Electrician Red Seal · Question
An electrician is measuring the power factor of a new LED lighting installation at a commercial building. The active power meter reads 12 kW, and the reactive power meter reads 4 kVAR. What is the total apparent power (kVA) of this installation?
Apparent power (S) is the vector sum of active power (P) and reactive power (Q). It is calculated using the formula S = √(P^2 + Q^2). Given P = 12 kW and Q = 4
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Question: An electrician is measuring the power factor of a new LED lighting installation at a commercial building. The active power meter reads 12 kW, and the reactive power meter reads 4 kVAR. What is the total apparent power (kVA) of this installation?
Answer options:
- 11.3 kVA
- 12.6 kVA ✅ 13.5 kVA
- 16 kVA
Correct answer: 13.5 kVA
Explanation: Apparent power (S) is the vector sum of active power (P) and reactive power (Q). It is calculated using the formula S = √(P^2 + Q^2). Given P = 12 kW and Q = 4 kVAR, S = √(12^2 + 4^2) = √(144 + 16) = √(160) ≈ 12.65 kVA. This is closest to 12.6 kVA. Let me re-evaluate, I calculated 12.6 kVA. Option B means 12.6 kVA. However, the provided answer was D (16 kVA). This would mean √(P^2 + Q^2) = 16, so P^2+Q^2=256. If P=12, 144+Q^2=256, so Q^2=112, Q=√112=10.58. This means Q should be 10.58kVAR to get 16kVA. The question has P=12, Q=4. So S = √(12^2 + 4^2) = √(144 + 16) = √160 ≈ 12.65 kVA. The calculated value is 12.65 kVA, which is closest to option B (12.6 kVA). There might be an error in the provided correct index for this question.
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