MULTIVECTOR REVIEW AND TRAINING CENTER
AC CIRCUIT
Part I – SINGLE PHASE SYSTEM
The length of time between a point in one cycle to the same point of the next cycle of an AC wave is _________
a. Frequency
b. Period
c. Magnitude
Polarity
In an experiment, a sinusoidal wave form is observed to complete 8 cycle in 25msec. determine the frequency of the wave form
a. 320 Hz
b. 40 Hz
c. 200 Hz
d. 64 Hz
REE – Sept. 2007
Wavelength is the distance traveled by an electronic wave during the time of one cycle. Given a wavelength of 12meters, what is the frequency?
a. 250 kHz
b. 25 kHz
c. 250 MHz
d. 25 MHz
If emf in a circuit is given by e = 100 sin 628t, the maximum value of voltage and frequency is __________
a. 100 V, 50 Hz
b. 100 V, 100 Hz
c. 502 V, 50 Hz
d. 502 V, 100 Hz
REE – April 2007
What is the complex expression for a given alternating current, I = 250sin(ωt – 25 deg)?
a. 227 + j106
b. 160 – j75
c. 227 – j106
d. 160 + j75
A sinusoidal voltage wave has an RMS value of 70.71V and a frequency of 60Hz. Determine the value of the voltage 0.0014 second after the wave crosses the ωt axis
a. 70.71 V
b. 100 V
c. 50 V
d. 141.42 V
An alternating current varying sinusoidally with frequency of 50Hz has an RMS value of 20A. at what time measured from the positive maximum value will the instantaneous current be 14.14A?
a. 1/600 sec
b. 1/200 sec
c. 1/300 sec
d. 1/400 sec
REE – April 2001
An alternating rectangular wave has a maximum value of 10 V and a frequency of 1 cycle per second. What is the average value of the wave?
a. 5 V
b. 10 V
c. 0 V
d. 7.07 V
REE – April 2003
What is the rms value of a square wave with an amplitude of 10 A and frequency of 1 HZ?
a. 0 A
b. 10 A
c. 5 A
d. 7.07 A
REE – October 2000
A sinusoidal current wave has a maximum value of 20A. what is the average value of one- half cycle?
a. 5
b. 12.7
c. 14.14
d. 0
REE – April 1997
A wire carries current I = 3 cos 314t amperes. What is the average current over 6 seconds?
a. 0 A
b. 1.5 A
c. 3.0 A
d. 0.532 A
The average value of the function i = 50 sin ωt + 30 sin 3ωt is equal to ________
a. 31.8 A
b. 25 A
c. 38.2 A
d. 51.43 A
Determine the rms value of a semi-circular current wave which has a maximum value of a.
a. 0.816 a
b. 0.237 a
c. 0.866 a
d. 0.707 a
The rms value of a half-wave rectified current is 100 A. its value for full wave rectification would be _________ amperes.
a. 141.4 A
b. 200 A
c. 200/π A
d. 40/π A
A half wave rectified sine wave has an average value of 100amp. What is the effective value?
a. 157 A
b. 444 A
c. 70.71 A
d. 100 A
The form factor of a half-wave rectified alternating current is _____________
a. 1.11
b. 1.57
c. 1.73
d. 1.0
Three alternating current are given by i1 = 141 sin (ωt + 45°); i2 = 30 sin (ωt + 90°); i3 = 20 cos (ωt - 120°). Find the equation of resultant current
a. 167 sin (ωt + 45.66°)
b. 74.6 sin ωt
c. 143.8 sin (ωt + 51.4°)
d. 64.7 sin (ωt - 45°)
REE – Sept. 2006
When the sole purpose of ac is to produce heat, the selection of conductor is base on value of the current
a. Average
b. Instantaneous
c. RMS
d. Peak
The maximum value of a sine wave AC voltage which will produce heat in a resistor at the same average rate as 115 V of direct current is ___________
a. 81.3 V
b. 115 V
c. 162.6 V
d. 230 V
A sinusoidal voltage source has a peak value of 150 volts. What equivalent DC voltage source would produce the same heating effect in a 1 ohm resistor?
a. 15 V
b. 212 V
c. 95 V
d. 106 V
The effective value of v(t) = 100+Asinωt is known to be 103.1. The amplitude A of the sine term is ______
a. 25
b. 4.85
c. 35.48
d. 100
An alternating current and a direct current flow simultaneously in the same conductor. If the effective value of the AC is 8A and DC is 12A, what will an AC ammeter read when connected in the circuit?
a. 14.42 A
b. 12 A
c. 11.66 A
d. 16.49 A
Find the reading of an AC voltmeter connected across the series source of 100sin (ωt – π/2) and 100sin ωt.
