1Which statement best describes an alternating current?
Alternating current and voltage
Easy
A.It flows in one direction with constant magnitude
B.It remains zero during every complete cycle
C.It changes magnitude and direction periodically
D.It changes magnitude but never changes direction
Correct Answer: It changes magnitude and direction periodically
Explanation:
Alternating current varies with time and reverses its direction periodically.
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2In common AC circuit notation, what do the lowercase symbols and usually represent?
Concept of notations (i, v, I, V)
Easy
A.Average current and voltage
B.Instantaneous current and voltage
C.RMS current and voltage
D.Maximum current and voltage
Correct Answer: Instantaneous current and voltage
Explanation:
Lowercase and commonly denote instantaneous values, while uppercase and commonly denote RMS values or phasors.
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3For the voltage V, what is the amplitude?
Amplitude
Easy
A. V
B. V
C. V
D. V
Correct Answer: V
Explanation:
The amplitude is the maximum value of the waveform, which is the coefficient of the sine function.
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4What is the phase angle of ?
Phase
Easy
A.
B.
C.
D.
Correct Answer:
Explanation:
In , the constant angle is the phase angle.
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5If and , how does relate to ?
Phase difference
Easy
A. lags by
B. is opposite to by
C. leads by
D. is in phase with
Correct Answer: lags by
Explanation:
The negative phase angle means that reaches corresponding points later than .
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6What is the RMS value of a sinusoidal voltage with peak value ?
RMS value of an AC signal
Easy
A.
B.
C.
D.
Correct Answer:
Explanation:
For a sinusoidal voltage, .
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7What is the average value of a pure sinusoidal current over one complete cycle?
Average value of an AC signal
Easy
A.
B.
C.
D.Zero
Correct Answer: Zero
Explanation:
Over a complete cycle, the equal positive and negative halves of a sinusoidal current cancel each other.
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8What is the complex impedance of an ideal inductor?
Complex representation of impedance
Easy
A.
B.
C.
D.
Correct Answer:
Explanation:
The impedance of an ideal inductor is , where represents a phase shift.
Incorrect! Try again.
9In a series RL circuit supplied by a sinusoidal voltage, how does the current relate to the supply voltage?
Steady-state analysis of RL circuits
Easy
A.Current is always zero
B.Current is opposite to the voltage
C.Current lags the voltage
D.Current leads the voltage
Correct Answer: Current lags the voltage
Explanation:
Inductance causes the current in a series RL circuit to lag behind the supply voltage.
Incorrect! Try again.
10In a series RC circuit supplied by a sinusoidal voltage, how does the current relate to the supply voltage?
Steady-state analysis of RC circuits
Easy
A.Current is opposite to the voltage
B.Current leads the voltage
C.Current is always zero
D.Current lags the voltage
Correct Answer: Current leads the voltage
Explanation:
Capacitance causes the current in a series RC circuit to lead the supply voltage.
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11What is the total impedance of a series RLC circuit?
Steady-state analysis of series RLC circuits
Easy
A.
B.
C.
D.
Correct Answer:
Explanation:
In a series RLC circuit, the net reactance is , so .
Incorrect! Try again.
12What condition produces resonance in a series RLC circuit?
Resonance in series RLC circuit
Easy
A.
B.
C.
D.
Correct Answer:
Explanation:
At resonance, inductive and capacitive reactances are equal, so the net reactance is zero.
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13What type of power factor does a series RL circuit have?
Power factor and power calculation in RL circuits
Easy
A.Negative power factor
B.Zero power factor
C.Leading power factor
D.Lagging power factor
Correct Answer: Lagging power factor
Explanation:
In an RL circuit, current lags voltage, so the circuit has a lagging power factor.
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14What type of power factor does a series RC circuit have?
Power factor and power calculation in RC circuits
Easy
A.Lagging power factor
B.Zero power factor
C.Leading power factor
D.Negative power factor
Correct Answer: Leading power factor
Explanation:
In an RC circuit, current leads voltage, so the circuit has a leading power factor.
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15Which formula gives the active power in a single-phase RLC circuit?
Power factor and power calculation in RLC circuits
Easy
A.
B.
C.
D.
