Lesson 5.7 — Single-Phase and Three-Phase Power

§00

Safety Briefing

⚡ Danger — 480V Three-Phase

Three-phase power at 480V is the most common source of severe electrical injury and electrocution in industrial facilities. Contact with energized 480V conductors is almost always fatal. Arc flash energy at 480V bus can reach hundreds of calories per cm².

🟡 Yellow Risk — L2 Guided Practice

In this lesson you learn to READ and UNDERSTAND three-phase systems. You do NOT work on energized 3-phase equipment as part of this lesson.

Application of this knowledge on real equipment requires QEP (Qualified Electrical Person) status and proper PPE per NFPA 70E Arc Flash requirements. At a minimum: arc-rated clothing, voltage-rated gloves, and face shield.

Any measurement of 3-phase circuits requires direct supervision by a QEP. Never assume a circuit is de-energized.

ℹ Level 2 Reminder

L2 lessons introduce skills through guided practice and demonstration. You are not authorized to perform unsupervised work on the systems discussed here until you reach the appropriate qualification level. Study this material, ask questions, and observe before you act.

§01

Overview

Almost all power delivered to industrial facilities arrives as 3-phase AC. Whether you are reading motor control center (MCC) drawings, troubleshooting a pump that won’t start, sizing a feeder conductor, or trying to understand why a breaker keeps tripping — you need to understand three-phase power.

Single-phase power is the foundation, but three-phase is the workhorse of industry. Nearly every motor larger than about 1 HP in an industrial facility is three-phase. Understanding why requires going back to the physics of AC power delivery.

This lesson covers:

Why three-phase power exists and its advantages over single-phase
How three-phase voltage waveforms are generated and the 120° phase relationship
Wye (Y) vs. delta (Δ) connections and how to identify them on drawings
Voltage relationships in wye systems — the √3 factor
Power calculations for both single-phase and three-phase systems
Common North American system voltages you will encounter in the field
Reading motor nameplates for phase, voltage, and current information

§02

Learning Objectives

Upon completion of this lesson you will be able to:

L5-07-01
Explain why three-phase power is used instead of single-phase for industrial applications, including the constant power delivery advantage and conductor efficiency advantage.
L5-07-02
Describe how three-phase voltage waveforms are generated and their 120° phase relationship, including the A-B-C phase sequence and its effect on motor rotation direction.
L5-07-03
Distinguish between wye (Y) and delta (Δ) configurations and correctly identify each connection type from an electrical schematic or wiring diagram.
L5-07-04
Calculate line voltage from phase voltage in wye systems using V_L = V_P × √3 (1.732), and apply this relationship to common industrial system voltages.
L5-07-05
Calculate apparent power (VA), true power (W), and reactive power (VAR) in both single-phase and three-phase systems using the appropriate formulas, including the √3 factor for three-phase.
L5-07-06
Identify the 4-wire wye system, explain why the neutral conductor exists, and state the condition under which neutral current approaches zero in a balanced system.
L5-07-07
Read a motor nameplate and correctly identify single-phase vs. three-phase equipment, rated voltage, full load amps (FLA), service factor (SF), insulation class, and NEMA design letter.

§03

Prerequisites

ℹ Required Prior Lessons

Lessons 5.1 through 5.6 are required before beginning this lesson. Pay particular attention to:

Lesson 5.3 — AC Principles: You must understand sinusoidal waveforms, RMS voltage, frequency, and power factor before proceeding. The √3 relationships in three-phase only make sense if you understand phasors and RMS values. Review power triangle (P, Q, S) and power factor angle.
Lesson 5.5 — Transformers: Three-phase transformers are how utility power is stepped down to facility voltages. Wye and delta connections appear throughout transformer design. You need to understand turns ratio before studying system voltage relationships.
Lesson 5.6 — Series/Parallel Circuits: Understanding how circuit elements combine is essential for reading single-line diagrams of 3-phase distribution systems and for troubleshooting.

§04

Why Three-Phase Power?

The Problem with Single-Phase

Single-phase power pulsates. Because instantaneous power equals voltage times current (p = v × i), and both v and i are sine waves in a resistive circuit, the instantaneous power oscillates between zero and its peak value. At 60 Hz, this means power hits zero 120 times per second — twice every cycle.

For a motor, this means torque is not constant. The motor receives power in pulses, creating vibration and stress on the shaft. Single-phase motors require starting capacitors, run capacitors, and centrifugal switches just to operate. They are mechanically less efficient, harder to start under load, and more maintenance-intensive.

