Symbolic Method Concordance
Symbolic Method
Section titled “Symbolic Method”Concordance status: generated from processed OCR/PDF text. Treat these as source-location aids until each passage is checked against the scan.
160 hits
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8 sources
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44 sections
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Matched Aliases
Section titled “Matched Aliases”symbolic, symbolic expression, symbolic method, symbolic representation
Source Distribution
Section titled “Source Distribution”| Source | Hits | Sections |
|---|---|---|
| Theory and Calculation of Alternating Current Phenomena | 48 | 12 |
| Theory and Calculation of Alternating Current Phenomena | 46 | 12 |
| Theory and Calculation of Alternating Current Phenomena | 24 | 7 |
| Theoretical Elements of Electrical Engineering | 22 | 5 |
| Theory and Calculation of Electric Circuits | 14 | 4 |
| Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients | 2 | 1 |
| Theory and Calculation of Electric Apparatus | 2 | 2 |
| Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients | 2 | 1 |
Section Hits
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Section titled “Representative Source Snippets”Theory Section 17: Impedance and Admittance - 11 hit(s)
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... d in ohms: reactance x. The e.m.f. consumed by reactance x is in quadrature with the current, that consumed by resistance r in phase with the current. Reactance and resistance combined give the impedance, + x2; or, in symbolic or vector representation, Z = r + jx. In general in an alternating-current circuit of current i, the e.m.f. e can be resolved in two components, a power component ei in phase with the current, and a wattless or reactiv ...Chapter 30: Quartbr-Fhase System - 10 hit(s)
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... .4, a = .1435, a = 8.2°. Impcdarice and Admittance, 283. In complex imaginary quantities, the alternating wave /* '»\ s = £" cos (<^ — cu) is represented by the symbol E — e (cos ci +y sin w) = c^ -\- je^ . By an extension of the meaning of this symbolic ex- pression, the oscillating wave E=^et~^^ cos (<^ — w) can be expressed by the symbol E = e (cos a> +y sin ui) dec a = {e^ +jc^ dec a, where a = tan a is the exponential decrement, a the angular decrement, t~^^** the numerical decrement. 414 APPEN ...Chapter 32: Quarter-Phase System - 10 hit(s)
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... have A = .4, a = .1435, a = 8.2°. Impedance and Admittance. 312. In complex imaginary quantities, the alternating wave * = e cos (* - ffl) is represented by the symbol E = e (cos w -\-j sin w) = <?x -\-jez . By an extension of the meaning of this symbolic ex- pression, the oscillating wave E = ee~a<t> cos (<f> — w) can be expressed by the symbol E = e (cos w -\-j sin w) dec a = (e± -\-j'e^) dec a, where a = tan a is the exponential decrement, a the angular decrement, e~27ra the numerical decrement. 50 ...Chapter 5: Symbolic Method - 9 hit(s)
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CHAPTER V SYMBOLIC METHOD 25. The graphical method of representing alternating-current phenomena affords the best means for deriving a clear insight into the mutual relation of the different alternating sine waves entering into the problem. For numerical calculation, however, th ...Chapter 27: Symbolic Representation Of General Alternating Waves - 9 hit(s)
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CHAPTER XXVII SYMBOLIC REPRESENTATION OF GENERAL ALTERNATING WAVES 259. The vector representation, A — a'^ -{- ja^'^ = a (cos d -\- j sin 6) of the alternating wave, A = tto cos {(f) — 6) apphes to the sine wave only. The general alternating wave, however, contains an infinite series ...Chapter 24: Symbolic Representation Of General Alternating Waves - 9 hit(s)
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CHAPTER XXIV. SYMBOLIC REPRESENTATION OF GENERAL ALTERNATING WAVES. 253. The vector representation, A = a1 +y<zu = a (cos a -\-j sin d) of the alternating wave, A — a0 cos (<£ — a) applies to the sine wave only. The general alternating wave, however, contains an in- finite series of ...Chapter 18: Oscillating Currents - 9 hit(s)
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... e have A = 0.4, a = 0.1435, a = 8.2°. Impedance and Admittance 184. In complex imaginary quantities, the alternating wave, z = e cos (0 — 6)^ is represented by the symbol, fl = e(cos d — j sin ^) = ei — je2» By an extension of the meaning of this symbolic expression, the oscillating wave, JS? = tt"*** cos {<t> — 6), can be expressed by the symbol, JjJ = e(cos 6 — j sin 0) dec a = (ei — je2) dec a, where a = tan a is the exponential decrement, a the angular decrement, e"^'** the numerical decrement. OSCILLATING ...Theory Section 14: Rectangular Coordinates - 8 hit(s)
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... ngle is the vertical compo- nent divided by the horizontal com- ponent, or the term with prefix j divided by the term without j. The total current intensity is obviously I = V> + i'2> (18) The capital letter I in the symbolic expression / = i + jif thus represents more than the / used in the preceding for total current, etc., and gives not only the intensity but also the phase. It is thus necessary to distinguish by the type of the latter the capit ...Chapter 5: Symbolic Method - 8 hit(s)
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CHAPTER V. SYMBOLIC METHOD. 23. The graphical method of representing alternating, current phenomena by polar coordinates of time affords the best means for deriving a clear insight into the mutual rela- tion of the different alternating sine waves entering into the problem. For n ...Chapter 12: Power, And Double Frequency Quantities In General - 8 hit(s)
