1In the context of AC circuits, which notation is conventionally used to represent the instantaneous value of a voltage?
A.
B.
C.
D.
Correct Answer:
Explanation:Lower case letters (like or ) are conventionally used to represent instantaneous values, while capital letters (like or ) represent RMS or DC values.
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2What is the relationship between angular frequency () and linear frequency ()?
A.
B.
C.
D.
Correct Answer:
Explanation:The angular frequency in radians per second is equal to times the frequency in Hertz.
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3The time taken by an alternating quantity to complete one full cycle is called:
A.Frequency
B.Amplitude
C.Time Period
D.Phase
Correct Answer: Time Period
Explanation:The Time Period () is the duration of one complete cycle of the alternating wave. It is the reciprocal of frequency ().
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4The maximum value attained by an alternating quantity during a positive or negative half cycle is known as:
A.RMS value
B.Average value
C.Instantaneous value
D.Amplitude
Correct Answer: Amplitude
Explanation:Amplitude (or Peak Value, or ) is the maximum displacement from the zero axis.
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5For a sinusoidal voltage , what is the Root Mean Square (RMS) value?
A.
B.
C.
D.
Correct Answer:
Explanation:For a sinusoidal wave, the RMS value is defined as the peak value divided by the square root of 2, which is approximately .
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6The average value of a sinusoidal alternating current over one complete cycle is:
A.
B.
C.Zero
D.
Correct Answer: Zero
Explanation:A sine wave is symmetrical. The positive area exactly cancels the negative area over a full cycle, resulting in an average value of zero.
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7The average value of a sinusoidal voltage over a half cycle is given by:
A.
B.
C.
D.
Correct Answer:
Explanation:The average value over a half cycle is .
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8Which factor is defined as the ratio of RMS value to the Average value?
A.Peak Factor
B.Form Factor
C.Power Factor
D.Q Factor
Correct Answer: Form Factor
Explanation:Form Factor = . For a sine wave, it is approximately 1.11.
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9What is the peak factor (crest factor) of a sinusoidal waveform?
A.1.11
B.1.414
C.0.707
D.0.637
Correct Answer: 1.414
Explanation:Peak factor is the ratio of Maximum Value to RMS Value ().
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10Two sinusoidal quantities are said to be in phase quadrature if their phase difference is:
A.
B.
C.
D.
Correct Answer:
Explanation:Phase quadrature implies a phase difference of 90 degrees or radians.
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11In the complex representation of impedance , what does the operator '' represent?
A.Rotation by
B.Rotation by counter-clockwise
C.Rotation by clockwise
D.A scalar multiplier
Correct Answer: Rotation by counter-clockwise
Explanation:In phasor algebra, multiplying a phasor by rotates it by in the counter-clockwise direction. Mathematically, .
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12What is the complex impedance of an ideal inductor with inductance at angular frequency ?
A.
B.
C.
D.
Correct Answer:
Explanation:Inductive reactance is . Since voltage leads current by , the impedance is represented as or .
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13What is the complex impedance of an ideal capacitor with capacitance ?
A.
B.
C.
D.
Correct Answer:
Explanation:Capacitive reactance is . Since current leads voltage by , the impedance is negative imaginary: or , which is equivalent to .
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14In a purely resistive AC circuit, what is the phase difference between voltage and current?
A.
B.
C.
D.
Correct Answer:
Explanation:In a pure resistor, the voltage and current are in phase, meaning the phase difference is zero.
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15In a series RL circuit, the current:
A.Leads the applied voltage
B.Lags the applied voltage
C.Is in phase with the voltage
D.Lags the voltage by exactly
Correct Answer: Lags the applied voltage
Explanation:Due to the inductor, the current in a series RL circuit lags behind the voltage by an angle between and .
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16The magnitude of impedance in a series RL circuit is given by:
A.
B.
C.
D.
Correct Answer:
Explanation:The impedance is the vector sum of resistance and reactance: .
