Chapter 4: Vector Representation
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Source Metadata
Section titled “Source Metadata”| Field | Value |
|---|---|
| Source | Theory and Calculation of Alternating Current Phenomena |
| Year | 1916 |
| Section ID | theory-calculation-alternating-current-phenomena-chapter-04 |
| Location | lines 2149-2759 |
| Status | candidate |
| Word Count | 3435 |
| Equation Candidates In Section | 54 |
| Figure Candidates In Section | 4 |
| Quote Candidates In Section | 0 |
Opening Source Excerpt
Section titled “Opening Source Excerpt”CHAPTER IV VECTOR REPRESENTATION 16. While alternating waves can be, and frequently are, rep- resented 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 alternating waves is given by their representation as vectors, in the so-called crank diagram. A vector, equal in length to the maximum value of the alternating wave, revolves at uniform speed so as to make a complete revolution per period, and the pro- jections of this revolving vector on the horizontal then denote the instantaneous values of the wave. Obviously, by this diagram only sine waves can be represented or, in general, waves which are so near sine shape that they can be represented by a sine. Let, for instance, 01Source-Located Theme Snippets
Section titled “Source-Located Theme Snippets”Waves / transmission lines
Section titled “Waves / transmission lines”CHAPTER IV VECTOR REPRESENTATION 16. While alternating waves can be, and frequently are, rep- resented 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 alternating waves is given by their represen ...Magnetism
Section titled “Magnetism”... as for instance, a synchronous motor circuit under the circumstances stated above. 23. As a further example, we may consider the diagram 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 and rising. The magnetic flux then passes its maxi- mum at the time ?? = 90°, and the phase of the magnetic f ...Impedance / reactance
Section titled “Impedance / reactance”... the parallelogram or the polygon of sine waves. Kirchhofif'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. (6) The resultant of all the currents toward a distributing point, as found by the parallelogram of sine waves, is zero. The power equation expressed graphically is as follows: The power of an alternating-current circuit is represented in vector represent ...Alternating current
Section titled “Alternating current”... e shape that they can be represented by a sine. Let, for instance, 01 represent in length the maximum value / of a sine wave of current. Assuming then a vector, 01, to revolve, left handed or in counter-clockwise direc- tion, so that it makes a complete revolution during each cycle or period U. If then at a certain moment of time, this vector stands in position 01 1 (Fig. 8), the projec- tion, 0A\, of 0I\ on the horizontal line 0.4 represents the instantaneous value of the current at this moment. At a later mo- ment, 01 has moved farther, to 01 ...Chapter-Local Concept Hits
Section titled “Chapter-Local Concept Hits”| Concept Candidate | Hits In Section | Status |
|---|---|---|
| Light | 2 | seeded |
| Frequency | 1 | seeded |
Chapter-Local Glossary Hits
Section titled “Chapter-Local Glossary Hits”| Term Candidate | Hits In Section | Status |
|---|---|---|
| counter e.m.f. | 12 | source-located candidate |
Equation Candidates
Section titled “Equation Candidates”| Candidate ID | OCR / PDF-Text Candidate | Source Location |
|---|---|---|
theory-calculation-alternating-current-phenomena-eq-candidate-0066 | Let, for instance, 01 represent in length the maximum value / of | line 2167 |
theory-calculation-alternating-current-phenomena-eq-candidate-0067 | a sine wave of current. Assuming then a vector, 01, to revolve, | line 2168 |
theory-calculation-alternating-current-phenomena-eq-candidate-0068 | stands in position 01 1 (Fig. 8), the projec- | line 2173 |
theory-calculation-alternating-current-phenomena-eq-candidate-0069 | 0/2 on OA is the instantaneous value at this later moment. The | line 2178 |
theory-calculation-alternating-current-phenomena-eq-candidate-0070 | If now the time, t, and thus the angle, ^ = 10 A = 2ir — (where | line 2184 |
theory-calculation-alternating-current-phenomena-eq-candidate-0071 | moment of time where the revolving vector 01 in Fig. 8 stands in | line 2189 |
theory-calculation-alternating-current-phenomena-eq-candidate-0072 | time represented by position OIi, i = I, and 01 passes through | line 2202 |
theory-calculation-alternating-current-phenomena-eq-candidate-0073 | i = I cos (?> - ??2), | line 2211 |
Figure Candidates
Section titled “Figure Candidates”| Candidate ID | OCR / PDF-Text Candidate | Source Location |
|---|---|---|
theory-calculation-alternating-current-phenomena-fig-010 | 21 Fig. 10. phase angle — /3’ = — (a’ — ??]) = 10 A, and the equations of | line 2262 |
theory-calculation-alternating-current-phenomena-fig-016 | ^E, Fig. 16. Fig. 17. | line 2534 |
theory-calculation-alternating-current-phenomena-fig-017 | Fig. 16. Fig. 17. the current by the angle, Q. The voltage consumed by the resist- | line 2537 |
theory-calculation-alternating-current-phenomena-fig-019 | Ei-< «; Fig. 19. The primary impressed e.m.f., Ep, must thus consist of the three components OEi, OEr, and OE^, and is, therefore, their | line 2704 |
Hidden-Gem Quote Candidates
Section titled “Hidden-Gem Quote Candidates”| Candidate ID | Candidate Passage | Source Location |
|---|---|---|
| No chapter-local candidates yet | - | - |
Modern Engineering Reading Prompts
Section titled “Modern Engineering Reading Prompts”- Waves / transmission lines: Map Steinmetz’s wave and line language onto modern distributed constants, propagation velocity, standing waves, and reflections.
- Magnetism: Track flux, reluctance, permeability, magnetizing force, and loss language against modern magnetic-circuit terminology.
- Impedance / reactance: Translate historical opposition terms into modern impedance, admittance, conductance, susceptance, and complex-plane notation.
- Alternating current: Compare Steinmetz’s AC language with modern sinusoidal steady-state analysis, RMS quantities, phase, and phasor notation.
- Dielectricity / capacity: Check whether the passage treats capacity, condensers, displacement, or dielectric stress as field storage rather than only circuit algebra.
Ether-Field Interpretive Boundary
Section titled “Ether-Field Interpretive Boundary”- Waves / transmission lines: Standing/traveling wave passages may support richer field interpretations; the page keeps those readings separate from verified Steinmetz wording.
- Magnetism: Centrifugal/divergent magnetic-field readings are interpretive overlays, not automatic historical claims.
- Dielectricity / capacity: A Wheeler-style reading may emphasize dielectric compression, field stress, and stored potential, but this page treats that as interpretation unless Steinmetz explicitly says it.
Promotion Checklist
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