Print this page The Square Root of Three (v3) in Electrical Calculations
David A. Snyder, P.E.
Course Outline
This 2 PDH course illustrates with scaled drawings and simple mathematics the geometry of three-phase voltages and currents from which the square root of three emerges as a common thread.
This course includes a multiple-choice quiz at the end, which is designed to enhance the understanding of the course materials.
Learning Objective
At the conclusion of this course, the student will:
- Understand the relationship between three-phase voltages;
- Understand how line currents going to balanced three-phase delta-connected loads are related to the currents inside of the delta;
- Understand how connecting a balanced three-phase load in wye instead of delta affects the voltage applied to the load and the resulting current;
- Understand the line currents going to balanced and unbalanced delta-connected and wye-connected three-phase loads;
- Understand how the KVA ratings of closed-delta and open-delta transformer banks are related;
- Understand the reason the square root of three (√3) appears in balanced, three-phase voltage drop calculations.
Intended Audience
Any engineer, designer, contractor, or technician who is involved in three-phase electrical circuits, calculations, and installations will benefit from this course. It is assumed that the Reader is familiar with vector representation of three-phase voltages and currents.
Benefit to Attendees
Upon successful completion of the course, the reader will have a thorough understanding of the reasons the square root of three (√3) is used in three-phase electrical calculations.
Course Introduction
Everyone knows that we divide the KW or KVA of a balanced three-phase load by the square root of three (√3) in order to get the full-load amps required by that load, but many people don’t realize why we do that. The square root of three is also used in voltage drop calculations for balanced three-phase loads. The square root of three is the relationship between the two voltages in a 480Y/277V system and between the two voltages in a 208Y/120V system. It is the 120° separation between each of the three-phase voltages that is the driving force behind our use of the square root of three in electrical calculations for three-phase systems.
Course Content
This course content is in the following PDF document:
The Square Root of Three (v3) in Electrical Calculations
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Course Summary
It is common practice to use the square root of three (√3) in three-phase electrical calculations, from transformer and load line currents to voltage-drop calculations, but why is that? The square root of three (√3) is an inescapable property of three-phase systems, and the reasons why are illustrated in this course with scaled drawings and simple mathematics.
Quiz
Once you finish studying the above course content, you need to take a quiz to obtain the PDH credits.
DISCLAIMER: The materials contained in the online course are not intended as a representation or warranty on the part of PDH Center or any other person/organization named herein. The materials are for general information only. They are not a substitute for competent professional advice. Application of this information to a specific project should be reviewed by a registered architect and/or professional engineer/surveyor. Anyone making use of the information set forth herein does so at their own risk and assumes any and all resulting liability arising therefrom.
