physics : class12 Volt-Ampere Reactive : Wattless Current : Electromagnetic Induction and Alternating Currents MCQ Questions and Answers
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Volt-Ampere Reactive
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MCQ Questions
1. An AC circuit has an rms voltage of 240 V, an rms current of 5 A, and a power factor of 0.6 lagging. What are its apparent power and volt-ampere reactive?
A.
1200 VA and 960 var
B.
1200 VA and 720 var
C.
720 VA and 960 var
D.
960 VA and 1200 var
Correct Answer:
1200 VA and 960 var
Explanation:
The apparent power is S = V_rms I_rms = 240 × 5 = 1200 VA. Since cos φ = 0.6, sin φ = 0.8, so the reactive power is Q = S sin φ = 1200 × 0.8 = 960 var. The lagging nature indicates inductive reactive power.
2. A purely inductive AC load is connected to a 230 V rms supply and draws 4 A rms. Which statement correctly describes its volt-ampere reactive?
A.
It consumes 920 W of average power and has 0 var reactive power
B.
It has 920 VA apparent power and 920 var inductive reactive power
C.
It has 0 VA apparent power and 920 var inductive reactive power
D.
It has 920 VA apparent power and 0 var reactive power
Correct Answer:
It has 920 VA apparent power and 920 var inductive reactive power
Explanation:
For a purely inductive load, the phase angle is 90 degrees, so the power factor is zero and average power is zero. However, S = VI = 230 × 4 = 920 VA, and |Q| = S sin 90° = 920 var. The reactive power is inductive.
3. Two AC loads are connected in parallel to the same 200 V rms supply. Load 1 consumes 800 W at unity power factor, while load 2 absorbs 600 var inductively. What is the total apparent power supplied?
A.
1000 VA
B.
1400 VA
C.
200 VA
D.
600 VA
Correct Answer:
1000 VA
Explanation:
The total active power is P = 800 W and the total reactive power is Q = 600 var, since the first load has zero reactive power. Therefore, the total apparent power is S = √(P² + Q²) = √(800² + 600²) = 1000 VA.
4. An AC circuit has apparent power 2500 VA and consumes 1500 W. If its reactive power is inductive, what is the magnitude of its volt-ampere reactive?
A.
1000 var
B.
2000 var
C.
2500 var
D.
4000 var
Correct Answer:
2000 var
Explanation:
The power triangle gives S² = P² + Q². Thus, Q = √(S² − P²) = √(2500² − 1500²) = √(4,000,000) = 2000 var. Because the reactive power is inductive, it is conventionally positive.
5. A capacitor and an inductor are connected in parallel across an AC source. The capacitor draws 900 var and the inductor absorbs 1400 var. Neglecting resistance, what is the net volt-ampere reactive of the combination?
A.
2300 var inductive
B.
500 var inductive
C.
500 var capacitive
D.
0 var
Correct Answer:
500 var inductive
Explanation:
Inductive reactive power is positive and capacitive reactive power is negative. Therefore, Q_net = 1400 − 900 = 500 var. The positive result means that the combination has a net inductive volt-ampere reactive.
6. An AC load has a current of 8 A rms and a power factor of 0.5 leading when connected to a 250 V rms source. What is its reactive power according to the usual sign convention?
A.
+1732 var
B.
−1732 var
C.
+1000 var
D.
−1000 var
Correct Answer:
−1732 var
Explanation:
The apparent power is S = 250 × 8 = 2000 VA. Since cos φ = 0.5, sin φ = √3/2. Thus |Q| = 2000 × √3/2 ≈ 1732 var. A leading current indicates capacitive behavior, so Q is negative: −1732 var.
7. A single-phase load has an apparent power of 5 kVA and a reactive power of 3 kVAR. What fraction of the apparent power is converted into average active power?
A.
0.4
B.
0.6
C.
0.8
D.
1.25
Correct Answer:
0.8
Explanation:
The active power is P = √(S² − Q²) = √(5² − 3²) kW = 4 kW. The fraction of apparent power represented by active power is P/S = 4/5 = 0.8, which is also the magnitude of the power factor.
8. A load draws 12 A rms from a 250 V rms supply at a lagging power factor of 0.8. A capacitor is connected in parallel to correct the overall power factor to unity. What reactive power must the capacitor supply?
A.
600 var capacitive
B.
1200 var capacitive
C.
1800 var capacitive
D.
3000 var capacitive
Correct Answer:
1800 var capacitive
Explanation:
The original apparent power is S = 250 × 12 = 3000 VA. With cos φ = 0.8, sin φ = 0.6, so the inductive reactive power is Q = 3000 × 0.6 = 1800 var. Unity power factor requires an equal capacitive reactive power of 1800 var to cancel it.
9. In an AC circuit, the rms voltage is 120 V and the rms current is 10 A. The current lags the voltage by 60 degrees. Which pair gives the average power and the volt-ampere reactive?
A.
600 W and 1039 var inductive
B.
1039 W and 600 var inductive
C.
1200 W and 0 var
D.
600 W and 600 var capacitive
Correct Answer:
600 W and 1039 var inductive
Explanation:
The apparent power is S = 120 × 10 = 1200 VA. Average power is P = S cos 60° = 1200 × 0.5 = 600 W. Reactive power is Q = S sin 60° = 1200 × 0.866 ≈ 1039 var. Since current lags voltage, the reactive power is inductive.
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