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Steinmetz Decoded

Symbolic AC And Complex Quantities

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Why This Family Matters

Section titled “Why This Family Matters”

Routes equations where Steinmetz turns alternating quantities into symbolic algebra.

364

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296

reviewable relation candidates.

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Candidate Formula Cards

Section titled “Candidate Formula Cards”
#1Theoretical Elements of Electrical EngineeringTheory Section 3: Generation of E.m.f.- line 1101
(e = 2 7r/n$ \sin r the instantaneous generated \mathrm{e.m.f.})
OCR source linee = 2 7r/n$ sin r the instantaneous generated e.m.f.
#2Theory and Calculation of Alternating Current PhenomenaChapter 5: Symbolic Method- line 3242
(B = 6’ + jh” = 6(\cos 13 + j \sin /3))
OCR source lineB = 6’ + jh” = 6(cos 13 + j sin /3)
#3Theory and Calculation of Alternating Current PhenomenaChapter 8: Circuits Containing Resistance, Inductance, And Capacity- line 4185
(is r - j (x -f x0} = r = .6, x + x0 = 0, and \tan S>0 = 0 ;)
OCR source lineis r - j (x -f x0} = r = .6, x + x0 = 0, and tan S>0 = 0 ;
#4Theory and Calculation of Alternating Current PhenomenaChapter 9: Circuits Containing Resistance, Inductive Reactance, And Condensive Reactance- line 5453
(is r - j {x + Xo) = r = 0.6, x -{- Xo = 0, and \tan do = 0; that)
OCR source lineis r - j {x + Xo) = r = 0.6, x -{- Xo = 0, and tan do = 0; that
#5Theory and Calculation of Electric ApparatusChapter 1: Speed Control Of Induction Motors- line 1689
(= - J = (\tan a - j) (7))
OCR source line= - J = (tan a - j) (7)
#6Theoretical Elements of Electrical EngineeringTheory Section 4: Power and Effective Values- line 1257
(If an alternating current i = I0 \sin 6 passes through a resist-)
OCR source lineIf an alternating current i = I0 sin 6 passes through a resist-
#7Theory and Calculation of Alternating Current PhenomenaChapter 1: Introduction- line 976
(1.) Ohm’s law : i = e j r, where r, the resistance, is a)
OCR source line1.) Ohm’s law : i = e j r, where r, the resistance, is a
#8Theory and Calculation of Alternating Current PhenomenaChapter 1: Introduction- line 1237
(1.) Ohm’s law : i = e j r, where r, the resistance, is a)
OCR source line1.) Ohm’s law : i = e j r, where r, the resistance, is a
#9Theory and Calculation of Alternating Current PhenomenaChapter 5: Symbolic Method- line 2645
(or, if E = e —je’ is the impressed \mathrm{e.m.f.}, and 7 = i ’ — ji’)
OCR source lineor, if E = e -\-je’ is the impressed E.M.F., and 7 = i ’ -\- ji’
#10Theory and Calculation of Alternating Current PhenomenaChapter 7: Polar Coordinates And Polar Diagrams- line 3818
(/, upon the \mathrm{e.m.f.}, or by IE \cos d, where 9 = angle of time-)
OCR source line/, upon the e.m.f., or by IE cos d, where 9 = angle of time-
#11Theory and Calculation of Alternating Current PhenomenaChapter 8: Capacity- line 4264
(but E = E^y I^E^j z. If x^ > - 2,t-, it raises, if ;r < - 2 jr,)