How Three-Phase Solves the Pulsation Problem

Three-phase power uses three voltages of equal magnitude and frequency, each separated by exactly 120° in time. When Phase A is near its zero crossing, Phase B and Phase C are each at 86.6% of peak, delivering substantial power. The three phases take turns at peak delivery, perfectly filling each other’s valleys.

The mathematical result is remarkable: the total instantaneous power in a balanced three-phase system is perfectly constant — it never pulsates, never hits zero. This gives three-phase motors their characteristic smooth, steady torque.

✓ Key Insight — Constant Power Delivery

Mathematically: P_A(t) + P_B(t) + P_C(t) = constant, for any balanced 3-phase load. This is why 3-phase motors run smoother, cooler, and longer than equivalent single-phase motors. It is also why virtually every industrial motor above 1 HP is three-phase.

Economic and Efficiency Advantages

Factor	Single-Phase	Three-Phase
Conductor usage	2 wires to deliver power	3 wires carry 173% the power of 2 wires at same V and I
Motor torque	Pulsating — requires capacitors and aux components	Constant — simple, robust squirrel-cage design
Motor frame size for same HP	Larger, heavier frame required	Smaller, lighter motors for identical output
Starting characteristics	Poor under load; needs capacitors	Excellent — self-starting with high locked-rotor torque
Distribution losses	Higher for equivalent power delivery	Lower — balanced load reduces I²R losses per conductor
Generator efficiency	Windings produce power for only half each cycle	All windings loaded simultaneously at all times

ℹ The 73% Rule

Three conductors in a 3-phase, 3-wire system can carry approximately 173% of the power that two conductors in a single-phase, 2-wire system carry, at the same voltage and current rating per conductor. You add only 50% more conductor (3 vs. 2) but deliver 73% more power. This efficiency advantage is why utilities transmit all long-distance power as three-phase.

§05

Three-Phase Waveforms

A three-phase system consists of three sinusoidal voltages of equal magnitude and equal frequency, separated by exactly 120° — one-third of a complete 360° cycle. On an oscilloscope, you see three identical sine waves spaced evenly in time.

Phase A (L1) — 0° reference

Phase B (L2) — 120° lagging

Phase C (L3) — 240° lagging

Animated three-phase waveforms rotating in real time. At any instant, the algebraic sum of all three instantaneous values equals zero in a balanced system.

Phase Sequence (Rotation)

The order in which the phases reach their positive peak is the phase sequence or phase rotation. The standard sequence in US industrial facilities is A-B-C (also called positive sequence or ACB depending on the standard). You may also see it called L1-L2-L3.

⚠ Phase Sequence and Motor Rotation — Critical Field Knowledge

The direction a three-phase induction motor rotates is entirely determined by phase sequence at its terminals. Swap any two of the three line connections at the motor — for example, swap L1 and L2 — and the motor reverses direction instantly.

This is both a useful commissioning tool (reverse a pump by swapping two leads at the starter) and a real hazard (incorrect wiring on initial installation will run equipment backward, potentially damaging the driven load or injuring workers). Always check rotation on initial commissioning before coupling the motor to its driven equipment. Use a rotation meter on the supply conductors, or bump-start the motor uncoupled and observe shaft direction.

The Zero-Sum Property of Balanced Three-Phase

At any instant in time, the sum of the three instantaneous phase voltages (or currents) in a balanced three-phase system equals exactly zero:

V_A(t) + V_B(t) + V_C(t) = 0 Balanced 3-phase instantaneous voltage sum = 0 at all times

This property has a critical practical consequence: in a perfectly balanced system, the neutral conductor carries zero current. The three phase currents cancel completely at the neutral point. As loads become unbalanced (different single-phase loads on each phase), the neutral carries the difference current.

§06

Wye (Y) Connection

The wye (or star) connection is the most common configuration in US industrial and commercial facilities. It uses four conductors: L1, L2, L3, and Neutral (N). Each phase winding is connected between a line conductor and a common central neutral point — giving the connection its Y-shaped appearance on a schematic.

When you see a system labeled 480Y/277V or 208Y/120V, the “Y” confirms it is wye-connected, and the two numbers are the line-to-line and line-to-neutral voltages respectively.

The Square-Root-of-3 Relationship

In a wye system, the line-to-line voltage (V_L) is larger than the line-to-neutral (phase) voltage (V_P) by a factor of √3 = 1.732. This comes from the geometry of adding two phasors that are 60° apart (because 180° − 120° = 60°).

