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Steinmetz Decoded

Impedance, Reactance, And Admittance

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Why This Family Matters

Section titled “Why This Family Matters”

Routes the formulas that became the everyday language of AC circuit calculation.

211

candidate records in this family.

122

reviewable relation candidates.

7

sources represented.

Candidate Formula Cards

Section titled “Candidate Formula Cards”
#1Theory and Calculation of Alternating Current PhenomenaChapter 4: Graphic Befrisxintation- line 2301
(resistance, r, and the reactance, x = 2irNLy - where A^ =)
OCR source lineresistance, r, and the reactance, x = 2irNLy - where A^ =
#2Theory and Calculation of Alternating Current PhenomenaChapter 7: Admittance, Conductance, Susceptance- line 3151
(the term conductance, g = 1 / r. If, then, a number of con-)
OCR source linethe term conductance, g = 1 / r. If, then, a number of con-
#3Theory and Calculation of Alternating Current PhenomenaChapter 7: Admittance, Conductance, Susceptance- line 3260
(1.) If r = QO , or x = oo , since in this case no current)
OCR source line1.) If r = QO , or x = oo , since in this case no current
#4Theory and Calculation of Alternating Current PhenomenaChapter 7: Admittance, Conductance, Susceptance- line 3266
(2.) If r = 0, since in this case the current which passes)
OCR source line2.) If r = 0, since in this case the current which passes
#5Theory and Calculation of Alternating Current PhenomenaChapter 7: Admittance, Conductance, Susceptance- line 3273
(1.) If x = oo , or r = oo .)
OCR source line1.) If x = oo , or r = oo .
#6Theory and Calculation of Alternating Current PhenomenaChapter 7: Admittance, Conductance, Susceptance- line 3329
(a maximum for r = x, where g - 1 / 2 r is equal to the)
OCR source linea maximum for r = x, where g - 1 / 2 r is equal to the
#7Theory and Calculation of Alternating Current PhenomenaChapter 7: Admittance, Conductance, Susceftance- line 3679
(1.) If r = oc , or ^ = 00 , since in this case no current)
OCR source line1.) If r = oc , or ^ = 00 , since in this case no current
#8Theory and Calculation of Alternating Current PhenomenaChapter 7: Admittance, Conductance, Susceftance- line 3685
(2.) If r = 0, since in this case the current which passes)
OCR source line2.) If r = 0, since in this case the current which passes
#9Theory and Calculation of Alternating Current PhenomenaChapter 7: Admittance, Conductance, Susceftance- line 3692
(1.) If ^ = Qo , or r = 00 .)
OCR source line1.) If ^ = Qo , or r = 00 .
#10Theory and Calculation of Alternating Current PhenomenaChapter 7: Admittance, Conductance, Susceftance- line 3694
(2.) If.r=0.)
OCR source line2.) If.r=0.
#11Theory and Calculation of Alternating Current PhenomenaChapter 7: Admittance, Conductance, Susceftance- line 3738
(hence, zY = (^’ + ^ (^’ + ^^ = 1 ;)
OCR source linehence, zY = (^’ + ^ (^’ + ^^ = 1 ;
#12Theory and Calculation of Alternating Current PhenomenaChapter 7: Admittance, Conductance, Susceftance- line 3762
(a maximum for r =x, where ^ = 1 / 2r is equal to the)
OCR source linea maximum for r =x, where ^ = 1 / 2r is equal to the
#13Theory and Calculation of Alternating Current PhenomenaChapter 8: Admittance, Conductance, Susceptance- line 4218
(1. If r = oo^ or a: = co ^ since in this case there is no current,)
OCR source line1. If r = oo^ or a: = co ^ since in this case there is no current,
#14Theory and Calculation of Alternating Current PhenomenaChapter 9: Circuits Containing Resistance, Inductive Reactance, And Condensive Reactance- line 5137