OCR source linebut E = E^y I^E^j z. If x^ > - 2,t-, it raises, if ;r < - 2 jr,
#12Theory and Calculation of Alternating Current PhenomenaChapter 9: Kbsistanci: And Kbactance Of Transmission Iine8- line 6819
(a maximum for dP^j db = 0, that is, according to § 61, if -)
OCR source linea maximum for dP^j db = 0, that is, according to § 61, if -
#13Theoretical Elements of Electrical EngineeringTheory Section 4: Power and Effective Values- line 1290
(\mathrm{e.m.f.}, e = EQ \sin 6.)
OCR source linee.m.f., e = EQ sin 6.
#14Four Lectures on Relativity and SpaceLecture 3: Gravitation And The Gravitational Fleld- line 3009
(at A and is \tan C02 = Vijv^ (thus being greater) when the)
OCR source lineat A and is tan C02 = Vijv^ (thus being greater) when the
#15Four Lectures on Relativity and SpaceLecture 4: The Characteristics Of Space A. The Geometry Of The Gravitational Field- line 4628
(R = j/VK. (15))
OCR source lineR = j/VK. (15)
#16General Lectures on Electrical EngineeringLecture 3: Light And Power Distribution- line 1459
(copper of No. 5, or j of ;j = ^: Cu. = ^)
OCR source linecopper of No. 5, or j of ;j = ^: Cu. = ^
#17Radiation, Light and IlluminationLecture 2: Relation Of Bodies To Radiation- line 1697
(FH = DH \sin a, and DL = DH \sin av (1))
OCR source lineFH = DH sin a, and DL = DH sin av (1)
#18Radiation, Light and IlluminationLecture 8: Arc Lamps And Arc Lighting- line 7233
(cubic hyperbolas: e^i = kz2; or, el =- £j and since we find for)
OCR source linecubic hyperbolas: e^i = kz2; or, el =- £j and since we find for
#19Radiation, Light and IlluminationLecture 10: Light Flux And Distribution- line 9574
(fc1 = 2 TT / \sin <t>dfa (3))
OCR source linefc1 = 2 TT / sin <t>dfa (3)
#20Theoretical Elements of Electrical EngineeringTheory Section 1: Magnetism and Electric Current- line 812
(\cos r = - - - - = 0.4)
OCR source linecos r = - - - - = 0.4
#21Theoretical Elements of Electrical EngineeringTheory Section 1: Magnetism and Electric Current- line 892
(iron is /z4 = 280 at B4 = 2850. Thus the field intensity/ H = - j)
OCR source lineiron is /z4 = 280 at B4 = 2850. Thus the field intensity/ H = - j
#22Theoretical Elements of Electrical EngineeringTheory Section 3: Generation of E.m.f.- line 1140
(e = 2 irfn&#36; \sin 2 IT} (t - ti))
OCR source linee = 2 irfn$ sin 2 IT} (t - ti)
#23Theoretical Elements of Electrical EngineeringTheory Section 3: Generation of E.m.f.- line 1141
(or, e = 2-jrfn&amp; \sin (6 - 0i),)
OCR source lineor, e = 2-jrfn& sin (6 - 0i),
#24Theoretical Elements of Electrical EngineeringTheory Section 4: Power and Effective Values- line 1260
(i*r = 702r sin2 0 = ^r C1 ~ \cos 2 0),)
OCR source linei*r = 702r sin2 0 = ^r C1 ~ cos 2 0),
#25Theoretical Elements of Electrical EngineeringTheory Section 4: Power and Effective Values- line 1423
(e = E0 \sin (0 - 0i) = 273 \sin (0 - 0i) ;)
OCR source linee = E0 sin (0 - 0i) = 273 sin (0 - 0i) ;
#26Theoretical Elements of Electrical EngineeringTheory Section 4: Power and Effective Values- line 1427
(e = 273 \sin 210 (t - h).)
OCR source linee = 273 sin 210 (t - h).