a. 100
b. 130.65
c. 170.71
d. 184.78
An impedance draws a current I = 10cos(ωt - 30°) A from a v = 220sin ωt volts. What is the power?
a. 550 W
b. 1100 W
c. 190.5 W
d. 1320 W
REE – October 2000
A series circuit has an applied voltage of V = 220 sin (ωt + 30°) and draws a current I = 10 sin (ωt - 30°). What is the average power and power factor of the circuit?
a. 1905 W, 86.6% lagging
b. 1905 W, 86.6% lagging
c. 2200 W, 100%
d. 1100 W, 50% lagging
The effective voltage across a circuit element is (20 + j10)V and the effective current through the element is 4 – j3 A. calculate the true and the reactive power taken by the element
a. 50W and 100VARS lagging
b. 20W and 100VARS leading
c. 110W and 20VARS lagging
d. 110W and 20VARS leading
A 110-volt AC line feeds two circuits in parallel. The current are (2.2 – j6.5)A and (1.8 – j3.5)A. the power consumed by the two circuits is approximately ___________
a. 1.185 W
b. 440 W
c. 755 W
d. 433 W
Find the average power in a resistance R = 10 ohms if the current in series form is I = 10 sin ωt + 5 sin 3ωt + 2 sin 5ωt amperes
a. 65.4 watts
b. 645 watts
c. 546 watts
d. 5.46 watts
If e = 100 sin (ωt +30°) – 50 cos 3ωt +25 sin (5ωt +150) and i = 20 sin (ωt + 40°) + 10 sin (3ωt +30°) – 5 sin (5ωt - 50°). Calculate the power in watts.
a. 1177
b. 919
c. 1043
d. 1224
REE – Sept. 2007
The capacitive reactance Xc of a circuit varies inversely as the capacitance C of the circuit. If the capacitance of a certain circuit is decreased by 25%, by what percentage will Xc change?
a. 25 % increase
b. 20 % increase
c. 66 2/3 % increase
d. 33 1/3 % increase
REE – April 2005
A circuit has a resistance of 20 ohms and a reactance of 30 ohms. What is the power factor of the circuit?
a. 0
b. 0.55
c. 0.832
d. 0.99
REE – Sept 2006
A two – element series circuit with R = 15 ohms, L = 20mH has an impedance of 30 ohms and an unknown angle. What is the frequency in HZ?
a. 2.0
b. 21
c. 2067
d. 207
REE – April 2007
Awhat are the two elements in a series circuit connection having a current and voltage of i = 13.42 sin (500t – 53.4°)A and v = 150 sin (500t +10°)V?
a. R = 8.8 Ω and L = 35mH
b. R = 6.3 Ω and L = 25mH
c. R = 7.5 Ω and L = 30mH
d. R = 5 Ω and L = 20mH
REE – Sept 2006
A two – element series circuit has V = 240 +j0 volts and current 51.96 – j30 A. what is the current in amperes which results when the resistance is reduced 50% of its former value?
a. 68.57 – j59.39
b. 68.57 +j59.39
c. 59.39 – j68.57
d. 59.39 +j68.57
REE – Sept 2001
In laboratory experiment, the impedance of a coil was obtained at 60Hz and 30Hz. These are 75.48 ohms and 57.44 ohms, respectively. What is the inductance of the coil?
a. 150 mH
b. 182.5 mH
c. 42.5 mH
d. 2.1 mH
REE – Sept 2002
A 10 Ω inductive resistor is connected in series with an unknown capacitance. At 60 Hz the impedance of the circuit is 10 + j11.72 at 30 Hz the impedance of the circuit is 10 – j5. What is the value of L in millihenrys?
a. 50
b. 500
c. 100
d. 250
REE – April 2007
A series RLC circuit has elements R = 50 Ω, L = 8mH and C = 2.22 microfarads. What is the equivalent impedance of the circuit if the frequency is 796 Hz?
a. 50 +j50 Ω
b. 50 +j130 Ω
c. 50 – j50 Ω
d. 50 – j130 Ω
REE – Sept 2004
A capacitor in series with a 200 Ω resistor draws a current of 0.3 ampere from 120volts, 60Hz source. What is the value of capacitor in microfarad?
a. 8.7
b. 9.7
c. 6.7
d. 7.7
A series circuit consisting of a 66.2 microfarad capacitor and a variable resistor. For what two values of resistance will the power taken by the circuit be 172.8 watts, if the impressed 60 cycle emf is 120V?
