Phase, RMS Value & Power Factor Explained
Learn phase, three-phase 120 degree shift, RMS peak over root 2, power factor meaning cos phi, 0.8 shipboard value, capacitor bank improvement, and motor kW vs alternator kVA ratings.
1. Phase — AC With Company
DC has no phase — one steady direction, nothing to be out of step with. AC earns the term the moment two waves share a circuit: in-phase means V and I peaks coincide (pure resistance), while lag or lead means magnetism or capacitance is borrowing energy mid-cycle.
In phase — 0°
V and I reverse together. Every amp works. Power factor 1.0, the best possible.
Three-phase — 120°
Three equal waves march in rotation: near-constant total power, self-starting motors, survival on two wires if one phase dies.
Where DC still rules
Battery-fed navigation, control, alarms, communications and emergency lighting — steady magnetism, zero frequency, unity power factor.
Examiner shorthand: no phase in DC; 120° spacing in three-phase; zero angle between I and V means resistive.
2. RMS — the Heating Truth
Meters read root-mean-square: peak ÷ √2 for sine waves. Peaks run √2 higher and size insulation; RMS sizes work, cable heating and protection settings.
- Peak to RMS sine rule: ÷ √2
- RMS means ~325 V peak: 230 V
- RMS means ~622 V peak: 440 V
Why it matters at sea: a 440 V bus peaks above 620 V every half-cycle — insulation, clearances and test voltages answer to the peak, while load current and heat answer to RMS.
3. Power Factor — From 0.8 Toward 1
Power factor is cos φ between V and I: 1.0 on pure resistance (best possible), ~0.8 across a working ship where motors magnetise as they labour. Reactive power is not lost — it sustains the magnetic field that lets a motor turn real power into torque — but it still rides the cables as extra current.
- Best possible (resistive): 1.0
- Usual shipboard value: 0.8
- Linking the two ratings: kW = kVA × pf
| Rating | Unit | Names | Why |
|---|---|---|---|
| Motor output | kW | Duty | Shaft load is matched in watts; in-phase current does the work |
| Alternator / transformer size | kVA | Size | Copper heats on total current whatever the pf — designer plans for worst case |
| Single-phase | kVA = V×A/1000 | Apparent | kW = kVA × pf |
| Three-phase | kVA = V×A×1.73/1000 | Apparent | kW = kVA × pf |
Improvement: lagging plant corrects with capacitor banks supplying leading reactive current locally instead of dragging it down the cables — less line current, lower I²R losses, stiffer volts. Lightly loaded motors sit at poor pf, which is why energy-manager starters trim voltage at light load; an over-excited synchronous machine can even serve as a synchronous capacitor.
Oral closer: quote 0.8 usual, 1.0 best, cos φ definition, less current for the same kW as the benefit, capacitor banks as the fix — then name kW for duty, kVA for size.
Practise this in the question bank
- Electrical General — 30 questions
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