#27Theoretical Elements of Electrical EngineeringTheory Section 5: Self-inductance and Mutual Inductance- line 1694
(e = - -j-. L 108 absolute units)
OCR source linee = - -j-. L 108 absolute units
#28Theoretical Elements of Electrical EngineeringTheory Section 7: Inductance in Alternating-current Circuits- line 2252
(34. An alternating current i = IQ \sin 2irft or i - I0 \sin 0)
OCR source line34. An alternating current i = IQ sin 2irft or i - I0 sin 0
#29Theoretical Elements of Electrical EngineeringTheory Section 7: Inductance in Alternating-current Circuits- line 2266
(i = /0 \sin 2 IT/ (t - t’),)
OCR source linei = /0 sin 2 IT/ (t - t’),
#30Theoretical Elements of Electrical EngineeringTheory Section 7: Inductance in Alternating-current Circuits- line 2272
(i = IQ \sin 6 passes through a circuit of resistance r and induc-)
OCR source linei = IQ sin 6 passes through a circuit of resistance r and induc-
#31Theoretical Elements of Electrical EngineeringTheory Section 7: Inductance in Alternating-current Circuits- line 2310
(2 irft = /o \sin 0) of effective value)
OCR source line2 irft = /o sin 0) of effective value
#32Theoretical Elements of Electrical EngineeringTheory Section 7: Inductance in Alternating-current Circuits- line 2321
(e’2 = - xI0 \cos 2 irft = - xIQ \cos 6,)
OCR source linee’2 = - xI0 cos 2 irft = - xIQ cos 6,
#33Theoretical Elements of Electrical EngineeringTheory Section 7: Inductance in Alternating-current Circuits- line 2337
(e’z = - xIQ \cos 0,)
OCR source linee’z = - xIQ cos 0,
#34Theory and Calculation of Alternating Current PhenomenaChapter 1: Introduction- line 1307
(ty : i = 7i \sin 2 TT N(t - A) + 7, \sin 6 TT N (t - /3))
OCR source linety : i = 7i sin 2 TT N(t - A) + 7, sin 6 TT N (t - /3)
#35Theory and Calculation of Alternating Current PhenomenaChapter 1: Introduction- line 1485
(i = 1 \sin 2 -wjl,)
OCR source linei = 1 sin 2 -wjl,
#36Theory and Calculation of Alternating Current PhenomenaChapter 1: Introduction- line 1486
(/ = / \sin =^ (/ - A) = /\sin 2 tt A” (/ - A) ;)
OCR source line/ = / sin =^ (/ - A) = /sin 2 tt A” (/ - A) ;
#37Theory and Calculation of Alternating Current PhenomenaChapter 1: Introduction- line 1487
(and i = I \cos 2 tt/^.)
OCR source lineand i = I cos 2 tt/^.
#38Theory and Calculation of Alternating Current PhenomenaChapter 1: Introduction- line 1495
(i = /1 \sin 2-KJ{t - ti) + h \sin 4 7r/(i - ^2))
OCR source linei = /1 sin 2-KJ{t - ti) + h sin 4 7r/(i - ^2)
#39Theory and Calculation of Alternating Current PhenomenaChapter 1: Introduction- line 1519
(i = Ai \sin 2 tt/^ + A2 \sin 4 x// + A3 \sin 6 tt/^ + …)
OCR source linei = Ai sin 2 tt/^ + A2 sin 4 x// + A3 sin 6 tt/^ + …
#40Theory and Calculation of Alternating Current PhenomenaChapter 1: Introduction- line 1533
(i = 7] \sin 2 Trf(t - ti) + 1 3 \sin 6 Trf(t - ts))
OCR source linei = 7] sin 2 Trf(t - ti) + 1 3 sin 6 Trf(t - ts)
#41Theory and Calculation of Alternating Current PhenomenaChapter 1: Introduction- line 1537
(i = A\ \sin 2Tvft + A3 \sin 6x/f + ^5 \sin lOvr/^ + …)