V_L = V_P × √3 = V_P × 1.732 Wye: line-to-line voltage from line-to-neutral voltage

V_P = V_L ÷ √3 = V_L ÷ 1.732 Wye: line-to-neutral voltage from line-to-line voltage

System Designation	V_L-L	V_L-N	Verification
480Y/277V	480V	277V	480 ÷ 1.732 = 277V ✓
208Y/120V	208V	120V	120 × 1.732 = 208V ✓
600Y/347V	600V	347V	600 ÷ 1.732 = 346.5V ✓

✓ Why Both Voltages Matter in the Field

480Y/277V systems (most common industrial): The 277V phase-to-neutral voltage powers commercial and industrial lighting. HID fixtures, fluorescent ballasts, and LED drivers rated 277V connect between one hot leg and neutral. The same switchboard that feeds 480V three-phase motors also feeds 277V lighting — from one transformer, one set of conductors, two voltage levels.

208Y/120V systems (commercial buildings): The familiar 120V single-phase outlet (for computers, power tools, etc.) is simply one hot leg and neutral from this system. The 208V three-phase feeds HVAC compressors and small motors. This is why office buildings have 120V receptacles and 208V equipment from the same panel.

The Role of the Neutral Conductor

Balanced three-phase loads only: Neutral current = 0A. The neutral is electrically unnecessary but still code-required. You’ll find it on the neutral bus, reading zero amps on a clamp meter when loads are balanced.
Unbalanced single-phase loads: When 120V or 277V loads are unevenly distributed across the three phases (the normal condition in any building), the neutral carries the difference current. Heavily unbalanced panels can have neutral currents approaching or exceeding line current.
Harmonic currents: Nonlinear loads (variable frequency drives, computers, LED drivers) generate 3rd-order harmonics that add rather than cancel in the neutral. This is why modern code requires oversized neutrals in circuits serving electronic loads.

Wye (Y) connection: three phase windings share a common neutral point. Each winding is the phase voltage (277V). Line-to-line voltage = 480V = 277V × √3.

L1 / Phase A

L2 / Phase B

L3 / Phase C

Neutral (N)

§07

Delta (Δ) Connection

The delta connection forms a closed triangle (Δ). Each phase winding connects directly between two line conductors. Delta uses only three conductors — there is no neutral conductor and no neutral point.

Delta systems are common for motor-only feeders, ungrounded industrial systems, and legacy industrial installations. If you encounter a 3-wire motor feeder with no neutral, it is fed from a delta source or a 3-wire wye source without a neutral run to the load.

Delta Voltage Relationship

In delta, the windings are the line connections — each winding spans directly between two line terminals. There is no separate neutral, so there is no phase-to-neutral voltage without an external reference. The line-to-line voltage equals the winding (phase) voltage:

V_L = V_P Delta: line voltage equals phase (winding) voltage — no √3 factor

A 480V delta system has 480V across every winding. There is no 277V available without an additional transformer step. Delta cannot supply 277V lighting or 120V single-phase loads directly.

Delta System Variations — Field Hazards

⚠ Corner-Grounded Delta

One corner of the delta triangle is connected to earth ground. This creates asymmetric voltages to ground: one phase reads 0V to ground, and the other two read full line voltage to ground. A technician expecting symmetric voltages (as in wye) can be fatally surprised. Always measure all three phases to ground before working on any unfamiliar delta system.

⚠ Ungrounded Delta

Nothing is connected to earth. A single ground fault does not immediately trip any overcurrent device — the circuit remains complete through the other two phases. The fault can persist silently for days or weeks. Meanwhile, the two unfaulted conductors are elevated above ground potential, making a second ground fault catastrophically dangerous. Requires an active ground fault monitor (often called a ground fault indicator or GFI panel).

⚡ High-Leg Delta (Wildcat Delta) — NEC 110.15

A 240V delta transformer bank with a center-tap neutral on one winding creates the “high-leg” (also called “wild leg” or “stinger leg”). This produces three asymmetric conditions:

Two legs at 120V to neutral — safe for standard 120V single-phase loads
One high leg at approximately 208V to neutral — this is the wild leg

Per NEC 110.15, the high leg conductor must be identified with orange color at every point where it is accessible. The high leg CANNOT supply 120V loads. A 120V device connected to the high leg will see 208V and almost certainly fail catastrophically — often with fire. Always check for orange wiring in older industrial panels from the 1970s–2000s era.

Delta (Δ) connection: each winding connects directly between two line terminals. No neutral point exists.
Line voltage = phase (winding) voltage = 480V.

