Q.1 What is the formula for the active power (P) in an AC circuit with voltage V, current I, and power factor PF?
P = V × I × PF
P = V ÷ I × PF
P = V × I ÷ PF
P = V + I × PF
Explanation - Active power is the real part of power, calculated by multiplying voltage, current, and the power factor.
Correct answer is: P = V × I × PF
Q.2 The apparent power (S) in an AC circuit is represented by which of the following expressions?
S = V × I × cos(φ)
S = V × I
S = V / I
S = V × I × sin(φ)
Explanation - Apparent power is the product of RMS voltage and RMS current, regardless of phase angle.
Correct answer is: S = V × I
Q.3 Which component in an AC circuit does not consume active power?
Resistor
Inductor
Capacitor
Both B and C
Explanation - Inductors and capacitors store energy but return it each cycle; they consume no net active power.
Correct answer is: Both B and C
Q.4 If a load has an apparent power of 10 kVA and a power factor of 0.8, what is its active power?
8 kW
12.5 kW
10 kW
4 kW
Explanation - Active power P = S × PF = 10 kVA × 0.8 = 8 kW.
Correct answer is: 8 kW
Q.5 What is the expression for reactive power (Q) in terms of apparent power (S) and power factor (PF)?
Q = S × sin(arccos(PF))
Q = S × PF
Q = S ÷ PF
Q = S × cos(arccos(PF))
Explanation - Reactive power is S multiplied by the sine of the phase angle, which is arccos(PF).
Correct answer is: Q = S × sin(arccos(PF))
Q.6 In a purely inductive circuit, the power factor is:
0
0.5
1
Negative
Explanation - An ideal inductor causes current to lag voltage by 90°, giving a power factor of cos(90°)=0.
Correct answer is: 0
Q.7 Which of the following represents the power triangle diagrammatically?
A right triangle with S as hypotenuse, P and Q as legs
A circle with S as radius
A square with P as diagonal
A line segment S = P + Q
Explanation - The power triangle shows apparent, active, and reactive power as the sides of a right triangle.
Correct answer is: A right triangle with S as hypotenuse, P and Q as legs
Q.8 An AC circuit has V = 120 V, I = 10 A, and φ = 30°. What is the active power?
1200 W
600 W
1040 W
2000 W
Explanation - P = V × I × cos(30°) = 120 × 10 × 0.866 ≈ 1040 W.
Correct answer is: 1040 W
Q.9 Which quantity is measured in volt-amperes reactive (VAR)?
Active Power
Reactive Power
Apparent Power
Power Factor
Explanation - Reactive power is measured in VARs, representing energy stored and released each cycle.
Correct answer is: Reactive Power
Q.10 If the apparent power is 15 kVA and the reactive power is 12 kVAR, what is the active power?
9 kW
12 kW
15 kW
21 kW
Explanation - P = √(S² - Q²) = √(15² - 12²) ≈ 9 kW.
Correct answer is: 9 kW
Q.11 A power factor of 0.9 lagging indicates:
Current leads voltage by about 25°
Current lags voltage by about 25°
Current lags voltage by 90°
Current leads voltage by 90°
Explanation - PF = cos(φ). cos⁻¹(0.9) ≈ 25°, so current lags voltage by that angle.
Correct answer is: Current lags voltage by about 25°
Q.12 What is the unit of power factor?
Volts
Amperes
Dimensionless
Watts
Explanation - Power factor is the cosine of the phase angle, a pure number without units.
Correct answer is: Dimensionless
Q.13 Which of these improves the power factor of an AC supply?
Adding more resistive load
Adding more inductive load
Adding power factor correction capacitors
Increasing line voltage
Explanation - Capacitors supply leading reactive power, offsetting lagging reactive power of inductive loads.
Correct answer is: Adding power factor correction capacitors
Q.14 The angle between voltage and current in an AC circuit is known as the:
Phase shift
Load factor
Frequency
Waveform
Explanation - It is the phase difference (φ) between voltage and current waveforms.
Correct answer is: Phase shift
Q.15 In a power triangle, if P = 3 kW and Q = 4 kVAR, what is S?
5 kVA
7 kVA
4 kVA
3 kVA
Explanation - S = √(P² + Q²) = √(3² + 4²) = 5 kVA.
Correct answer is: 5 kVA
Q.16 Which expression correctly represents reactive power for a capacitive load?
Q = V × I × sin(φ)
Q = V × I × cos(φ)
Q = -V × I × sin(φ)
Q = V × I × sin(φ)
Explanation - For capacitive loads, reactive power is negative, indicating leading power factor.
Correct answer is: Q = -V × I × sin(φ)
Q.17 What does a power factor of 1 indicate about the circuit?
All power is reactive
All power is active
No power is used
Voltage equals current
Explanation - PF = 1 (cos(0°)) means voltage and current are in phase, so all power is real.
Correct answer is: All power is active
Q.18 Which of the following is NOT a type of power in AC circuits?
Active power
Reactive power
Apparent power
Total power
Explanation - The three recognized types are active, reactive, and apparent; 'total' is not a distinct type.