OCR source linei = A\ sin 2Tvft + A3 sin 6x/f + ^5 sin lOvr/^ + …
#42Theory and Calculation of Alternating Current PhenomenaChapter 1: Introduction- line 1568
(i = Ai \sin 2 vNt + A, \sin 4 ttNI + A, \sin C irNl + …)
OCR source linei = Ai sin 2 vNt + A, sin 4 ttNI + A, sin C irNl + …
#43Theory and Calculation of Alternating Current PhenomenaChapter 4: Graphic Representation- line 2109
(E0 = V(^ \cos w + Ir)2 -f- (E \sin w + Ix)z.)
OCR source lineE0 = V(^ cos w + Ir)2 -f- (E sin w + Ix)z.
#44Theory and Calculation of Alternating Current PhenomenaChapter 4: Graphic Befrisxintation- line 2201
(Thus, for instance, at the amplitude AOB^ == </>j = 2ir/j/ T’)
OCR source lineThus, for instance, at the amplitude AOB^ == </>j = 2ir/j/ T’
#45Theory and Calculation of Alternating Current PhenomenaChapter 4: Vector Representation- line 2211
(i = I \cos (?> - ??2),)
OCR source linei = I cos (?> - ??2),
#46Theory and Calculation of Alternating Current PhenomenaChapter 4: Vector Representation- line 2248
(i = / \cos (?? - /3))
OCR source linei = / cos (?? - /3)
#47Theory and Calculation of Alternating Current PhenomenaChapter 4: Vector Representation- line 2268
(e = E \cos (i? 4- a’) -)
OCR source linee = E cos (i? 4- a’) -
#48Theory and Calculation of Alternating Current PhenomenaChapter 4: Vector Representation- line 2270
(i = I \cos {t} + /3’))
OCR source linei = I cos {t} + /3’)
#49Theory and Calculation of Alternating Current PhenomenaChapter 4: Vector Representation- line 2279
(i = I \cos (?? - /3))
OCR source linei = I cos (?? - /3)
#50Theory and Calculation of Alternating Current PhenomenaChapter 5: Symbolic Method- line 2385
(ffo = Vfr2 + S^2 + 20^ \sin Wi,)
OCR source lineffo = Vfr2 + S^2 + 20^ sin Wi,
#51Theory and Calculation of Alternating Current PhenomenaChapter 5: Symbolic Method- line 2531
(since y’2 = - 1, j = V- 1 ;)
OCR source linesince y’2 = - 1, j = V- 1 ;
#52Theory and Calculation of Alternating Current PhenomenaChapter 4: Vector Representation- line 2552
(Ea = V{E \cos 6 4- /r)2 + (E \sin 6 + Ixy.)
OCR source lineEa = V{E COS 6 4- /r)2 + (E sin 6 + Ixy.
#53Theory and Calculation of Alternating Current PhenomenaChapter 5: Symbouc Mbthod- line 2759
(100 volts, and /j = 75 amperes, for a non-inductive secon-)
OCR source line100 volts, and /j = 75 amperes, for a non-inductive secon-
#54Theory and Calculation of Alternating Current PhenomenaChapter 5: Symbolic Method- line 2767
(- /V) , \tan w0 =)
OCR source line- /V) , tan w0 =
#55Theory and Calculation of Alternating Current PhenomenaChapter 5: Symbouc Mbthod- line 2810
(&#36;Fo = V^H^i’ + 2 IFSFi \sin Wi ,)
OCR source line$Fo = V^H^i’ + 2 IFSFi sin Wi ,
#56Theory and Calculation of Alternating Current PhenomenaChapter 5: Symbolic Method- line 2842
(h = 7 \sin ^ is the vertical component of the sine wave.)
OCR source lineh = 7 sin ^ is the vertical component of the sine wave.
#57Theory and Calculation of Alternating Current PhenomenaChapter 5: Symbolic Method- line 2961
(j’ = - 1,)
OCR source linej’ = - 1,
#58Theory and Calculation of Alternating Current PhenomenaChapter 5: Symbolic Method- line 2988