((d) If X = 0, that is, if the receiver circuit is non-inductive,)
OCR source line(d) If X = 0, that is, if the receiver circuit is non-inductive,
#15Theory and Calculation of Alternating Current PhenomenaChapter 4: Graphic Representation- line 2141
(E0> a resistance \mathrm{e.m.f.}, Er = fr, a reactance \mathrm{e.m.f.},)
OCR source lineE0> a resistance E.M.F., Er = fr, a reactance E.M.F.,
#16Theory and Calculation of Alternating Current PhenomenaChapter 1: Introduction- line 1127
(the \mathrm{e.m.f.} consumed by reactance is : <?2 = /v/;, :)
OCR source linethe E.M.F. consumed by reactance is : <?2 = /v/;, :
#17Theory and Calculation of Alternating Current PhenomenaChapter 1: Introduction- line 1382
(and the ratio, e I i = 2 ir A^Ly is the magnetic reactance :)
OCR source lineand the ratio, e I i = 2 ir A^Ly is the magnetic reactance :
#18Theory and Calculation of Alternating Current PhenomenaChapter 4: Graphic Representation- line 2243
(To overcome the reactance, x0 = 2 •*• n0 L0 , of the pri-)
OCR source lineTo overcome the reactance, x0 = 2 •*• n0 L0 , of the pri-
#19Theory and Calculation of Alternating Current PhenomenaChapter 7: Admittance, Conductance, Susceptance- line 3232
(y = Vr1 + P ;)
OCR source liney = Vr1 + P ;
#20Theory and Calculation of Alternating Current PhenomenaChapter 7: Admittance, Conductance, Susceptance- line 3251
(reactance x = 0, or in continuous-current circuits, is the)
OCR source linereactance x = 0, or in continuous-current circuits, is the
#21Theory and Calculation of Alternating Current PhenomenaChapter 7: Admittance, Conductance, Susceptance- line 3254
(Again, only in circuits with zero resistance (r = 0) is)
OCR source lineAgain, only in circuits with zero resistance (r = 0) is
#22Theory and Calculation of Alternating Current PhenomenaChapter 7: Admittance, Conductance, Susceptance- line 3327
(b, decreases from b = 1 / x at r = 0, to # = 0 at r = cc ;)
OCR source lineb, decreases from b = 1 / x at r = 0, to # = 0 at r = cc ;
#23Theory and Calculation of Alternating Current PhenomenaChapter 7: Admittance, Conductance, Susceptance- line 3328
(while the conductance, g - 0 at r = 0, increases, reaches)
OCR source linewhile the conductance, g - 0 at r = 0, increases, reaches
#24Theory and Calculation of Alternating Current PhenomenaChapter 7: Admittance, Conductance, Susceptance- line 3545
(from g = 1 / r to 0, and the susceptance passing from 0 at)
OCR source linefrom g = 1 / r to 0, and the susceptance passing from 0 at
#25Theory and Calculation of Alternating Current PhenomenaChapter 7: Admittance, Conductance, Susceptance- line 3546
(x = 0 to the maximum, b = 1 / 2 r = g =1 / ‘2 x at x = r,)
OCR source linex = 0 to the maximum, b = 1 / 2 r = g =1 / ‘2 x at x = r,
#26Theory and Calculation of Alternating Current PhenomenaChapter 7: Admittance, Conductance, Susceftance- line 3673
(Again, only in circuits with zero resistance (r = 0) is)
OCR source lineAgain, only in circuits with zero resistance (r = 0) is
#27Theory and Calculation of Alternating Current PhenomenaChapter 7: Admittance, Conductance, Susceftance- line 3761
(while the conductance, ^ = at r=0, increases, reaches)
OCR source linewhile the conductance, ^ = at r=0, increases, reaches
#28Theory and Calculation of Alternating Current PhenomenaChapter 7: Admittance, Conductance, Susceftance- line 3841
(jr = to the maximum, ^ = l/2r = ^=l/2;r at-r=r,)
OCR source linejr = to the maximum, ^ = l/2r = ^=l/2;r at-r=r,