Correct answer is: Total power
Q.19 A 60 Hz AC supply has a voltage of 230 V and an inductive load draws 5 A RMS. Calculate the apparent power.
1150 VA
115 VA
11500 VA
11500 W
Explanation - S = V × I = 230 × 5 = 1150 VA.
Correct answer is: 1150 VA
Q.20 If the phase angle φ is 120°, what is the power factor?
-0.5
0.5
-1
1
Explanation - PF = cos(120°) = -0.5, indicating a leading power factor (capacitive behavior).
Correct answer is: -0.5
Q.21 Which device is typically used to measure apparent power?
Ammeter
Volt-ampere meter (VAM)
Power meter
Oscilloscope
Explanation - A VAM directly measures apparent power (VA).
Correct answer is: Volt-ampere meter (VAM)
Q.22 Reactive power does not contribute to:
Heat generation in resistors
Magnetic field generation in inductors
Electrical field generation in capacitors
Both A and C
Explanation - Reactive power circulates energy but does not dissipate as heat in pure reactive components.
Correct answer is: Heat generation in resistors
Q.23 What is the effect of a poor power factor on a power distribution system?
Increased voltage drop
Reduced current carrying capacity
Both A and B
No effect
Explanation - Poor PF raises line currents, increasing voltage drops and requiring larger conductors.
Correct answer is: Both A and B
Q.24 Which of the following is a direct consequence of adding capacitors for power factor correction?
Lower reactive power
Higher reactive power
Lower apparent power
Both A and C
Explanation - Capacitors supply leading reactive power, reducing Q and thus reducing S.
Correct answer is: Both A and C
Q.25 For a load with S = 20 kVA and PF = 0.8 lagging, calculate reactive power (Q).
12 kVAR
16 kVAR
10 kVAR
8 kVAR
Explanation - Q = S × sin(arccos(0.8)) ≈ 20 × 0.6 = 12 kVAR.
Correct answer is: 12 kVAR
Q.26 In which scenario does the apparent power equal the active power?
PF = 0
PF = 1
PF = 0.5
PF = -1
Explanation - When PF is 1, reactive power is zero, so S = P.
Correct answer is: PF = 1
Q.27 A transformer rated at 10 kVA has a load drawing 8 kW. What is the power factor?
0.8
0.64
1.25
0.5
Explanation - PF = P / S = 8 / 10 = 0.8.
Correct answer is: 0.8
Q.28 Which formula gives the power factor for a circuit with known active and reactive power?
PF = P / √(P² + Q²)
PF = Q / √(P² + Q²)
PF = √(P² + Q²) / P
PF = P × Q
Explanation - Power factor is the ratio of real power to apparent power.
Correct answer is: PF = P / √(P² + Q²)
Q.29 Which component in an AC circuit causes current to lag voltage by 90 degrees?
Resistor
Inductor
Capacitor
Diode
Explanation - An ideal inductor creates a 90° lag between voltage and current.
Correct answer is: Inductor
Q.30 In a star-connected load, if each phase draws 10 A RMS at 230 V, what is the total apparent power of the three-phase system?
6.6 kVA
3.3 kVA
11.0 kVA
15.0 kVA
Explanation - S_total = √3 × V_line × I_phase = 1.732 × 230 × 10 ≈ 6.6 kVA.
Correct answer is: 6.6 kVA
Q.31 Reactive power is measured in:
Watts
Volt-Amperes
Volt-Amperes Reactive
Watt-Hours
Explanation - Reactive power’s unit is VAR, representing energy exchanged each cycle.
Correct answer is: Volt-Amperes Reactive
Q.32 Which of the following best describes a lagging power factor?
Current leads voltage
Current lags voltage
Voltage leads current
Voltage lags current
Explanation - Lagging indicates inductive loads where current follows voltage.
Correct answer is: Current lags voltage
Q.33 A load consumes 5 kW of active power and has a reactive power of 3 kVAR. What is its apparent power?
6 kVA
7 kVA
8 kVA
10 kVA
Explanation - S = √(5² + 3²) ≈ 7 kVA.
Correct answer is: 7 kVA
Q.34 When correcting power factor, which device is inserted in series with the load?
Capacitor bank
Inductor bank
Resistor bank
Diode bank
Explanation - Capacitors supply leading reactive power to offset lagging loads.
Correct answer is: Capacitor bank
Q.35 If the active power of a load is 4 kW and the apparent power is 5 kVA, what is the reactive power?
3 kVAR
1 kVAR
2 kVAR
4 kVAR
Explanation - Q = √(S² - P²) = √(5² - 4²) = 3 kVAR.
Correct answer is: 3 kVAR
Q.36 The power factor is often expressed as:
A ratio of voltages
A ratio of currents
A ratio of real to apparent power
A ratio of frequency to phase angle
Explanation - PF = P / S, the cosine of the phase angle.
Correct answer is: A ratio of real to apparent power
Q.37 Which of these is true for a perfectly balanced three-phase AC system with unity power factor?
S = 3 × V_line × I_line
S = √3 × V_line × I_line
S = V_line × I_line
S = V_phase × I_phase
Explanation - Apparent power for three-phase is √3 times the product of line voltage and current.