L1 / Phase A

L2 / Phase B

L3 / Phase C

§08

Power in Single-Phase and Three-Phase Systems

Single-Phase Power Formulas

S = V × ISingle-phase apparent power (volt-amperes, VA)

P = V × I × PFSingle-phase true (real) power (watts, W)

Q = V × I × sin(θ)Single-phase reactive power (volt-amperes reactive, VAR)

PF = cos(θ) = P ÷ SPower factor — ratio of true to apparent power

Three-Phase Power Formulas

Three-phase power adds a √3 factor. This arises from the geometry of three phasors equally spaced 120° apart: their vector sum is larger than any one individually by the factor √3. Use line-to-line voltage and line current in all three-phase power formulas.

S = √3 × V_L × I_L = 1.732 × V_L × I_LThree-phase apparent power (VA) — always use line voltage and line current

P = √3 × V_L × I_L × PFThree-phase true (real) power (watts)

I_L = S ÷ (√3 × V_L)Three-phase line current from apparent power — use for conductor sizing

HP = kW ÷ 0.746Motor shaft horsepower from input kilowatts (1 HP = 746 W)

ℹ Always Use Line Values in Three-Phase Formulas

When using S = √3 × V_L × I_L, always use line-to-line voltage and line current. These are the values on motor nameplates and clamp-meter readings. The √3 factor internally accounts for whether the system is wye or delta. You do not need to know wye vs. delta to use this formula.

Power Comparison — Same Conductor Gauge, Different Systems

Configuration	Current / Conductor	Power Delivered	Relative Efficiency
1-phase, 2-wire, 120V	100A	12,000 VA	Baseline (1×)
1-phase, 2-wire, 240V	100A	24,000 VA	2× baseline
3-phase, 3-wire, 208V	100A	36,059 VA	3.0× — 50% more wire, 3× more power
3-phase, 3-wire, 480V	100A	83,136 VA	6.9× baseline — the industrial standard

Note: 3-phase 208V calculation: 1.732 × 208 × 100 = 36,026 VA. 3-phase 480V: 1.732 × 480 × 100 = 83,136 VA.

Worked Example — Feeder Sizing

A 30 HP three-phase motor at 480V has efficiency η = 93.6% and power factor PF = 0.87. What is the expected full-load line current?

Output = 30 HP × 746 W/HP = 22,380 W
Input = Output ÷ η = 22,380 ÷ 0.936 = 23,909 W
Apparent power S = P ÷ PF = 23,909 ÷ 0.87 = 27,482 VA
Line current I_L = S ÷ (1.732 × 480) = 27,482 ÷ 831 = 33.1 A
Nameplate will show approximately 34A FLA

§09

Interactive 3-Phase Power Calculator

Power Calculator

Enter system type, voltage, current, and power factor. All results update instantly.

System Type

Voltage

Custom Voltage (V)

Current I_L (A)

Power Factor (0–1)

Apparent Power (S)

—

True Power (P)

—

Reactive Power (Q)

—

Est. Motor HP

—

Motor HP → Line Current

Enter nameplate HP, system voltage, motor efficiency, and power factor to find expected full-load line current and overload relay set point.

Motor HP

Supply Voltage (V)

Efficiency η (0–1)

Power Factor (0–1)

Phase Current Imbalance Checker

Enter measured current on each phase. NEMA MG1 limits current imbalance to 5% for proper motor operation. Excessive imbalance causes overheating and premature winding failure. A 1% voltage imbalance creates approximately 6–10% current imbalance.

Phase A (A)

Phase B (A)

Phase C (A)

§10

Common 3-Phase System Voltages in North America

You will encounter these systems regularly. Memorize the 480Y/277V system — it is the default for US industrial work and the system you will work around most frequently in the field.

System	Configuration	V_L-L	V_L-N	Common Applications
208Y/120V	Wye, 4-wire	208V	120V	Commercial buildings, light industrial, office HVAC, data centers
240/120V High-Leg Δ	High-leg delta, 4-wire	240V	120V (2 legs) / 208V (orange leg)	Legacy commercial/industrial — pre-1980s. Orange high leg cannot supply 120V loads per NEC 110.15
480Y/277V	Wye, 4-wire	480V	277V	Most common US industrial — motors, MCCs, switchgear, distribution panelboards, 277V industrial lighting
480Δ (ungrounded)	Delta, 3-wire	480V	N/A — no neutral	Motor-only feeders; older industrial; requires GFI monitoring; no single-phase loads possible without transformer
600Y/347V	Wye, 4-wire	600V	347V	Canadian standard — direct equivalent of US 480Y/277V; common in all Canadian industrial facilities
4,160V	Delta or wye	4,160V	Varies	Primary distribution, large motors (>500 HP), utility sub-transmission to facility service entrance
13.8 kV	Wye, 3-wire or 4-wire	13,800V	7,967V	Utility distribution primary voltage; facility primary if very large industrial campus; mine distribution

