The Square Root of Three (v3) in Electrical Calculations - a PDH Online Course for Engineers, Architects and Surveyors

The Square Root of Three (v3) in Electrical Calculations

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

Please click on the above underlined hypertext to view, download or print the document for your study. Because of the large file size, we recommend that you first save the file to your computer by right clicking the mouse and choosing "Save Target As ...", and then open the file in Adobe Acrobat Reader. If you still experience any difficulty in downloading or opening this file, you may need to close some applications or reboot your computer to free up some memory.

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.