#29Theory and Calculation of Alternating Current PhenomenaChapter 8: Admittance, Conductance, Susceptance- line 4093
(is the sum of the individual resistances, K = ri + r2 + ra + …)
OCR source lineis the sum of the individual resistances, K = ri + r2 + ra + …
#30Theory and Calculation of Alternating Current PhenomenaChapter 8: Admittance, Conductance, Susceptance- line 4114
(is the sum of the individual conductances, or G = gi — g2 —)
OCR source lineis the sum of the individual conductances, or G = gi -\- g2 -\-
#31Theory and Calculation of Alternating Current PhenomenaChapter 8: Admittance, Conductance, Susceptance- line 4212
(Again, only in circuits with zero resistance (r = 0) is the)
OCR source lineAgain, only in circuits with zero resistance (r = 0) is the
#32Theory and Calculation of Alternating Current PhenomenaChapter 8: Admittance, Conductance, Susceptance- line 4331
(resistance, r, is varied from r = 0 to r = 00^ the susceptance,)
OCR source lineresistance, r, is varied from r = 0 to r = 00^ the susceptance,
#33Theory and Calculation of Alternating Current PhenomenaChapter 8: Admittance, Conductance, Susceptance- line 4333
(6, decreases from 6 = - at r = 0, to 6 = 0 at r = 00 ; while the)
OCR source line6, decreases from 6 = - at r = 0, to 6 = 0 at r = 00 ; while the
#34Theory and Calculation of Alternating Current PhenomenaChapter 8: Admittance, Conductance, Susceptance- line 4351
(z = /r2 + x2 = -•)
OCR source linez = \/r2 + x2 = -•
#35Theory and Calculation of Alternating Current PhenomenaChapter 8: Admittance, Conductance, Susceptance- line 4363
(^ = - to 0, and the susceptance passing from 0 at x = 0 to the)
OCR source line^ = - to 0, and the susceptance passing from 0 at x = 0 to the
#36Theory and Calculation of Alternating Current PhenomenaChapter 8: Admittance, Conductance, Susceptance- line 4365
(maximum, 6 = i7- = y = .^ata; = r, and to 6 = 0 at x = oo .)
OCR source linemaximum, 6 = i7- = y = .^ata; = r, and to 6 = 0 at x = oo .
#37Theory and Calculation of Alternating Current PhenomenaChapter 8: Capacity- line 4429
(series reactance continues up to ;r^ = ± 1.6, or, ;r = - 2;r,)
OCR source lineseries reactance continues up to ;r^ = ± 1.6, or, ;r = - 2;r,
#38Theory and Calculation of Alternating Current PhenomenaChapter 8: Capacity- line 4437
(At ;r^ = ± .8, ;r = ^ .8, the total impedance of the circuit)
OCR source lineAt ;r^ = ± .8, ;r = ^ .8, the total impedance of the circuit
#39Theory and Calculation of Alternating Current PhenomenaChapter 9: Circuits Containing Resistance, Inductive Reactance, And Condensive Reactance- line 4752
(Eo = ^^7T^;)
OCR source lineEo = ^^7T^;
#40Theory and Calculation of Alternating Current PhenomenaChapter 9: Circuits Containing Resistance, Inductive Reactance, And Condensive Reactance- line 4853
(LINDRESISTAJUGECONSTAJ^T n =.2)
OCR source lineLINDRESISTAJUGECONSTAJ^T n =.2
#41Theory and Calculation of Alternating Current PhenomenaChapter 9: Circuits Containing Resistance, Inductive Reactance, And Condensive Reactance- line 4855
(V._^ n = .8)
OCR source lineV._^ n = .8
#42Theory and Calculation of Alternating Current PhenomenaChapter 9: Circuits Containing Resistance, Inductive Reactance, And Condensive Reactance- line 4975
((a) To = 0.2 ohm (Curve I))
OCR source line(a) To = 0.2 ohm (Curve I)
#43Theory and Calculation of Alternating Current PhenomenaChapter 9: Circuits Containing Resistance, Inductive Reactance, And Condensive Reactance- line 4976
((6) ro = 0.8 ohm (Curve II))
OCR source line(6) ro = 0.8 ohm (Curve II)
