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Chapter 4: Graphic Representation

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FieldValue
SourceTheory and Calculation of Alternating Current Phenomena
Year1900
Section IDtheory-calculation-alternating-current-phenomena-1900-chapter-04
Locationlines 1743-2321
Statuscandidate
Word Count3152
Equation Candidates In Section39
Figure Candidates In Section8
Quote Candidates In Section0
CHAPTER IV. GRAPHIC REPRESENTATION. 14. While alternating waves can be, and frequently are, represented graphically in rectangular coordinates, with the time as abscissae, and the instantaneous values of the wave as ordinates, the best insight with regard to the mutual relation of different alternate waves is given by their repre- sentation in polar coordinates, with the time as an angle or the amplitude, — one complete period being represented by one revolution, — and the instantaneous values as radii vectores. Fig. 8. Thus the two waves of Figs. 2 and 3 are represented in polar coordinates in Figs. 8 and 9 as closed characteristic curves, which, by their intersection with the radius vector, give the instantaneous value of the wave, corresponding to the time represented by the amplitude of the radius vector. These instantaneous values
CHAPTER IV. GRAPHIC REPRESENTATION. 14. While alternating waves can be, and frequently are, represented graphically in rectangular coordinates, with the time as abscissae, and the instantaneous values of the wave as ordinates, the best insight with regard to the mutual relation of different alternate waves is given by their repre- sent ...
... f parallelogram or tJie polygon of sine waves. Kirchhoff's laws now assume, for alternating sine waves, the form : — a.) The resultant of all the E.M.Fs. in a closed circuit, as found by the parallelogram of sine waves, is zero if the counter E.M.Fs. of resistance and of reactance are included. b.} The resultant of all the currents flowing towards a GRAPHIC REPRESENTATION. 23 distributing point, as found by the parallelogram of sine waves, is zero. The energy equation expressed graphically is as follows : The power of an alternating-curren ...
... or instance, a synchro- nous motor circuit under the circumstances stated above. 21. As a further example, we may consider the dia- gram of an alternating-current transformer, feeding through its secondary circuit an inductive load. For simplicity, we may neglect here the magnetic hysteresis, the effect of which will be fully treated in a separate chapter on this subject. Let the time be counted from the moment when the magnetic flux is zero. The phase of the flux, that is, the amplitude of its maximum value, is 90° in this case, and, consequently, ...
... tes, with the time as an angle or the amplitude, — one complete period being represented by one revolution, — and the instantaneous values as radii vectores. Fig. 8. Thus the two waves of Figs. 2 and 3 are represented in polar coordinates in Figs. 8 and 9 as closed characteristic curves, which, by their intersection with the radius vector, give the instantaneous value of the wave, corresponding to the time represented by the amplitude of the radius vector. These instantaneous values are positive if in the direction of the radius vector, and n ...
Concept CandidateHits In SectionStatus
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Light2seeded
Ether1seeded
Term CandidateHits In SectionStatus
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Candidate IDOCR / PDF-Text CandidateSource Location
theory-calculation-alternating-current-phenomena-1900-eq-candidate-006415. The sine wave, Fig. 1, is represented in polarline 1789
theory-calculation-alternating-current-phenomena-1900-eq-candidate-00651= OC, represents the intensity of the wave ; and the am-line 1792
theory-calculation-alternating-current-phenomena-1900-eq-candidate-0066where </> = 2 IT / / T is the instantaneous value of the ampli-line 1800
theory-calculation-alternating-current-phenomena-1900-eq-candidate-0067tude corresponding to the instantaneous value, 2, of the wave.line 1801
theory-calculation-alternating-current-phenomena-1900-eq-candidate-0068Thus, for instance, at the amplitude AOBl = ^ = 2 ^ / Tline 1805
theory-calculation-alternating-current-phenomena-1900-eq-candidate-0069(Fig. 10), the instantaneous value is OB’ ; at the amplitudeline 1806
theory-calculation-alternating-current-phenomena-1900-eq-candidate-0070AO£2 = <f>2 = 27T/2/ T, the instantaneous value is ~OJ3”, andline 1807
theory-calculation-alternating-current-phenomena-1900-eq-candidate-0071is then V2 times the vector OC, so that the instantaneousline 1832
Candidate IDOCR / PDF-Text CandidateSource Location
theory-calculation-alternating-current-phenomena-1900-fig-011nates by a vector, which by its length, OC, denotes the in- Fig. 11. tensity, and by its amplitude, AOC, the phase, of the sineline 1892
theory-calculation-alternating-current-phenomena-1900-fig-012be sent into a non-inductive circuit at an E.M.F. of E Fig. 12. volts. What will be the E.M.F. required at the generator end of the line ?line 1936
theory-calculation-alternating-current-phenomena-1900-fig-013E? 0 Fig. 13. 18. We may, however, introduce the effect of the induc-line 1989
theory-calculation-alternating-current-phenomena-1900-fig-014E.V o Fig. 14. of the impressed E.M.F., in the latter case being of opposite phase. According to the nature of the problem, either theline 2025
theory-calculation-alternating-current-phenomena-1900-fig-015—X« Fig. 15. 19. Coming back to the equation found for the E.M.F.line 2062
theory-calculation-alternating-current-phenomena-1900-fig-018E0 = V(^ cos w + Ir)2 -f- (E sin w + Ix)z. Fig. 18. If, however, the current in the receiving circuit is leading, as -is the case when feeding condensers or syn-line 2112
theory-calculation-alternating-current-phenomena-1900-fig-017’E. Fig. 17. a circuit with leading current, as, for instance, a synchro- nous motor circuit under the circumstances stated above.line 2152
theory-calculation-alternating-current-phenomena-1900-fig-020same E.M.F. and current ; or conversely, at a given primary Fig. 20. impressed E.M.F., E0, the secondary E.M.F., E^ will be smaller with an inductive, and larger with a condenserline 2295
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  • Waves / transmission lines: Map Steinmetz’s wave and line language onto modern distributed constants, propagation velocity, standing waves, and reflections.
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  • Alternating current: Compare Steinmetz’s AC language with modern sinusoidal steady-state analysis, RMS quantities, phase, and phasor notation.
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