a. 83.33 and 3.33 ohms
b. 53.33 and 30 ohms
c. 5.33 and 3.0 ohms
d. 83.33 and 5.33 ohms
REE – April 2004
Reactances are connected in series Xc1 = 100, Xc2 = 40, XL1 = 30, XL2 = 70. What is the net reactance?
a. 80 Xc
b. 40 Xc
c. 60 XL
d. 50 XL
A series circuit composed of 0.2 H inductor and 74 microfarad capacitor is connected to a 60V variable frequency source. At what frequency will the current be 4 A with laggng power factor.
a. 47.767 Hz
b. 74.68 Hz
c. 60 Hz
d. 50 Hz
REE – Sept 2005
Which is not 180 degrees apart?
a. XL and Ic
b. Xc and Ic
c. IL and Ic
d. Xc and XL
A 30 ohms resistor is connected in parallel with an inductor of inductive reactance XL. the combination is then connected in series with a capacitor of reactance Xc. what is the value of XL and Xc if the total impedance is 1.92 ohms?
a. 7.84, 7.34
b. 47.4, 47.3
c. 44.8, 84.2
d. 84.7, 34.7
An impedance of 100 ohms resistance and an unknown inductance is connected across the capacitor. The resulting impedance is a pure resistance of 500 ohms if ω = 105 rad/sec. calculate the values of inductor and capacitor.
a. 1 μf and 2 mH
b. 5 μf and 1 mH
c. 7 μf and 3 mH
d. 0.04 μf and 2 mH
REE – April 1997
The phase shift between the voltage and current vector is due to the following loads except one.
a. Magnetic coils
b. Electric flat iron
c. Power capacitors
d. Fluorescent lamp
REE – March 1998
A 50μf and 100μf capacitors are connected in series and across a 100 sin (ωt + 30°) voltage. Write the equation of the current.
a. 1.26 sin (ωt +120°)
b. 1.26 sin (ωt + 90°)
c. 5.65 sin (ωt +120°)
d. 5.65 sin (ωt +90°)
REE – April 2007
Find the value of an impedance which requires -1,540 vars at 230V rms and 10A rms.
a. 17.40 – j15.00
b. 16.82 – j15.69
c. 17.09 – j15.39
d. 17.62 – j14.78
REE – Sept. 2006
A 10 ohm resistor is connected in parallel to an impedance Z = 3+ j4 ohms. Find the circuit power factor.
a. 0.6 lagging
b. 0.866 lagging
c. 0.609 lagging
d. 0.809 lagging
REE – March 1998
A 25 ohms resistor connected in series with a coil of 50 ohms resistance and 150mH inductance. What is the power factor of the circuit?
a. 85 %
b. 80 %
c. 90 %
d. 75 %
The maximum values of alternating voltage and current are 400V and 20A, respectively, in a circuit connected to 50Hz spply and these quantities are sinusoidal. The instantaneous values of voltage and current are 283 V and 10 A respectively at t = 0 both increasing positively. What is the power factor of the circuit?
a. 0.707
b. 0.83
c. 0.85
d. 0.966
Two impedances ZA = 4 + j6 Ω and ZB = 6 + j12 Ω are connected in parallel. The apparent power for the impedance B is 1490VZ. Determine the total apparent power
a. 4250 VA
b. 3290 VA
c. 2652 VA
d. 8031 VA
REE – October 1996
The resistor of 6Ω and unknown impedance coil in series draw 12 A from a 120 V, 60 Hz line. If the real power taken from the line is 1152 watts, what is the coil inductance?
a. 15.9 mH
b. 10 mH
c. 20 mH
d. 1.59 mH
Two coils A and B are connected in series across a 240 V, 50 Hz supply. The resistance of A is 5 ohms and the inductance of B is 0.015H. if the input from the supply is 3 kW and 2 kVAR, find the inductance of A and resistance of B.
a. 0.0132 H and 8.3 Ω
b. 0.215 H and 3.8 Ω
c. 0.026 H and 12 Ω
d. 0.031 H and 5.3 Ω
A current of 5 A flows through a non inductive resistance in series with a choking coil when supplied at 250 V, 50 Hz. If the voltage across the resistance is 120 V and across the coil is 200 V. calculate the power absorbed by the coil in watts
a. 168.75 W
b. 137.5 W
c. 51.37 W
d. 75.31 W
A feeder supplies two loads, one at 50 amperes at 50% power factor, the other 150 amperes at unity power factor. The total current supplied by the feeder is approximately ____________.
a. 180 A
b. 200 A
c. 175 A
d. 150 A
A single phase, 7.46 kW motor is supplied from a 400 V, 50 Hz AC mains. If its efficiency is 85 % and the power factor is 0.8 lagging, find the reactive component of the input current.
