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ElectricalCalculationsHandbookEC&MsThis page intentionally left blank.EC&MsElectricalCalculationsHandbookJohn M.Paschal,Jr.,P.E.McGraw-HillNew YorkSan FranciscoWashington,D.C.AucklandBogotCaracasLisbonLondonMadridMexico CityMilanMontrealNew DelhiSan JuanSingaporeSydneyTokyoTorontoCopyright 2001 by The McGraw-Hill Companies,Inc.All rights reserved.Manufactured in theUnited States of America.Except as permitted under the United States Copyright Act of 1976,nopart of this publication may be reproduced or distributed in any form or by any means,or storedin a database or retrieval system,without the prior written permission of the publisher.0-07-141480-0The material in this eBook also appears in the print version of this title:0-07-136095-6.All trademarks are trademarks of their respective owners.Rather than put a trademark symbolafter every occurrence of a trademarked name,we use names in an editorial fashion only,and tothe benefit of the trademark owner,with no intention of infringement of the trademark.Wheresuch designations appear in this book,they have been printed with initial caps.McGraw-Hill eBooks are available at special quantity discounts to use as premiums and salespromotions,or for use in corporate training programs.For more information,please contactGeorge Hoare,Special Sales,at george_hoaremcgraw- or(212)904-4069.TERMS OF USEThis is a copyrighted work and The McGraw-Hill Companies,Inc.(“McGraw-Hill”)and itslicensors reserve all rights in and to the work.Use of this work is subject to these terms.Exceptas permitted under the Copyright Act of 1976 and the right to store and retrieve one copy of thework,you may not decompile,disassemble,reverse engineer,reproduce,modify,create deriva-tive works based upon,transmit,distribute,disseminate,sell,publish or sublicense the work orany part of it without McGraw-Hills prior consent.You may use the work for your own non-commercial and personal use;any other use of the work is strictly prohibited.Your right to usethe work may be terminated if you fail to comply with these terms.THE WORK IS PROVIDED“AS IS”.McGRAW-HILL AND ITS LICENSORS MAKE NOGUARANTEES OR WARRANTIES AS TO THE ACCURACY,ADEQUACY OR COM-PLETENESS OF OR RESULTS TO BE OBTAINED FROM USING THE WORK,INCLUD-ING ANY INFORMATION THAT CAN BE ACCESSED THROUGH THE WORK VIAHYPERLINK OR OTHERWISE,AND EXPRESSLY DISCLAIM ANY WARRANTY,EXPRESS OR IMPLIED,INCLUDING BUT NOT LIMITED TO IMPLIED WARRANTIESOF MERCHANTABILITYOR FITNESS FOR APARTICULAR PURPOSE.McGraw-Hill andits licensors do not warrant or guarantee that the functions contained in the work will meet yourrequirements or that its operation will be uninterrupted or error free.Neither McGraw-Hill norits licensors shall be liable to you or anyone else for any inaccuracy,error or omission,regard-less of cause,in the work or for any damages resulting therefrom.McGraw-Hill has no respon-sibility for the content of any information accessed through the work.Under no circumstancesshall McGraw-Hill and/or its licensors be liable for any indirect,incidental,special,punitive,consequential or similar damages that result from the use of or inability to use the work,even ifany of them has been advised of the possibility of such damages.This limitation of liability shallapply to any claim or cause whatsoever whether such claim or cause arises in contract,tort orotherwise.DOI:10.1036/0071414800ContentsPrefacexiiiChapter 1.Basic Electrical Working Definitions and Concepts1Voltage as Potential Difference1Current3Resistance4Direct-Current(dc)Voltage Sources4Direct and Alternating Current5dc Voltage6Current Flow in a Resistive Circuit15Current Flow in a Series Resistive Circuit16Voltage Division in a Series Circuit18Power Rating of a Resistor18ac Voltage23ac Circuits with Resistance23ac Phase Angle and Power26Current and Power in a Single-Phase ac Circuit33Current and Power in a Three-Phase ac Circuit33Inductive Reactance42Capacitive Reactance46Impedance52Chapter 2.Three-Phase Systems55Wye-Connected Systems58Delta-Connected Systems60vxi For more information about this book,click here.List of Problems Copyright 2001 by The McGraw-Hill Companies,Inc.Click here for Terms of Use.Chapter 3.Mathematics for Electrical Calculations,Power Factor Correction,and Harmonics69Changing Vectors from Rectangular to Polar Form and Back Again69Adding Vectors70Multiplying or Dividing Vectors74Solving for Current and Power Factor in an ac Circuit Containing Only Inductive Reactance75Solving for Current and Power Factor in an ac Circuit Containing Both Inductive Reactance and Resistance in Series with One Another77Solving for Current and Power Factor in an ac Circuit Containing Two Parallel Branches That Both Have InductiveReactance and Resistance in Series with One Another77Solving for Current and Power Factor in an ac Circuit Containing Parallel Branches,One of Which Has InductiveReactance and Resistance in Series with One Another and the Other of Which Has a Capacitive Reactance79Electrical Power