(system of ordinary numbers, this definition of j = V - 1 does)
OCR source linesystem of ordinary numbers, this definition of j = V - 1 does
#59Theory and Calculation of Alternating Current PhenomenaChapter 5: Symbolic Method- line 3040
(I = {a + a’) +j(6 + 6’).)
OCR source lineI = {a + a’) +j(6 + 6’).
#60Theory and Calculation of Alternating Current PhenomenaChapter 5: Symbolic Method- line 3206
(or e.o = /(e + ir)- + {ix^, \tan ^o = - 77^-)
OCR source lineor e.o = \/(e + ir)- + {ix^, tan ^o = - 77^-
#61Theory and Calculation of Alternating Current PhenomenaChapter 5: Symbolic Method- line 3243
(0 = 0’+ jc” = c(\cos T + j \sin 7))
OCR source line0 = 0’+ jc” = c(cos T + j sin 7)
#62Theory and Calculation of Alternating Current PhenomenaChapter 5: Symbolic Method- line 3254
(^ = -[\cos (a + |3 - 7) + j \sin (a + |8 - 7)],)
OCR source line^ = -[cos (a + |3 - 7) + j sin (a + |8 - 7)],
#63Theory and Calculation of Alternating Current PhenomenaChapter 7: Polar Coordinates And Polar Diagrams- line 3710
(c = OC \cos (0 - 0o).)
OCR source linec = OC cos (0 - 0o).
#64Theory and Calculation of Alternating Current PhenomenaChapter 8: Circuits Containing Resistance, Inductance, And Capacity- line 3758
(Z -jx0 = r-j(x +#e).)
OCR source lineZ -jx0 = r-j(x +#e).
#65Theory and Calculation of Alternating Current PhenomenaChapter 7: Polar Coordinates And Polar Diagrams- line 3849
(i = I \cos’ (?9 - 0))
OCR source linei = I cos’ (?9 - 0)
#66Theory and Calculation of Alternating Current PhenomenaChapter 8: Circuits Containing Resistance, Inductance, And Capacity- line 4151
(circuit •- z= 1 Qj r = 1>0> x= 0 (Curve j))
OCR source linecircuit •- z= 1 Qj r = 1>0> x= 0 (Curve j)
#67Theory and Calculation of Alternating Current PhenomenaChapter 8: Circuits Containing Resistance, Inductance, And Capacity- line 4323
(&amp;Q = ro JXoi ZQ = V f0 -j- Xo ,)
OCR source line&Q = ro JXoi ZQ = V f0 -j- Xo ,
#68Theory and Calculation of Alternating Current PhenomenaChapter 8: Capacity- line 4438
(is r - y (.r + ;r^) = r = .6, x + x^ = 0, and \tan w^ = ;)
OCR source lineis r - y (.r + ;r^) = r = .6, x + x^ = 0, and tan w^ = ;
#69Theory and Calculation of Alternating Current PhenomenaChapter 8: Capacity- line 5327
(X = .9, X = Oy X = - .9, and Z^ = .3 -j .4.)
OCR source lineX = .9, X = Oy X = - .9, and Z^ = .3 -j .4.
#70Theory and Calculation of Alternating Current PhenomenaChapter 9: Kbsistanci: And Kbactance Of Transmission Iine8- line 6913
(this case, a = ::^j 2 r,,, while in a continuous-current circuit)
OCR source linethis case, a = ::^j 2 r,,, while in a continuous-current circuit
#71Theory and Calculation of Electric ApparatusChapter 1: Speed Control Of Induction Motors- line 1457
(Zo = r„+ j”j:0 =0.1 +0.3j;)
OCR source lineZo = r„+ j”j:0 =0.1 +0.3j;
#72Theory and Calculation of Electric ApparatusChapter 1: Speed Control Of Induction Motors- line 1699
(Assuming \tan a = 0.6, which is a fair value for a closed mag-)
OCR source lineAssuming tan a = 0.6, which is a fair value for a closed mag-