1
In the context of AC circuits, which notation is conventionally used to represent the instantaneous value of a voltage?
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Explanation:
Lower case letters (like or ) are conventionally used to represent instantaneous values, while capital letters (like or ) represent RMS or DC values.
2
What is the relationship between angular frequency ( ) and linear frequency ( )?
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Correct Answer:
Explanation:
The angular frequency in radians per second is equal to times the frequency in Hertz.
3
The time taken by an alternating quantity to complete one full cycle is called:
A. Amplitude
B. Frequency
C. Phase
D. Time Period
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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 ( ).
4
The maximum value attained by an alternating quantity during a positive or negative half cycle is known as:
A. Instantaneous value
B. Average value
C. Amplitude
D. RMS value
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Correct Answer: Amplitude
Explanation:
Amplitude (or Peak Value, or ) is the maximum displacement from the zero axis.
5
For a sinusoidal voltage , what is the Root Mean Square (RMS) value?
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Explanation:
For a sinusoidal wave, the RMS value is defined as the peak value divided by the square root of 2, which is approximately .
6
The average value of a sinusoidal alternating current over one complete cycle is:
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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.
7
The average value of a sinusoidal voltage over a half cycle is given by:
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Explanation:
The average value over a half cycle is .
8
Which factor is defined as the ratio of RMS value to the Average value?
A. Q Factor
B. Form Factor
C. Peak Factor
D. Power Factor
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Correct Answer: Form Factor
Explanation:
Form Factor = . For a sine wave, it is approximately 1.11.
9
What is the peak factor (crest factor) of a sinusoidal waveform?
A. 0.637
B. 1.414
C. 1.11
D. 0.707
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Correct Answer: 1.414
Explanation:
Peak factor is the ratio of Maximum Value to RMS Value ( ).
10
Two sinusoidal quantities are said to be in phase quadrature if their phase difference is:
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Explanation:
Phase quadrature implies a phase difference of 90 degrees or radians.
11
In the complex representation of impedance , what does the operator ' ' represent?
A. Rotation by
B. A scalar multiplier
C. Rotation by counter-clockwise
D. Rotation by clockwise
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Correct Answer: Rotation by counter-clockwise
Explanation:
In phasor algebra, multiplying a phasor by rotates it by in the counter-clockwise direction. Mathematically, .
12
What is the complex impedance of an ideal inductor with inductance at angular frequency ?
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Explanation:
Inductive reactance is . Since voltage leads current by , the impedance is represented as or .
13
What is the complex impedance of an ideal capacitor with capacitance ?
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Explanation:
Capacitive reactance is . Since current leads voltage by , the impedance is negative imaginary: or , which is equivalent to .
14
In a purely resistive AC circuit, what is the phase difference between voltage and current?
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Explanation:
In a pure resistor, the voltage and current are in phase, meaning the phase difference is zero.
15
In a series RL circuit , the current:
A. Is in phase with the voltage
B. Leads the applied voltage
C. Lags the applied voltage
D. Lags the voltage by exactly
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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 .
16
The magnitude of impedance in a series RL circuit is given by:
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Explanation:
The impedance is the vector sum of resistance and reactance: .
17
In a series RC circuit , the phase angle is given by:
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Correct Answer:
Explanation:
From the impedance triangle, , so .
18
Which of the following describes the power factor of a series RC circuit?
A. Unity
B. Leading
C. Zero
D. Lagging
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Correct Answer: Leading
Explanation:
In an RC circuit, the current leads the voltage, resulting in a leading power factor.
19
The total voltage applied to a series RL circuit with resistor voltage and inductor voltage is:
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Correct Answer:
Explanation:
AC voltages in series are added geometrically (phasor sum), not algebraically. Since and are apart, .
20
For a series RLC circuit, the total impedance is:
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Explanation:
The net reactance is the difference between inductive and capacitive reactance ( ). The total impedance is the hypotenuse of the impedance triangle.
21
In a series RLC circuit, if , the circuit behaves as:
A. Capacitive
B. Resistive
C. Inductive
D. Resonant
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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.
22
What is the condition for resonance in a series RLC circuit?
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Explanation:
Resonance occurs when the inductive reactance equals the capacitive reactance, cancelling each other out.
23
At resonance, the impedance of a series RLC circuit is:
A. Minimum and equal to
B. Equal to
C. Maximum
D. Zero
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Correct Answer: Minimum and equal to
Explanation:
Since , the impedance , which is the minimum possible impedance for the circuit.
24
What is the resonant frequency of a series RLC circuit?
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Explanation:
Derived from . Solving for gives .
25
At series resonance, the current in the circuit is:
A. Minimum
B. Infinite
C. Maximum
D. Zero
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Correct Answer: Maximum
Explanation:
Because impedance is at its minimum ( ), the current is at its maximum.
26
The power factor of a series RLC circuit at resonance is:
A. 0
B. 1 (Unity)
C. 0.5 leading
D. 0.5 lagging
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Correct Answer: 1 (Unity)
Explanation:
At resonance, the circuit is purely resistive ( ), so the phase angle is and .