#44Theory and Calculation of Alternating Current PhenomenaChapter 9: Circuits Containing Resistance, Inductive Reactance, And Condensive Reactance- line 4979
(X = -1- 1.0 to a; = - 1.0 ohm.)
OCR source lineX = -1- 1.0 to a; = - 1.0 ohm.
#45Theory and Calculation of Alternating Current PhenomenaChapter 9: Circuits Containing Resistance, Inductive Reactance, And Condensive Reactance- line 4981
(As shown, / and E are smallest for x = 0, r = 1.0, or for)
OCR source lineAs shown, / and E are smallest for x = 0, r = 1.0, or for
#46Theory and Calculation of Alternating Current PhenomenaChapter 9: Circuits Containing Resistance, Inductive Reactance, And Condensive Reactance- line 4982
(the non-inductive receiver circuit, and largest for x = ± 1.0,)
OCR source linethe non-inductive receiver circuit, and largest for x = ± 1.0,
#47Theory and Calculation of Alternating Current PhenomenaChapter 9: Circuits Containing Resistance, Inductive Reactance, And Condensive Reactance- line 4983
(r = 0, or for the wattless circuit, in which latter a series resist-)
OCR source liner = 0, or for the wattless circuit, in which latter a series resist-
#48Theory and Calculation of Alternating Current PhenomenaChapter 9: Circuits Containing Resistance, Inductive Reactance, And Condensive Reactance- line 4996
(For ro = 0.8 and x = 0, x = -^ 0.8, x = - 0.8, the vector)
OCR source lineFor ro = 0.8 and x = 0, x = -^ 0.8, x = - 0.8, the vector
#49Theory and Calculation of Alternating Current PhenomenaChapter 9: Circuits Containing Resistance, Inductive Reactance, And Condensive Reactance- line 5044
(Z ^ r -^jx, z = Vr2”+x2-)
OCR source lineZ ^ r -^jx, z = Vr2”+x2-
#50Theory and Calculation of Alternating Current PhenomenaChapter 9: Circuits Containing Resistance, Inductive Reactance, And Condensive Reactance- line 5122
(or, Xo = - 2x.)
OCR source lineor, Xo = - 2x.
#51Theory and Calculation of Alternating Current PhenomenaChapter 9: Circuits Containing Resistance, Inductive Reactance, And Condensive Reactance- line 5140
(E = ^0^ _ Eo)
OCR source lineE = ^0^ _ Eo
#52Theory and Calculation of Alternating Current PhenomenaChapter 9: Circuits Containing Resistance, Inductive Reactance, And Condensive Reactance- line 5177
(I r=1.0 x = 0 ■^ =)
OCR source lineI r=1.0 x = 0 ■^ =
#53Theory and Calculation of Alternating Current PhenomenaChapter 9: Circuits Containing Resistance, Inductive Reactance, And Condensive Reactance- line 5179
(HI r = -6 x=-.8)
OCR source lineHI r = -6 x=-.8
#54Theory and Calculation of Alternating Current PhenomenaChapter 9: Circuits Containing Resistance, Inductive Reactance, And Condensive Reactance- line 5422
(z = 1.0, r = 1.0, a; = 0 (Curve I))
OCR source linez = 1.0, r = 1.0, a; = 0 (Curve I)
#55Theory and Calculation of Alternating Current PhenomenaChapter 9: Circuits Containing Resistance, Inductive Reactance, And Condensive Reactance- line 5423
(z = 1.0, r = 0.6, X = 0.8 (Curve II))
OCR source linez = 1.0, r = 0.6, X = 0.8 (Curve II)
#56Theory and Calculation of Alternating Current PhenomenaChapter 9: Circuits Containing Resistance, Inductive Reactance, And Condensive Reactance- line 5424
(z = 1.0, r = 0.6, X = - 0.8 (Curve III).)
OCR source linez = 1.0, r = 0.6, X = - 0.8 (Curve III).
#57Theory and Calculation of Alternating Current PhenomenaChapter 9: Circuits Containing Resistance, Inductive Reactance, And Condensive Reactance- line 5446
(value £■ = 167 volts, or E = Eq- This rise of potential by)
OCR source linevalue £■ = 167 volts, or E = Eq- This rise of potential by
