛺 and L = 0.5 H is suddenly connected to a 250-v supply.
Find the voltage across R at 1 time constant.
A. 185 V
B. 15.8 V
C.158 V
D. 18.5 V
3. A 60 µF capacitor is connected in series with a 40,000-ohm resistor. If the
capacitor is initially uncharged, determine the resistor and capacitor voltages when t
= 1.5 times the time constant for a suddenly applied source emf of 120 volts.
A. 26.78 V, 93.22 V B. 120 V, 0 V
C. 93.22 V, 26.78 V D. 0 V, 120 V
4. The field circuit of a 125-volt dc generator has a resistance of 50 ohms
inductance of 12.3 henrys. A discharge resistor of 144 ohms is connected
across the field winding at the instant the main switch is opened. What
appears at the winding terminals at t = 0, and what is the initial rate of
change?
A. 125 V, 39.43 A/s
B. 360 V, 39.43 A/s
C. 125 V, -39.43 A/s
D. 360 V, -39.43 A/S
and an
directly
voltage
current
5. The initial rate of current rise in an RL circuit is 300 amp per sec when 120 volts is
suddenly impressed. What is the inductance of the circuit?
A 2.5H
B. 5 H
C. 1 H
D. 0.4 H
6. If the circuit resistance of Prob. #5 is 30 𝛺, calculate the rate of current change
when the current is 2.6 amp.
A. 300 A/s
B. 150 A/s
C. 105 A/s
D. 78 A/s
7. A coil having a resistance of 10 𝛺 and an inductance of 4 H is switched across a
20-V dc source. Calculate the time taken by the current to reach 50% of its final
steady value.
A.0.028 sec
B. 0.64 sec
C. 2.329 sec
D. 0.277 sec
8. The current in 600-volt series RC circuit is to be limited to a maximum of 30 ma,
and the time constant is to be 4 sec. Calculate the values of R and C.
A. 200 𝛺 and 200 μF
C. 20 𝛺and 20 μF
B. 20,000 𝛺 and 200 μF
D. 20,000 𝛺 and 20 μF
9. A circuit whose resistance is 20 𝛺 and inductance of 10 H has a steady voltage of
100 V suddenly applied to it. For the instant of 0.5 second after the voltage is
applied, determine the total power input to the circuit.
A. 400 watts
B. 316 watts
C. 200 watts
D. 116 watts
10. A series RC circuit with R = 100 ohms and C= 25 μF has a sinusoidal voltage
source e=250 sin(500t+) volts applied at a time when ∅=0°. Find the current,
assuming there is no initial charge on the capacitor.
A. 1.28 e−400t + 1.952 sin(500t + 38.66°)
C.-1.22e−400t + 1.952 sin(500t − 38.66°)
B. -1.22 e−400t + 1.952 sin(500t + 38.66°)
D. 1.28 e−400t + 1.952 sin(500t − 38.66°)
SUPPLEMENTARY PROBLEMS- THREE PHASE SYSTEMS
1.When phase sequence of a three-phase sytem is reversed.
a phase currents change in angle not in magnitude
b. phase currents are changed
a total power consumed is changed
d. phase power are changed
2.Determine the line voltage 𝑉𝑐𝑎 if 𝑉𝑏𝑛 = 277∠80° and the phase sequence is BAC.
a. 480∠-10° V
b. 480∠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 impedance of the wye-connected load if one phase current 𝐼𝑐 =
3.2∠75° A.
a. 30.6 - j30.6 𝛺
b. 30.6 + j 30.6 𝛺
c. 11.2 + 1 41.8 𝛺
d. 11.2 - j41.8 𝛺
4.Three equal impedances of (25+ j30) 𝛺 are connected in wye to 240 V, 60 Hz,
three-phase 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 μF
b. 80 μF
c. 70 μF
d. 60 μF
5. A delta-connected load draws 17.28 kW from 240 V, balanced three-phase supply.
What is the resistance of the load if the reactance is equal to 5 ohms?
a. 5 𝛺
b. 7.5 𝛺
c. 10 𝛺
d. 2.5 𝛺
6. Three identical impedances of 15∠60° ohms are connected in star to a threephase, 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. 123 V
b. 240 V
c. 416 V
d. 213 V
7. A delta connected load having an impedance of (300 + j210) 𝛺 per phase is
supplied from 480 V, three-phase supply through a line having an impedance of
(4+j8) 𝛺 per wire. What is the total power supplied to the load?
a. 1418 W
b. 473 W
c. 454 W
d. 1363 W
REE- Oct. 1996
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 𝛺
B. 965 𝛺
C. 1,142 𝛺
D. 1,045 𝛺
9. A certain load takes 300 kW at 400 V. A three-phase capacitor bank rated 15 KVA
per phase is connected in parallel with the load to raise the power fact of the load to
90% lagging. What is the power factor of the load before correction?
a. 99%
b. 92%
c. 95%
d. 88%
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%?
