A new multifunction meter on a factory board shows three power figures. Which one is turned into work in the ovens and motors, and counted by the kWh meter?

Active power (kW) is the power turned into mechanical work, heat or light, and it is what the kWh meter counts. Apparent power is tempting because it is the biggest figure, but it is just r.m.s. volts times amps. Reactive power builds magnetic fields and does no work, and power factor is a ratio, not a power.

A fixed meter on a main switchboard reads 120 kW and 90 kvar. What is the power factor?

From the power triangle, kVA = √(120² + 90²) = 150 kVA, so PF = kW ÷ kVA = 120 ÷ 150 = 0.80. The 0.75 is kvar ÷ kW, which is tan φ, not the power factor. The 0.60 is kvar ÷ kVA (sin φ), and 1.33 is kW ÷ kvar, which cannot be a power factor because it is above 1.

A design sheet sized a sub-main for a new 60 kW three-phase 400 V line at 87 A, as if the power factor were 1. Logging shows the line actually runs at 0.75. What line current does it really draw?

I = P ÷ (√3 × VL × PF) = 60,000 ÷ (1.732 × 400 × 0.75) = 115.5 A. The 86.6 A figure is the design sheet’s mistake of leaving out the power factor. 200 A comes from leaving out √3, and 65.0 A from multiplying by the power factor instead of dividing, which would make a poor power factor look helpful.

Free mock exam

Power quality: power factor and harmonics — Industrial Electrical Practice

Free topic-focused mock exam: all 30 questions on Power quality: power factor and harmonics, drawn from the wider Industrial Electrical bank. 35-minute timer, 70% to pass, worked explanation on every question. Use this when you've taken the full mock once and want to drill the topics you got wrong.

Questions: 30
Time limit: 35 min
Pass mark: 70% · 21/30
Question bank: 30

Free, no sign-up. Retake as many times as you like — the questions are reshuffled, with the answer order changed.

Sample questions

01A new multifunction meter on a factory board shows three power figures. Which one is turned into work in the ovens and motors, and counted by the kWh meter?
- AReactive power, in kvar
- BActive power, in kW
- CApparent power, in kVA
- DPower factor, no unit
Why: Active power (kW) is the power turned into mechanical work, heat or light, and it is what the kWh meter counts. Apparent power is tempting because it is the biggest figure, but it is just r.m.s. volts times amps. Reactive power builds magnetic fields and does no work, and power factor is a ratio, not a power.
02A fixed meter on a main switchboard reads 120 kW and 90 kvar. What is the power factor?
- A0.60
- B0.75
- C1.33
- D0.80
Why: From the power triangle, kVA = √(120² + 90²) = 150 kVA, so PF = kW ÷ kVA = 120 ÷ 150 = 0.80. The 0.75 is kvar ÷ kW, which is tan φ, not the power factor. The 0.60 is kvar ÷ kVA (sin φ), and 1.33 is kW ÷ kvar, which cannot be a power factor because it is above 1.
03A design sheet sized a sub-main for a new 60 kW three-phase 400 V line at 87 A, as if the power factor were 1. Logging shows the line actually runs at 0.75. What line current does it really draw?
- A65.0 A
- B115.5 A
- C86.6 A
- D200.0 A
Why: I = P ÷ (√3 × VL × PF) = 60,000 ÷ (1.732 × 400 × 0.75) = 115.5 A. The 86.6 A figure is the design sheet’s mistake of leaving out the power factor. 200 A comes from leaving out √3, and 65.0 A from multiplying by the power factor instead of dividing, which would make a poor power factor look helpful.

Common questions

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