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17In a series RC circuit, the phase angle is given by:
A.
B.
C.
D.
Correct Answer:
Explanation:From the impedance triangle, , so .
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18Which of the following describes the power factor of a series RC circuit?
A.Unity
B.Lagging
C.Leading
D.Zero
Correct Answer: Leading
Explanation:In an RC circuit, the current leads the voltage, resulting in a leading power factor.
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19The total voltage applied to a series RL circuit with resistor voltage and inductor voltage is:
A.
B.
C.
D.
Correct Answer:
Explanation:AC voltages in series are added geometrically (phasor sum), not algebraically. Since and are apart, .
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20For a series RLC circuit, the total impedance is:
A.
B.
C.
D.
Correct Answer:
Explanation:The net reactance is the difference between inductive and capacitive reactance (). The total impedance is the hypotenuse of the impedance triangle.
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21In a series RLC circuit, if , the circuit behaves as:
A.Resistive
B.Inductive
C.Capacitive
D.Resonant
Correct Answer: Inductive
Explanation:If the inductive reactance is greater than the capacitive reactance, the net reactance is inductive, and the current lags the voltage.
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22What is the condition for resonance in a series RLC circuit?
A.
B.
C.
D.
Correct Answer:
Explanation:Resonance occurs when the inductive reactance equals the capacitive reactance, cancelling each other out.
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23At resonance, the impedance of a series RLC circuit is:
A.Zero
B.Maximum
C.Minimum and equal to
D.Equal to
Correct Answer: Minimum and equal to
Explanation:Since , the impedance , which is the minimum possible impedance for the circuit.
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24What is the resonant frequency of a series RLC circuit?
A.
B.
C.
D.
Correct Answer:
Explanation:Derived from . Solving for gives .
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25At series resonance, the current in the circuit is:
A.Minimum
B.Maximum
C.Zero
D.Infinite
Correct Answer: Maximum
Explanation:Because impedance is at its minimum (), the current is at its maximum.
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26The power factor of a series RLC circuit at resonance is:
A.
B.0.5 lagging
C.0.5 leading
D.1 (Unity)
Correct Answer: 1 (Unity)
Explanation:At resonance, the circuit is purely resistive (), so the phase angle is and .
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27The Quality Factor (Q-factor) of a series resonant circuit is given by:
A.
B.
C.
D.
Correct Answer:
Explanation:Q-factor is voltage magnification, defined as . Substituting , we get .
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28In AC circuits, Active Power (Real Power) is calculated as:
A.
B.
C.
D.
Correct Answer:
Explanation:Active power is the power actually consumed by the resistance, given by .
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29The unit of Reactive Power () is:
A.Watt (W)
B.Volt-Ampere (VA)
C.Volt-Ampere Reactive (VAR)
D.Joule (J)
Correct Answer: Volt-Ampere Reactive (VAR)
Explanation:Reactive power represents energy oscillating between source and reactive components, measured in VAR.
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30Apparent Power () is the product of:
A.RMS Voltage and RMS Current
B.Average Voltage and Average Current
C.Peak Voltage and Peak Current
D.Active Power and Power Factor
Correct Answer: RMS Voltage and RMS Current
Explanation:Apparent Power , measured in Volt-Amperes (VA).
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31Power factor is defined as the ratio of:
A.Resistance to Impedance ()
B.Impedance to Resistance ()
C.Resistance to Reactance ()
D.Reactance to Resistance ()
Correct Answer: Resistance to Impedance ()
Explanation:From the impedance triangle, .
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32If the power factor is 0.8 lagging, it means:
A.The circuit is capacitive
B.The circuit is purely resistive
C.Current lags voltage and energy is stored in magnetic fields
D.Current leads voltage
Correct Answer: Current lags voltage and energy is stored in magnetic fields
Explanation:Lagging power factor indicates an inductive circuit where current lags voltage.
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33In a three-phase system, the voltages of the three phases are displaced from each other by:
A.
B.
C.
D.