⚠ “460V” vs “480V” — Nameplate Tolerance Explained

Motors rated “460V” are designed for use on 480V systems. The 460V nameplate rating reflects the expected voltage at the motor terminals after line drop through the feeder conductors under full load. The National Electrical Code and NEMA allow ±10% from nameplate voltage for motor operation. Running a 460V-rated motor on 480V supply is within this tolerance and is the design intent.

§11

Reading a Three-Phase Motor Nameplate

Every motor nameplate contains all the information needed to select proper wire size, overcurrent protection, motor starter, overload relay, and drive (if variable speed). Learning to read nameplates quickly and accurately is a fundamental field skill.

⚡ ACME INDUSTRIAL MOTORS — NAMEPLATE DATA

HP30

VOLTS460

AMPS (FLA)34.0 A

PHASE3 PH

HERTZ60 Hz

RPM1,765

SF (Service Factor)1.15

EFF (Efficiency)93.6%

PF (Power Factor)0.87

INS CLASSF

NEMA FRAME215T

DESIGNB

CODE LETTERG

ENCLOSURETEFC

Field-by-Field Explanation

Field	Value	What It Means in the Field
HP	30 HP	Rated mechanical shaft output. 30 HP = 22.4 kW of mechanical power delivered to the driven equipment.
VOLTS	460V	Designed for 480V systems. Nameplate says 460V to account for expected line drop. Accept 414V–506V (±10% of 460V).
AMPS (FLA)	34.0 A	Full Load Amps — current drawn at rated load, voltage, and frequency. Primary number for overload relay sizing. Set relay to 100–115% of FLA per NEC 430.52.
PHASE	3 PH	Three-phase motor. Requires three-phase supply. Do not connect to single-phase without a phase converter (performance will be poor).
HERTZ	60 Hz	Designed for 60 Hz. On a 50 Hz grid (Europe, most of Asia), synchronous speed and output torque are reduced by 5/6 = 83%.
RPM	1,765	Full-load shaft speed. Synchronous speed for 4-pole motor at 60 Hz = 1,800 RPM. Slip = (1800−1765)/1800 = 1.9%. Used to select gearbox and coupling.
SF	1.15	Service Factor — motor can sustain 1.15 × 34A = 39.1A continuously without thermal damage, at the cost of higher temperature rise and reduced efficiency. Not intended for continuous operation at SF.
EFF	93.6%	Motor efficiency at rated full load. Electrical input = 22,380W (30 HP × 746) ÷ 0.936 = 23,910W. NEMA Premium Efficiency threshold for 30 HP = 93.0% — this motor exceeds it.
PF	0.87	Power factor at full load. Induction motors draw lagging current due to magnetizing reactance. PF < 1.0 always. VFDs and capacitor banks are used to correct low power factor.
INS CLASS	F	Insulation Class — maximum continuous winding temperature. Class F = 155°C max. Class H = 180°C. Higher class allows higher ambient temperature and longer motor life. Class F motor running in Class B (130°C) conditions has significant thermal margin.
NEMA FRAME	215T	Standardized mounting dimensions. 215T defines shaft height (5.375"), bolt pattern, and shaft diameter (1.375"). Any 215T motor from any manufacturer mounts identically — enables direct replacement without baseplate changes.
DESIGN	B	NEMA design letter. Design B = standard general-purpose: normal starting torque (150% FLT), normal starting current, low slip. Design C = high starting torque for hard-to-start loads (conveyors, compressors). Design D = very high starting torque, high slip (punch presses).
CODE LETTER	G	Starting kVA code. Code G = 5.6–6.3 kVA/HP locked-rotor kVA. For 30 HP: starting kVA = 30 × 6.0 = 180 kVA. Used to size feeder for inrush current and determine motor controller requirements. Higher code = higher inrush.
ENCLOSURE	TEFC	Totally Enclosed Fan Cooled — sealed against dust and moisture, external fan on shaft provides cooling. Suitable for most industrial outdoor and dirty environments. ODP (Open Drip-Proof) is indoor-only.