#58Theory and Calculation of Alternating Current PhenomenaChapter 9: Circuits Containing Resistance, Inductive Reactance, And Condensive Reactance- line 5448
(series reactance continues up to Xo = + 1.6, or, Xo = - 2x,)
OCR source lineseries reactance continues up to Xo = + 1.6, or, Xo = - 2x,
#59Theory and Calculation of Alternating Current PhenomenaChapter 9: Circuits Containing Resistance, Inductive Reactance, And Condensive Reactance- line 5452
(At rro = ± 0.8, x = + 0.8, the total impedance of the circuit)
OCR source lineAt rro = ± 0.8, x = + 0.8, the total impedance of the circuit
#60Theory and Calculation of Alternating Current PhenomenaChapter 9: Kbsistanci: And Kbactance Of Transmission Iine8- line 7006
(constant susceptance b = - .142 \)
OCR source lineconstant susceptance b = - .142 \
#61Theory and Calculation of Electric ApparatusChapter 1: Speed Control Of Induction Motors- line 2664
(Z0 = r0 + jxo = primary self-inductive impedance;)
OCR source lineZ0 = r0 + jxo = primary self-inductive impedance;
#62Theory and Calculation of Electric ApparatusChapter 2: Multiple Squirrel-Cage Induction Motor- line 3668
(Zi = r2 + jx2 = self-inductive impedance at full frequency,)
OCR source lineZi = r2 + jx2 = self-inductive impedance at full frequency,
#63Theory and Calculation of Electric ApparatusChapter 2: Multiple Squirrel-Cage Induction Motor- line 3684
(Z0 = r0 + jx0 = primary self -inductive impedance, and)
OCR source lineZ0 = r0 + jx0 = primary self -inductive impedance, and
#64Theory and Calculation of Electric ApparatusChapter 4: Induction Motor With Secondary Excitation- line 5940
(l’”» = 8 - jk = primiiry exciting admittance)
OCR source linel’”» = 8 - jk = primiiry exciting admittance
#65Theory and Calculation of Alternating Current PhenomenaChapter 5: Symbouc Mbthod- line 3119
(then X = 2, icNL = magnetic reactance.)
OCR source linethen X = 2, icNL = magnetic reactance.
#66Theory and Calculation of Alternating Current PhenomenaChapter 8: Admittance, Conductance, Susceptance- line 4221
(2. If r = 0, since in this case the current in the circuit is in)
OCR source line2. If r = 0, since in this case the current in the circuit is in
#67Theory and Calculation of Alternating Current PhenomenaChapter 8: Admittance, Conductance, Susceptance- line 4227
(1. If a; = 00, or r = oo .)
OCR source line1. If a; = 00, or r = oo .
#68Theory and Calculation of Alternating Current PhenomenaChapter 8: Admittance, Conductance, Susceptance- line 4341
(then decreases again, reaching gr = 0 at r = «» .)
OCR source linethen decreases again, reaching gr = 0 at r = «» .
#69Theory and Calculation of Alternating Current PhenomenaChapter 9: Circuits Containing Resistance, Inductive Reactance, And Condensive Reactance- line 4972
(ceiver circuit, for £“0 = const. = 100 volts, z = \ ohm; hence)
OCR source lineceiver circuit, for £“0 = const. = 100 volts, z = \ ohm; hence
#70Theory and Calculation of Alternating Current PhenomenaChapter 9: Circuits Containing Resistance, Inductive Reactance, And Condensive Reactance- line 5449
(where E = 100 volts again; and for Xq > 1.6 the voltage drops)
OCR source linewhere E = 100 volts again; and for Xq > 1.6 the voltage drops
#71Theory and Calculation of Alternating Current PhenomenaChapter 7: Admittance, Conductance, Susceptance- line 3275
(2.) If * = 0.)
OCR source line2.) If * = 0.
#72Theory and Calculation of Alternating Current PhenomenaChapter 8: Admittance, Conductance, Susceptance- line 4315
(hence, 22^2 = (^.2 _[_ 3.2) (-^2 -|- 52) = ;[.)
OCR source linehence, 22^2 = (^.2 _[_ 3.2) (-^2 -|- 52) = ;[.