Correct Answer:
Explanation:
Active power is , where and are RMS values and is the power factor.
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16In a balanced three-phase system, what is the phase displacement between adjacent phase voltages?
Three-phase circuits
Easy
A.
B.
C.
D.
Correct Answer:
Explanation:
The three phase voltages of a balanced system have equal magnitudes and are separated by .
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17Which set is commonly used to identify the three phase conductors of a three-phase supply?
Numbering and interconnection of three phases
Easy
A., , and
B., , and
C., , and
D., , and
Correct Answer: , , and
Explanation:
The three phases are commonly identified as , , and , corresponding to the three phase conductors.
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18How are the three phase windings connected in a delta connection?
Delta or mesh connection
Easy
A.End to end in a closed loop
B.Together at one neutral point
C.In parallel across one phase
D.Separately without interconnection
Correct Answer: End to end in a closed loop
Explanation:
In a delta connection, each winding is joined end to end with the others to form a closed loop.
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19For a balanced star-connected network, what is the relation between line voltage and phase voltage ?
Relations between line and phase voltages and currents in star networks
Easy
A.
B.
C.
D.
Correct Answer:
Explanation:
In a balanced star connection, line voltage is times the phase voltage, while line current equals phase current.
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20For a balanced delta-connected network, what is the relation between line current and phase current ?
Relations between line and phase voltages and currents in delta networks
Easy
A.
B.
C.
D.
Correct Answer:
Explanation:
In a balanced delta connection, line current is times the phase current, while line voltage equals phase voltage.
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21A sinusoidal voltage completes 250 cycles in 5 seconds. What are its frequency and time period?
Alternating current and voltage
Medium
A. and
B. and
C. and
D. and
Correct Answer: and
Explanation:
The frequency is . Therefore, .
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22In AC circuit notation, and are given. What do and represent, respectively?
Concept of notations (i, v, I, V)
Medium
A.Maximum current and average current
B.Average current and maximum current
C.Instantaneous current and RMS current
D.RMS current and instantaneous current
Correct Answer: Instantaneous current and RMS current
Explanation:
A lowercase symbol such as denotes an instantaneous value, while the uppercase phasor magnitude commonly denotes an RMS value.
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23For the voltage , what is the amplitude of the equivalent single sinusoid?
Amplitude
Medium
A.
B.
C.
D.
Correct Answer:
Explanation:
The sine and cosine components are in quadrature, so the amplitude is .
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24At , the signal has what instantaneous value and initial trend?
Phase
Medium
A. and increasing
B. and decreasing
C. and increasing
D. and decreasing
Correct Answer: and increasing
Explanation:
At , . Its derivative is proportional to , which is positive, so the voltage is increasing.
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25Given and , what is the phase relationship between voltage and current?
Phase difference
Medium
A.Voltage leads current by
B.Voltage leads current by
C.Current leads voltage by
D.Current leads voltage by
Correct Answer: Voltage leads current by
Explanation:
The phase difference is , so voltage leads current by .
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26A symmetrical square-wave current alternates between and for equal time intervals. What is its RMS value?
RMS value of an AC signal
Medium
A.
B.
C.
D.
Correct Answer:
Explanation:
The square of the current is always . Thus, .
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27A sinusoidal current has a peak value of . What is its average value over one positive half-cycle?
Average value of an AC signal
Medium
A.
B.
C.
D.
Correct Answer:
Explanation:
The half-cycle average of a sinusoid is .
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28An impedance is given by . Which polar representation and circuit behavior are correct?
Complex representation of impedance
Medium
A., capacitive
B., inductive
C., capacitive
D., inductive
Correct Answer: , capacitive
Explanation:
The magnitude is and the angle is . Negative reactance indicates capacitive behavior.
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29A series RL circuit with and is connected to a RMS supply. What is the current phasor when the supply voltage is the reference?
Steady-state analysis of RL circuits
Medium
A.
B.
C.
D.
Correct Answer:
Explanation:
The impedance is . Hence, .
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30A series RC circuit has , , and an applied voltage of RMS. What is the supply current?
Steady-state analysis of RC circuits
Medium
A.
B.
C.
D.
Correct Answer:
Explanation:
The impedance is . Therefore, , so current leads voltage.