a. 54 HP
b. 43 HP
c. 33 HP
d. 35 HP
11. A three-phase, wye-connected induction motor is connected to a 480 V, threephase supply. It draws a current of 15 amperes at 80% power factor. A delta
connected reactance is connected in parallel with the motor and the combination
draws 15 amperes. What is the value of the element?
a. 57.4 μF
b. 122.5 μF
c. 28.7 μF
d. 245.0 μF
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 voltage coil across lines A and B
reads 800 W. The potential coil is then connected across lines A and C with 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. 0.87 leading
13. In two-wattmeter method, the readings of the wattmeter will be identical when
__________.
a. load in one of the two phases is zero
b. power factor is unity
c. power factor is 0.5
d. neutral is earthed
19. A three-phase, three-wire, 240 V CBA system supplies power to a wye-connected
load with impedances of 𝑍𝑎 = 𝑍𝑏 = 25∠90° 𝛺, 𝑍𝑐 = 20∠0° 𝛺. Find the total power.
a. 1,553 W
b. 2,589 W
c. 1,883 W
d. 2,104 W
14. A wye-connected balanced three-phase load draws 75 A from 230 V, 60 Hz,
source. To measure the total power, two wattmeters are connected in lines A and C
and reads 8,625 W and 17,250 W. respectively. Determine the impedance of the
balanced load.
a. 3.07∠30° 𝛺
b. 3.77∠-30° 𝛺
c. 1.77∠30° 𝛺
d. 1.77∠-30° 𝛺
20. A 100 V, balanced three-phase source has two single phase loads. The first load
has an impedance of (5+ jX) ohms and connected across lines A and B. The second
load is connected across B and C and has an impedance of (R-j2) ohms. Determine
the values of R and X, if the current in line B is 25.93∠-102 37° A and the ratio of X to
R is 1.5.
a. 2 𝛺,3 𝛺
b. 3 𝛺 , 4.5 𝛺
c. 4 𝛺,6 𝛺
d. 5 𝛺,7.5 𝛺
15. Two wattmeters are used to measure the power drawn by a balanced threephase load from a 440 V, three-phase source. The wattmeters are connected in lines
A and B and reads 10 kW and -2.5 kW. When a capacitor is connected in parallel
with the load and 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%
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 = 35∠-42.5° A, 𝐼𝑏 =60∠165° A, 𝐼𝑐 = 48∠38° A. However, it was found out that
the instrument used in measuring the current in line B is defective. What is the total
power drawn from the source?
a. 15,593 W
b. 9,180 W
c. 16,728 W
d. 24,000 W
16. The ratio 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. 7.74∠13.9° 𝛺
b. 7.74∠-13.9° 𝛺
c. 2.58∠41.4° 𝛺
d. 2.58∠-41.4° 𝛺
22. Three single phase loads are connected between lines of a 280 V, balanced
three-phase source. The currents measured in lines B and C are: 𝐼𝑏 =85.22∠-72.5° A,
𝐼𝑐 =60.71∠170° A. What is the negative sequence component of the currents?
a. 39.21∠105 2° A
b. 33.93∠161.6° A
c. 37.64∠-104.5° A d. 41.82∠72.8° A
17. A balanced 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 & 18,920W
23. A balanced three-phase 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 B and C. Determine
the impedance of the resistor so that the current in line C is zero.
a. 17.32 +j10 𝛺
b. 8.66+j5 𝛺
c. 10+ j30 𝛺
d. 5+ j15 𝛺
18. A 25 HP induction motor is operating at rated load from a three-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
24. Three identical resistances connected in star carry a line 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. 12 A
b. 4 A
c. 8A
d. 36 A
25. A three-phase induction motor delivers 150 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. Determine the capacitance required per phase.
a. 428 μF
b. 142.6 μF
c. 1283 μF
d. 3850 μF
26. A balanced star connected load is supplied from a symmetrical three phase, 400
volts ABC system. The current in each phase is 30 amperes and lags 30 behind the
line voltage. What is the total power?
a. 18,000 W
b. 10,393 W
c. 20,785 W
d. 31,177 W
27. A balanced delta load with impedances of 15-j9 ohms s connected to a threephase 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.150V
d. 87 V
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 twowattmeter method. If one wattmeter gives zero deflection, determine the values of R
and 𝑋𝐿 for a line voltage of 230 V.
a. 3.2, 10 𝛺
b. 5.2, 10 𝛺
c. 3.2,9 𝛺
d. 5.2,9 𝛺
29. Floating neutral in a three-phase supply is undesirable because it will cause
_________.
a high voltage across the load
b. unequal line voltage across the load
c. low voltage across the load
d. it has no effect on the load
REE-Oct. 1997
30. The sequence currents of a three-phase current are
Zero sequence current = 14.13 cis 17.34°
Positive sequence current = 708.26 cis (-31°)
Negative sequence current = 2.98 cis 10.06°
Determine the phase A current.
a. 720 cis (-30°)
b. 730 cis (-15.2°)
c. 710 cis 88°
d. 695 cis 15.2°