Correct Answer:
Explanation:In a balanced three-phase system, the phase voltages are equal in magnitude and displaced by .
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34The order in which the voltages in the three phases reach their maximum positive value is called:
A.Phase Difference
B.Phase Sequence
C.Alternation
D.Frequency
Correct Answer: Phase Sequence
Explanation:Phase sequence (e.g., R-Y-B) describes the chronological order of peak values.
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35In a Star (Wye) connected three-phase system, the relationship between Line Current () and Phase Current () is:
A.
B.
C.
D.
Correct Answer:
Explanation:In a star connection, the line conductor is in series with the phase winding, so the current is the same.
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36In a Star (Wye) connected system, the Line Voltage () relates to the Phase Voltage () as:
A.
B.
C.
D.
Correct Answer:
Explanation:The line voltage is the vector difference of two phase voltages, resulting in a magnitude of times the phase voltage.
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37In a Delta (Mesh) connected three-phase system, the relationship between Line Voltage () and Phase Voltage () is:
A.
B.
C.
D.
Correct Answer:
Explanation:In a delta connection, the line conductors are connected directly across the phase windings, so .
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38In a Delta (Mesh) connected system, the Line Current () relates to the Phase Current () as:
A.
B.
C.
D.
Correct Answer:
Explanation:In delta, the line current is the vector difference of two phase currents, resulting in .
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39The total active power in a balanced three-phase circuit (Star or Delta) is given by:
A.
B.
C.
D.
Correct Answer:
Explanation:Total power is . Substituting line values for either Star or Delta yields .
Explanation:A Star connection has a common point (neutral point) allowing for a neutral wire, making it a 3-phase 4-wire system.
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41What is the unit of Admittance ()?
A.Ohm ()
B.Henry (H)
C.Farad (F)
D.Siemens (S) or Mho
Correct Answer: Siemens (S) or Mho
Explanation:Admittance is the reciprocal of impedance (), measured in Siemens (S) or Mho ().
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42The real part of Admittance is called:
A.Resistance
B.Reactance
C.Conductance
D.Susceptance
Correct Answer: Conductance
Explanation:Admittance , where is Conductance (real part).
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43If the frequency of the AC supply is increased, the capacitive reactance ():
A.Increases
B.Decreases
C.Remains constant
D.Becomes zero
Correct Answer: Decreases
Explanation:Since , reactance is inversely proportional to frequency. Increasing decreases .
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44If the frequency of the AC supply is increased, the inductive reactance ():
A.Increases
B.Decreases
C.Remains constant
D.Becomes infinite
Correct Answer: Increases
Explanation:Since , reactance is directly proportional to frequency. Increasing increases .
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45Which of the following represents the bandwidth of a series RLC circuit?
A.
B.
C.
D.All of the above
Correct Answer: All of the above
Explanation:Bandwidth is the difference between half-power frequencies, related to resonant frequency/Q-factor, and determined by component values (in rad/s) or in Hz.
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46At half-power frequencies in a series RLC circuit, the current is:
A.
B.
C.
D.Zero
Correct Answer:
Explanation:At half-power points, the power is half the maximum, which means voltage and current are (or 0.707) of their maximum values.
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47The phase angle between Line Voltage and Phase Voltage in a Star connected system is:
A.
B.
C.
D.
Correct Answer:
Explanation:In a star connection, the line voltage leads the respective phase voltage by .
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48In a circuit with , what is the magnitude of the impedance?
A.
B.
C.
D.
Correct Answer:
Explanation:.
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49Instantaneous power in a pure resistive circuit is always:
A.Positive
B.Negative
C.Zero
D.Alternating positive and negative
Correct Answer: Positive
Explanation:Since voltage and current are in phase in a resistor, their product is always positive (or zero), meaning the resistor always absorbs power.
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50What is the value of the 'operator ' squared ()?
A.1
B.-1
C.j
D.
Correct Answer: -1
Explanation:Since , squaring it yields .
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