27
The Quality Factor (Q-factor) of a series resonant circuit is given by:
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Explanation:
Q-factor is voltage magnification, defined as . Substituting , we get .
28
In AC circuits, Active Power (Real Power) is calculated as:
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Explanation:
Active power is the power actually consumed by the resistance, given by .
29
The unit of Reactive Power ( ) is:
A. Volt-Ampere (VA)
B. Joule (J)
C. Volt-Ampere Reactive (VAR)
D. Watt (W)
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Correct Answer: Volt-Ampere Reactive (VAR)
Explanation:
Reactive power represents energy oscillating between source and reactive components, measured in VAR.
30
Apparent 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
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Correct Answer: RMS Voltage and RMS Current
Explanation:
Apparent Power , measured in Volt-Amperes (VA).
31
Power factor is defined as the ratio of:
A. Impedance to Resistance ( )
B. Reactance to Resistance ( )
C. Resistance to Reactance ( )
D. Resistance to Impedance ( )
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Correct Answer: Resistance to Impedance ( )
Explanation:
From the impedance triangle, .
32
If the power factor is 0.8 lagging, it means:
A. The circuit is purely resistive
B. Current lags voltage and energy is stored in magnetic fields
C. The circuit is capacitive
D. Current leads voltage
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Correct Answer: Current lags voltage and energy is stored in magnetic fields
Explanation:
Lagging power factor indicates an inductive circuit where current lags voltage.
33
In a three-phase system, the voltages of the three phases are displaced from each other by:
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Explanation:
In a balanced three-phase system, the phase voltages are equal in magnitude and displaced by .
34
The order in which the voltages in the three phases reach their maximum positive value is called:
A. Frequency
B. Phase Difference
C. Alternation
D. Phase Sequence
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Correct Answer: Phase Sequence
Explanation:
Phase sequence (e.g., R-Y-B) describes the chronological order of peak values.
35
In a Star (Wye) connected three-phase system, the relationship between Line Current ( ) and Phase Current ( ) is:
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Explanation:
In a star connection, the line conductor is in series with the phase winding, so the current is the same.
36
In a Star (Wye) connected system, the Line Voltage ( ) relates to the Phase Voltage ( ) as:
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Explanation:
The line voltage is the vector difference of two phase voltages, resulting in a magnitude of times the phase voltage.
37
In a Delta (Mesh) connected three-phase system, the relationship between Line Voltage ( ) and Phase Voltage ( ) is:
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Explanation:
In a delta connection, the line conductors are connected directly across the phase windings, so .
38
In a Delta (Mesh) connected system, the Line Current ( ) relates to the Phase Current ( ) as:
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Explanation:
In delta, the line current is the vector difference of two phase currents, resulting in .
39
The total active power in a balanced three-phase circuit (Star or Delta) is given by:
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Explanation:
Total power is . Substituting line values for either Star or Delta yields .
40
Which three-phase connection requires four wires (3 phases + 1 neutral)?
A. Series Connection
B. Star Connection
C. Delta Connection
D. Mesh Connection
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Correct Answer: Star Connection
Explanation:
A Star connection has a common point (neutral point) allowing for a neutral wire, making it a 3-phase 4-wire system.
41
What is the unit of Admittance ( )?
A. Ohm ( )
B. Farad (F)
C. Henry (H)
D. Siemens (S) or Mho
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Correct Answer: Siemens (S) or Mho
Explanation:
Admittance is the reciprocal of impedance ( ), measured in Siemens (S) or Mho ( ).
42
The real part of Admittance is called:
A. Reactance
B. Conductance
C. Susceptance
D. Resistance
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Correct Answer: Conductance
Explanation:
Admittance , where is Conductance (real part).
43
If the frequency of the AC supply is increased, the capacitive reactance ( ):
A. Decreases
B. Increases
C. Becomes zero
D. Remains constant
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Correct Answer: Decreases
Explanation:
Since , reactance is inversely proportional to frequency. Increasing decreases .
44
If the frequency of the AC supply is increased, the inductive reactance ( ):
A. Remains constant
B. Becomes infinite
C. Decreases
D. Increases
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Correct Answer: Increases
Explanation:
Since , reactance is directly proportional to frequency. Increasing increases .
45
Which of the following represents the bandwidth of a series RLC circuit?
A.
B.
C.
D. All of the above
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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.
46
At half-power frequencies in a series RLC circuit, the current is:
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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.
47
The phase angle between Line Voltage and Phase Voltage in a Star connected system is:
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Explanation:
In a star connection, the line voltage leads the respective phase voltage by .
48
In a circuit with , what is the magnitude of the impedance?
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49
Instantaneous power in a pure resistive circuit is always:
A. Positive
B. Zero
C. Negative
D. Alternating positive and negative
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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.
50
What is the value of the 'operator ' squared ( )?
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Correct Answer: -1
Explanation:
Since , squaring it yields .