a. 16.46 A
b. 21.96 A
c. 27.43 A
d. 21 A
REE – October 1996
A capacitor is rated 100 KVAR, 380 V, 50 Hz. What will its rating be at 60 Hz, 220 V?
a. 50 KVAR
b. 40 KVAR
c. 90.9 KVAR
d. 57.7 KVAR
A series RLC circuit consists of 20 ohms resistance, 0.2H inductance and an unknown capacitance. What is the value of the capacitance if the circuit has a leading angle of 45° at 60 Hz
a. 35.18 μF
b. 47.9 μF
c. 27.8 μF
d. 30.7 μF
A fluorescent lamp and its inductive ballast draw a 1.0 A current at 50% lagging power factor from a 120 V, 60 Hz source. What is the overall power factor when a 26.5μF capacitor is connected across the fixture?
a. 0.832 lagging
b. 0.832 leading
c. 0.5 leading
d. 0.5 lagging
A 3 HP, 120 V, 60Hz induction motor operating at 80 % efficiency and 0.866 lagging power factor is to be used temporarily with 240 V, 60 Hz source. What resistance in series with the motor will be required for the motor to have 120V across its terminals at full load?
a. 6.68 Ω
b. 4.77 Ω
c. 13.76 Ω
d. 9.54 Ω
A fluorescent lamp 80 W at 0.7 pf lagging from a 230 V 50 Hz supply is to e corrected to unity power factor. What element should be placed in ___________ for this purpose?
a. Series, 59.4 μF
b. Parallel, 4.95 μF
c. Series, 31.2 μF
d. Parallel, 8.36 μF
REE – October 2000
A series circuit consists of 20 ohms resistance, a 150mH inductance and an unknown capacitance. The circuit is supplied with a voltage v = 100 sin 377t. Find the value of capacitance at resonance.
a. 42 μF
b. 47 μF
c. 34.65 μF
d. 72.57 μF
A 50 ohms resistance, 30 ohms inductive reactance and 25 ohms capacitive reactance are connected in series across a 100 V, 60 Hz supply. What will be its resonant frequency?
a. 65.726 Hz
b. 53 Hz
c. 25 Hz
d. 54.77 Hz
REE – April 2005
A series RLC circuit has R = 10ohms, L = 40 x 10-6 H and C = 60 x 10-12 F. what is the resosnant of the circuit in MHz?
a. 20.17
b. 3.24
c. 4.49
d. 1.62
REE – April 2001
A 5 mH pure inductance is connected in parallel with one microfarad capacitor. What frequency will the circuit be in antiresonance?
a. 250 Hz
b. 2250 Hz
c. 60 Hz
d. 100 Hz
REE – October 1998
One leg of a radio tuned circuit has a capacitance of 1 x 10-9 F. it is tuned at 200 kHz. What is the inductance of the other leg in Henry?
a. 6.33 x 10-4
b. 20 x 10-3
c. 8.25 x 10-5
d. 120 x 10-3
A coil having a Q-factor of 5 is connected in series with an ideal capacitor across an ac source of 60 V. calculate the voltage across the capacitor at resonance.
a. 150 V
b. 300 V
c. 12 V
d. 65 V
REE – April 2004
A series RLC circuit has a resistance of 15 ohms and an inductive reactance of 1500 ohms. What is the Q – factor of the circuit at resonance?
a. 120
b. 100
c. 140
d. 150
REE- April 2004
A tuned circuit is resonance at 4MHz. its Q is 100. What is its bandwidth?
a. 4 kHz
b. 400 kHz
c. 400 Hz
d. 40 kHz
REE – Sept. 2007
A circuit has load impedance Z = 50 + j80Ω. Determine the parallel impedance required to correct the power factor to unity.
a. 32 μF
b. 36 μF
c. 24 μF
d. 28 μF
A circuit consisting of a capacitor in series with a resistance of 10ohms is connected in parallel with a coil having a reactance and resistance of 17.32 ohms and 10 ohms, respectively. What is the reactance of the capacitor that will draw minimum current from a 230 V, 60Hz supply?
a. 17.32 Ω
b. 10.32 Ω
c. 5.78 Ω
d. 22.18 Ω
REE – April 2007
An impedance Z 3 is in series to the two impedance Z 1 = 10 +j10 Ω and Z 2 = 20 –j30 Ω that are connected parallel. What is the value of the impedance Z 3 in ohms that will produce resonant circuit?
a. j13.1
b. -j5.4
c. j5.4
d. –j13.1