✓ Field Tip — Identifying 3-Phase Equipment at a Glance

Three-phase equipment shows one or more of:

“3 PH” or “3∅” in the phase field
Three terminal screws labeled T1, T2, T3 (motor side) or L1, L2, L3 (line side)
Voltage labeled 208, 230, 460, or 480 (without a slash) alongside “3PH”
A wiring diagram showing a triangle or Y with three connections

Single-phase shows “1 PH” or “1∅”, or simply two terminals, or a voltage of 115V, 120V, 208V/1PH, or 240V/1PH.

§12

Knowledge Assessment

Answer all five questions, then click Submit All Answers to see your score. A score of 4/5 (80%) or higher is required to complete this lesson.

Q1 — In a 480Y/277V wye system, what is the voltage measured from L1 to the neutral conductor?

A) 480V B) 277V C) 208V D) 120V

Q2 — A 480V three-phase motor draws 45A on each line conductor. What is the approximate apparent power?

A) 21,600 VA (480 × 45) B) 37,411 VA (√3 × 480 × 45) C) 64,800 VA (480 × 45 × 3) D) 480 VA

Q3 — A three-phase delta transformer bank has a high leg (wild leg). Per NEC Section 110.15, what color must the high leg conductor be identified with at all accessible points?

A) Blue B) Orange C) Red D) White with orange stripe

Q4 — A three-phase induction motor is running clockwise and needs to run counterclockwise. What is the correct method to reverse its rotation?

A) Increase the supply voltage B) Swap any two of the three line connections at the motor terminals C) Swap all three line connections simultaneously D) Change from wye to delta connection internally

Q5 — A perfectly balanced 480Y/277V system supplies only three-phase loads — no single-phase loads are connected to the neutral. What current flows in the neutral conductor?

A) Equal to line current multiplied by √3 B) Equal to line current C) Equal to line current divided by √3 D) Zero — the three balanced phase currents cancel completely at the neutral point

0/5

§13

Summary

✓ Key Takeaways — Lesson 5.7

Three-phase delivers constant, non-pulsating power because three sine waves offset 120° fill each other’s valleys. No torque pulsation means smoother motors, less vibration, longer bearing life.
Wye (Y) systems have four conductors (L1, L2, L3, N) and two usable voltages: line-to-line (480V) and line-to-neutral (277V). The √3 factor (1.732) relates them: 277 × 1.732 = 480V.
Delta (Δ) systems have three conductors and no neutral. Line voltage equals phase (winding) voltage. Beware corner-grounded, ungrounded, and high-leg delta configurations — each has unique hazards.
The √3 factor (1.732) appears in every three-phase calculation: wye voltage conversion, three-phase apparent power (S = √3 × V_L × I_L), and line current calculation.
Phase sequence (A-B-C) determines motor rotation. Swap any two phases at the motor terminals to reverse rotation. Use a phase rotation meter on initial commissioning.
Neutral current in a balanced 3-phase system = 0A. Imbalance between phases (unequal single-phase loading) drives neutral current. Nonlinear loads add 3rd harmonic current to the neutral.
Motor nameplates contain everything needed: FLA for overload sizing, rated voltage, HP and efficiency for power calculations, SF for overload tolerance, insulation class for environmental suitability, and NEMA frame for physical replacement dimensions.

Formula Reference Card

Formula	Variables	Use For
V_L = V_P × 1.732	V_L = line-to-line, V_P = line-to-neutral	Wye: find line voltage from phase voltage
V_P = V_L ÷ 1.732	Same	Wye: find phase voltage from line voltage
S = V × I	Single-phase	Single-phase apparent power (VA)
S = 1.732 × V_L × I_L	Three-phase	Three-phase apparent power (VA)
P = S × PF	Any system	True power from apparent power (W)
I_L = S ÷ (1.732 × V_L)	Three-phase	Line current from apparent power — feeder sizing
HP = kW ÷ 0.746	Motor	Shaft horsepower from electrical kilowatts
V_L = V_P (delta)	Delta only	Delta: line voltage equals winding voltage

ℹ Coming Up Next

Lesson 5.8 — Grounding and Bonding: Building directly on this lesson, 5.8 covers why and how three-phase systems are grounded, the critical difference between grounding (connecting to earth) and bonding (connecting metal parts together), NEC Article 250 grounding requirements for 480V wye systems, ground fault protection methods for both wye and delta systems, and how arc flash energy relates to grounding configuration. Grounding and bonding errors are a leading cause of electrical fatalities in industrial facilities.