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... nt chosen as co-ordinate center) and their connection the dif- ference of potential in phase and intensity. Algebraically these vectors are represented by complex quantities. The impedance, admittance, etc., of the circuit is a complex quantity also, in symbolic denotation. Thus current, E.M.F., impedance, and admittance are related by multiplication and division of complex quantities similar as current, E.M.F., resistance, and conductance are related by Ohms law in direct current circuits. In direct current c ...Chapter 37: Quarter-Phase System - 6 hit(s)
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... characteristic of line and cable, 44 dielectric and dynamic, 159 factor of general wave, 383 Coefficient of eddy currents, 138 of hysteresis, 123 Combination of sine waves, 31 Compensation for lagging currents by condensance, 72 Condensance in symbolic expression, 36 Condenser as reactance and suscep- tance, 96 with distorted wave, 384 motor on distorted wave, 392 motor, single-phase induction, 249, 257 synchronous, 339 Conductance of circuit with induc- tive line, 84 direct current, 55 due to eddy curre ...Chapter 5: Symbouc Mbthod - 6 hit(s)
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... mined analytically by two numerical quanti- ties — the length, Of, or intensity ; and the amplitude, AO/, or phase <o, of the wave, /. Instead of denoting the vector which represents the sine wave in the polar diagram by the polar coordinates. §26] SYMBOLIC METHOD. 35 / and w, we can represent it by its rectangular coordinates, a and b (Fig. 22), where — a = /cos u> is the horizontal component, ^ = /sin 0) is the vertical component of the sine wave. This representation of the sine wave by its rectangular ...Chapter 16: Power, And Double-Frequency Quantities In - 5 hit(s)
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... hosen as coordi- nate center), and their connection the difference of potential in phase and intensity. Algebraically these vectors are represented by complex quan- tities. The impedance, admittance, etc., of the circuit is a com- plex quantity also, in symbolic denotation. Thus current, voltage, impedance, and admittance are related by multiplication and division of complex quantities in the same way as current, voltage, resistance, and conductance are related by Ohm's law in direct-current circuits. In direc ...Chapter 7: Polar Coordinates And Polar Diagrams - 4 hit(s)
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... crank diagram discussed in Chapter IV. It may be called the time diagram or polar diagram, and is used to a considerable extent in the literature, thus must be familiar to the engineer, though in the following we shall in graphic representation and in the symbolic representation based thereon, use the crank diagram of Chapters IV and V. In the time diagram as well as in the crank diagram, instead of the maximum value of the wave, the effective value, or square root of mean square, may be used as the vector, which is more conven ...Chapter 22: Armature Reactions Of Alternators - 3 hit(s)
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... ., OEi. The armature resistance, r, consumes an e.m.f., OEi, in phase with the current, which subtracts vectorially from the actual generated e.m.f., and thus gives the terminal voltage, OE. 194. Analytically, these reactions are best calculated by the symbolic method. ARMATURE REACTIONS OF ALTERNATORS 275 Let the impressed m.in.f., or field-excitation, Fo, be chosen as the imaginary axis, hence represented by ^ Fo = + jfo (1) Let / = u — ji2 = armature current. (2) The m.m.f. of the armature then is Fi =nl ...Chapter 29: Symmetrical Polyphase Systems - 3 hit(s)
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... in(^ - -^y, ' . I ^ 2{n - l)x\ The next e.m.f. is, again, ei = E sin (/3 - 2 x) = E sin /3. In the vector diagram the n e.m.fs. of the symmetrical n-phase system are represented by n equal vectors, following each other under equal angles. Since in symbolic writing rotation by - of a period, or angle 2 TT . ..... — , IS represented by multiplication with 27r , . . 27r COS h 7 sin — = e, n 71 the e.m.fs. of the symmetrical polyphase system are E; 27r . . . 2 ( 27r , . . 27r\ (cos \- J sin — = ...Chapter 24: Symmetbicaii Polyphase Ststems - 3 hit(s)
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... n ( )8 — 2(n - l)ir ^) The next E.M.F. is again : ^i = /^ s\n (P — 2 w) = £ sin /S. In the polar diagram the ;/ E.M.Fs. of the symmetrical «-phase system are represented by ;/ equal vectors, follow- ing each other under equal angles. Since in symbolic writing, rotation by 1/// of a period, or angle 2ir/;/, is represented by multiplication with: cos h J sm = c , the E.M.Fs. of the symmetrical polyphase system are: £• §236] SYMMETRICAL POLYPHASE SYSTEMS, 351 E I cos ^^ + J sin ^^ ) = ^ c ; \ u ...Chapter 13: Distributed Capacity, Inductance, Resistance, And Leakage - 3 hit(s)
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... d from (29), V^ = (2^2f/)7r- <37') These substituted in (26) give, f- (38.) 4/7 (2£ + l)7rx /=(2TTi)-^cosL^H The oscillating discharge of a line can thus follow any of the forms given by making k — 0, 1, 2, 3 . . .in equation (38). Reduced from symbolic representation to absolute values 186 ALTERNATING-CURRENT PHENOMENA. by multiplying E with cos 2 * Nt and / with sin 2 TT A7/ and omitting j, and substituting A7" from equation (34), we have, (2£+l)7rx — sin — JT— - — -cos 2/ where ^4 is an integration constan ...