Impedance and admittance

Chapter Impedance and admittance

Teach Yourself Electricity and Electronics Third Edition Book
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Summary of Contents

Teach Yourself Electricity and Electronics Third Edition Book

  • 15CHAPTERImpedance andadmittanceYOU’VE SEEN HOW INDUCTIVE AND CAPACITIVE REACTANCE CAN BE REPRE-sented along a line perpendicular to resistance. In this chapter, you’ll put all three ofthese quantities—R, XL, and XC—together, forming a complete, working definition ofimpedance. You’ll also get acquainted with admittance, impedance’s evil twin.To express the behavior of alternating-current (ac) circuits, you need two dimen-sions, because ac has variable frequency along with variable current. One dimension(resistance) will suffice for dc, but not for ac.In this chapter and the two that follow, the presentation is rather mathematical. Youcan get a grasp of the general nature of the subject matter without learning how to doall of the calculations presented. The mathematics is given for those of you who wish togain a firm understanding of how ac circuits behave.Imaginary numbersWhat does the lowercase j actually mean in expressions of impedance such as 4 j7 and45j83? This was briefly discussed earlier in this book, but what is this thing, really?Mathematicians use the lowercase letter i to represent j. (Mathematicians andphysicists/engineers often differ in notation as well as in philosophy.) This imaginarynumber is the square root of 1. It is the number that, when multiplied by itself, gives1. So ij, and jj1.The entire set of imaginary numbers derives from this single unit. The square of animaginary number is negative—always. No real number has this property. Whether areal number is positive, zero, or negative, its square can never be negative—never.The notion of j (or i, if you’re a mathematician) came about simply because somemathematicians wondered what the square root of 1 would behave like, if there weresuch a thing. So the mathematicians “imagined” the existence of this animal, and foundthat it had certain properties. Eventually, the number i was granted a place among the264Copyright © 2002, 1997, 1993 by The McGraw-Hill Companies. Click here for terms of use.