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31A series RLC circuit has , , and . If the applied voltage is RMS, what is the current?
Steady-state analysis of series RLC circuits
Medium
A.
B.
C.
D.
Correct Answer:
Explanation:
The net reactance is , so . Thus, .
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32A series RLC circuit has and . Approximately at what frequency does resonance occur?
Resonance in series RLC circuit
Medium
A.
B.
C.
D.
Correct Answer:
Explanation:
The resonant frequency is . Substitution gives .
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33A series RL load with and is connected to a RMS supply. What are its power factor and real power?
Power factor and power calculation in RL circuits
Medium
A. leading and
B. lagging and
C. leading and
D. lagging and
Correct Answer: lagging and
Explanation:
Here , so and lagging. Real power is .
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34A series RC load has and across a RMS supply. What are its power factor and real power?
Power factor and power calculation in RC circuits
Medium
A. lagging and
B. leading and
C. leading and
D. lagging and
Correct Answer: leading and
Explanation:
The impedance magnitude is , giving . The power factor is leading, and .
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35A series RLC load has , , and . It is connected to a RMS supply. What are the power factor and real power?
Power factor and power calculation in RLC circuits
Medium
A. leading and
B. leading and
C. lagging and
D. lagging and
Correct Answer: lagging and
Explanation:
The net reactance is , so and . Thus, the power factor is lagging and .
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36A balanced three-phase load draws a line current of from a line-to-line supply at a power factor of . What is the total real power?
Three-phase circuits
Medium
A.
B.
C.
D.
Correct Answer:
Explanation:
For a balanced three-phase load, . Thus, .
Incorrect! Try again.
37Three phase voltages are , , and . What is their phase sequence?
Numbering and interconnection of three phases
Medium
A.
B.
C.
D.
Correct Answer:
Explanation:
Phase 1 reaches its positive maximum first, followed by phase 2 and then phase 3. Therefore, the phase sequence is .
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38Three identical impedances are connected in delta across a balanced three-phase supply. If each impedance has magnitude , what is the magnitude of the line current?
Delta or mesh connection
Medium
A.
B.
C.
D.
Correct Answer:
Explanation:
In delta, the phase voltage is , so . Hence, .
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39A balanced star-connected load has a phase voltage of and a phase current of . What are the corresponding line voltage and line current?
Relations between line and phase voltages and currents in star networks
Medium
A. and
B. and
C. and
D. and
Correct Answer: and
Explanation:
For a star connection, and .
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40A balanced delta-connected load draws a line current of from a three-phase supply. What are the phase voltage and phase current?
Relations between line and phase voltages and currents in delta networks
Medium
A. and
B. and
C. and
D. and
Correct Answer: and
Explanation:
For a delta connection, and .
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41A periodic voltage is given by V. If is the fundamental period of , which expression represents ?
Alternating current and voltage
Hard
A. V
B. V
C. V
D. V
Correct Answer: V
Explanation:
The component frequencies are Hz and Hz, so ms. A shift of adds to the fundamental but to the second harmonic, reversing only the fundamental.
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42Using the conventional RMS phasor notation with cosine as reference, the instantaneous current is A. Which statement is correct?
Concept of notations (i, v, I, V)
Hard
A. A and A
B. A and A
C. A and A
D. A and A
Correct Answer: A and A
Explanation:
Lowercase denotes the instantaneous quantity. Uppercase denotes its RMS phasor, whose magnitude is A and phase is .
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43A nonsinusoidal voltage is V. What is the amplitude of its fundamental component?
Amplitude
Hard
A. V
B. V
C. V
D. V
Correct Answer: V
Explanation:
The two fundamental-frequency terms combine to give amplitude V. The term is a separate harmonic.
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44Express V in the standard form with and . What is ?
Phase
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
Since , the voltage is , giving .
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45Voltage leads voltage by , and current lags by . What is the phase relationship between and ?
Phase difference
Hard
A. leads by
B. leads by
C. leads by
D. leads by
Correct Answer: leads by
Explanation:
Taking as the reference gives and . Thus leads by .
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46Over each period , a voltage equals V for , V for , and V for . What is its RMS value?