Correct answer is: S = √3 × V_line × I_line
Q.38 A capacitor bank provides 2 kVAR of reactive power. If the line voltage is 480 V, what is the required current per phase in a balanced 3-phase system?
10 A
5.4 A
15 A
20 A
Explanation - Q_total = 3 × V_phase × I_phase. V_phase = 480/√3 ≈ 277 V. So I = 2kVAR / (3×277) ≈ 5.4 A.
Correct answer is: 5.4 A
Q.39 What is the main reason engineers use power factor correction in industrial plants?
To increase voltage levels
To reduce the amount of reactive power drawn
To increase current consumption
To lower AC frequency
Explanation - Improved PF reduces line losses and allows smaller conductors.
Correct answer is: To reduce the amount of reactive power drawn
Q.40 For an AC load, the product of RMS voltage and RMS current is called:
Active power
Apparent power
Reactive power
Power triangle
Explanation - S = V × I gives apparent power in VA.
Correct answer is: Apparent power
Q.41 In a power triangle, the angle φ is 0°. What type of load is it?
Resistive
Inductive
Capacitive
None of the above
Explanation - Zero phase angle means voltage and current are in phase, indicating a purely resistive load.
Correct answer is: Resistive
Q.42 Which of the following indicates a leading power factor?
PF > 1
PF < 0
PF = 1
PF = 0.5
Explanation - Negative PF corresponds to leading power factor (capacitive behavior).
Correct answer is: PF < 0
Q.43 A 50 kVA transformer supplies a load drawing 35 kW active power. What is its power factor?
0.7
0.5
0.85
0.35
Explanation - PF = P / S = 35 / 50 = 0.7.
Correct answer is: 0.7
Q.44 If the active power is 0 W, what is the power factor of the load?
0
1
-1
Cannot be determined
Explanation - Zero active power indicates a purely reactive load, so PF = 0.
Correct answer is: 0
Q.45 Which of the following devices is used to measure both active and reactive power simultaneously?
Multimeter
Power analyzer
Voltmeter
Ammeter
Explanation - Power analyzers display P, Q, and S values together.
Correct answer is: Power analyzer
Q.46 The magnitude of the power triangle’s hypotenuse is:
Active power
Reactive power
Apparent power
Power factor
Explanation - Apparent power (S) is the vector sum of P and Q.
Correct answer is: Apparent power
Q.47 For a load with S = 10 kVA and PF = 0.8 lagging, what is the phase angle φ?
36.9°
53.1°
45°
30°
Explanation - φ = arccos(0.8) ≈ 36.9°.
Correct answer is: 36.9°
Q.48 What happens to the active power if the voltage is increased by 10% while current and power factor remain unchanged?
Increases by 10%
Increases by 20%
Decreases by 10%
Stays the same
Explanation - P = V × I × PF, so a 10% rise in V yields a 10% rise in P.
Correct answer is: Increases by 10%
Q.49 Which of the following best describes reactive power in an AC circuit?
Energy dissipated as heat
Energy stored and returned each cycle
Energy converted to mechanical work
Energy transferred to a load
Explanation - Reactive power represents energy that oscillates between source and reactive elements.
Correct answer is: Energy stored and returned each cycle
Q.50 A three-phase load draws 60 A per phase at 415 V line-to-line with unity power factor. What is the total active power?
90 kW
85 kW
120 kW
140 kW
Explanation - P_total = √3 × V_line × I × PF = 1.732 × 415 × 60 ≈ 90 kW.
Correct answer is: 90 kW
Q.51 If a capacitor provides -6 kVAR of reactive power, what is its effect on the circuit’s power factor?
Makes it lagging
Makes it leading
Reduces the magnitude of reactive power but not PF
Has no effect on PF
Explanation - -6 kVAR indicates leading reactive power, improving the PF toward unity.
Correct answer is: Makes it leading
Q.52 Which quantity is measured in VA?
Active power
Reactive power
Apparent power
Power factor
Explanation - Apparent power units are volt-amperes (VA).
Correct answer is: Apparent power
Q.53 In a power triangle, if P = 6 kW and φ = 45°, what is the apparent power S?
8.49 kVA
9.9 kVA
6 kVA
7 kVA
Explanation - S = P / cos(45°) = 6 / 0.7071 ≈ 8.49 kVA.
Correct answer is: 8.49 kVA
Q.54 Which of the following is the primary goal of power factor correction in commercial buildings?
Maximize reactive power
Minimize apparent power
Maximize apparent power
Minimize active power
Explanation - Reducing S lowers line losses and improves utility billing.
Correct answer is: Minimize apparent power
Q.55 A single-phase AC circuit has V = 120 V, I = 2 A, and φ = 30°. What is the reactive power?
40 VAR
41.6 VAR
60 VAR
120 VAR
Explanation - Q = V × I × sin(30°) = 120 × 2 × 0.5 = 120 VAR. (Wait calculation: 120*2=240, sin30=0.5 => 120 VAR.)
Correct answer is: 120 VAR