RMS value of an AC signal
Hard
A. V
B. V
C. V
D. V
Correct Answer: V
Explanation:
The mean square is . Therefore, V.
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47For , what is the average value over the first quarter-cycle, ?
Average value of an AC signal
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
The interval average is . The two integral contributions are and , yielding .
Incorrect! Try again.
48Two impedances and are connected in parallel. What is their equivalent impedance?
Complex representation of impedance
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
.
Incorrect! Try again.
49A series RL circuit has and . It is supplied by V. What is the steady-state current?
Steady-state analysis of RL circuits
Hard
A. A
B. A
C. A
D. A
Correct Answer: A
Explanation:
The impedance is . Hence A RMS.
Incorrect! Try again.
50A series RC circuit with and is connected to V RMS. What is the capacitor-voltage phasor?
Steady-state analysis of RC circuits
Hard
A. V
B. V
C. V
D. V
Correct Answer: V
Explanation:
, so A. Thus V.
Incorrect! Try again.
51A series RLC circuit has , , and . With V RMS, what is the phasor voltage across the series combination of and ?
Steady-state analysis of series RLC circuits
Hard
A. V
B. V
C. V
D. V
Correct Answer: V
Explanation:
, so A. The combined reactance is , giving V.
Incorrect! Try again.
52A series RLC circuit has , mH, and F. Which pair gives its lower and upper half-power angular frequencies?
Resonance in series RLC circuit
Hard
A. rad/s and rad/s
B. rad/s and rad/s
C. rad/s and rad/s
D. rad/s and rad/s
Correct Answer: rad/s and rad/s
Explanation:
At half power, . The two positive solutions are approximately and rad/s; their difference also equals rad/s.
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53A series RL load takes kW from a V RMS supply at a power factor of lagging. What is the load impedance?
Power factor and power calculation in RL circuits
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
A, so . With , and .
Incorrect! Try again.
54A series RC load has and and is connected to a V RMS supply. What is its complex power?
Power factor and power calculation in RC circuits
Hard
A. VA
B. VA
C. VA
D. VA
Correct Answer: VA
Explanation:
, so A. Therefore W and var, giving VA.
Incorrect! Try again.
55A series RLC load has , , and . It is supplied at V RMS. Which set of power quantities is correct?
Power factor and power calculation in RLC circuits
Hard
A. kW, kvar, power factor
B. kW, kvar, power factor lagging
C. kW, kvar, power factor leading
D. kW, kvar, power factor lagging
Correct Answer: kW, kvar, power factor lagging
Explanation:
, so A. Thus kW, kvar, and the power factor is lagging.
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56In an unbalanced four-wire star load, the phase currents from source to load are A, A, and A. What is the magnitude of the neutral current?
Three-phase circuits
Hard
A. A
B. A
C. A
D. A
Correct Answer: A
Explanation:
The phasor sum is A. The neutral conductor carries the return current, whose magnitude is therefore A.
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57A balanced positive-sequence source has , , and . If external leads 2 and 3 are interchanged while lead 1 is unchanged, what are the new sequence and the new ?
Numbering and interconnection of three phases
Hard
A.Sequence -- and
B.Sequence -- and
C.Sequence -- and
D.Sequence -- and
Correct Answer: Sequence -- and
Explanation:
Interchanging any two leads reverses the phase sequence. The new lead-2 voltage is the original , so .
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58A balanced delta load has branch impedance . For positive sequence, let V. What is line current ?
Delta or mesh connection
Hard
A. A
B. A
C. A
D. A
Correct Answer: A
Explanation:
A. In a balanced delta, A.
Incorrect! Try again.
59A balanced positive-sequence star load has per-phase impedance . If V, what is phase current ?
Relations between line and phase voltages and currents in star networks
Hard
A. A
B. A
C. A
D. A
Correct Answer: A
Explanation:
For positive sequence, V. Dividing by gives A.
Incorrect! Try again.
60In a balanced positive-sequence delta load, the line current is A. What is the branch current ?
Relations between line and phase voltages and currents in delta networks
Hard
A. A
B. A
C. A
D. A
Correct Answer: A
Explanation:
For a balanced positive-sequence delta, . Hence A.
Incorrect! Try again.
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