Chapter 7: Polar Coordinates And Polar Diagrams
Research workbench, not a finished commentary page.
This page is generated from processed source text and candidate catalogs. It exists to help researchers decide what to verify, promote, and deeply decode next.
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-07 |
| Location | lines 3619-4087 |
| Status | candidate |
| Word Count | 2051 |
| Equation Candidates In Section | 25 |
| Figure Candidates In Section | 7 |
| Quote Candidates In Section | 0 |
Opening Source Excerpt
Section titled “Opening Source Excerpt”CHAPTER VII POLAR COORDINATES AND POLAR DIAGRAMS 42. The graphic representation of alternating waves in rec- tangular coordinates, with the time as abscissae and the instan- taneous values as ordinates, gives a picture of their wave structure, as shown in Figs. 1 to 5. It does not, however, show their periodic character as well as the representation in polar coordi- nates, with the time as the angle or the amplitude — one complete period being represented by one revolution — and the instan- taneous values as radius vectors; the polar coordinate system, in which the independent variable, the angle, is periodic, obvi- ously lends itself better to the representation of periodic functions, as alternating waves. Thus the two waves of Figs. 2 and 3 are represented in polar coordinates in Figs. 36 and 37 asSource-Located Theme Snippets
Section titled “Source-Located Theme Snippets”Waves / transmission lines
Section titled “Waves / transmission lines”CHAPTER VII POLAR COORDINATES AND POLAR DIAGRAMS 42. The graphic representation of alternating waves in rec- tangular coordinates, with the time as abscissae and the instan- taneous values as ordinates, gives a picture of their wave structure, as shown in Figs. 1 to 5. It does not, however, show their periodic character as well as the representation in polar coordi- nates ...Complex quantities
Section titled “Complex quantities”... differing from the 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 convenient ...Impedance / reactance
Section titled “Impedance / reactance”... 40.) POLAR COORDINATES AND POLAR DIAGRAMS 49 Kirchhoff's laws now assume, for alternating sine waves, the form : (o) 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 parallelo- gram of sine waves, is zero. The power equation expressed graphically is as follows: The power of an alternating- current circuit is represented in polar coord ...Alternating current
Section titled “Alternating current”... GRAMS 42. The graphic representation of alternating waves in rec- tangular coordinates, with the time as abscissae and the instan- taneous values as ordinates, gives a picture of their wave structure, as shown in Figs. 1 to 5. It does not, however, show their periodic character as well as the representation in polar coordi- nates, with the time as the angle or the amplitude — one complete period being represented by one revolution — and the instan- taneous values as radius vectors; the polar coordinate system, in which the independent variable, th ...Chapter-Local Concept Hits
Section titled “Chapter-Local Concept Hits”| Concept Candidate | Hits In Section | Status |
|---|---|---|
| Ether | 1 | seeded |
Chapter-Local Glossary Hits
Section titled “Chapter-Local Glossary Hits”| Term Candidate | Hits In Section | Status |
|---|---|---|
| ether | 1 | seeded |
Equation Candidates
Section titled “Equation Candidates”| Candidate ID | OCR / PDF-Text Candidate | Source Location |
|---|---|---|
theory-calculation-alternating-current-phenomena-eq-candidate-0190 | 43. The sine wave. Fig. 1, is represented in polar coordinates | line 3655 |
theory-calculation-alternating-current-phenomena-eq-candidate-0191 | of the wave; and the amplitude of the diameter OC, ^ 0o = AOC, | line 3658 |
theory-calculation-alternating-current-phenomena-eq-candidate-0192 | 1 = 1 cos {0 — ^o), | line 3662 |
theory-calculation-alternating-current-phenomena-eq-candidate-0193 | where 0 = 2ir — is the instantaneous value of the ampHtude | line 3668 |
theory-calculation-alternating-current-phenomena-eq-candidate-0194 | for instance, at the amplitude, AOBi = 6i = 2w- (Fig- 38), the | line 3676 |
theory-calculation-alternating-current-phenomena-eq-candidate-0195 | instantaneous value is OB’; at the amphtude, AOB2 = 62 = | line 3680 |
theory-calculation-alternating-current-phenomena-eq-candidate-0196 | 2 Try, the instantaneous value is OB”, and negative, since in | line 3682 |
theory-calculation-alternating-current-phenomena-eq-candidate-0197 | The angle, 0, so represents the time, and increasing time is | line 3687 |
Figure Candidates
Section titled “Figure Candidates”| Candidate ID | OCR / PDF-Text Candidate | Source Location |
|---|---|---|
theory-calculation-alternating-current-phenomena-fig-037 | represented by an increase of angle B in counter-clockwise rota- FiG. 37 tion. That is, the positive direction, or increase of time, is | line 3691 |
theory-calculation-alternating-current-phenomena-fig-041 | ^i Fig. 41. Fig. 42. | line 3828 |
theory-calculation-alternating-current-phenomena-fig-042 | Fig. 41. Fig. 42. then appear in the vector representation of the time diagram or | line 3831 |
theory-calculation-alternating-current-phenomena-fig-043 | E^-^ Fig. 43. Fig. 45. | line 3856 |
theory-calculation-alternating-current-phenomena-fig-045 | Fig. 43. Fig. 45. lagging behind the voltage: | line 3859 |
theory-calculation-alternating-current-phenomena-fig-046 | then means: Fig. 46. POLAR COORDINATES AND POLAR DIAGRAMS 51 | line 3872 |
theory-calculation-alternating-current-phenomena-fig-048 | ^ Fig. 48. R’ | line 4049 |
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.
- Complex quantities: Track how Steinmetz preserves geometric rotation and quadrature while translating the same operation into symbolic form.
- 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.
- 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
Section titled “Promotion Checklist”- Open the full source text and the scan or raw PDF.
- Verify the chapter boundary and surrounding context.
- Promote exact quotations only after checking the source image.
- Move mathematical candidates into canonical equation pages only after formula typography is corrected.
- Move diagram candidates into the diagram archive only after image extraction, crop verification, and manifest creation.
- Keep Steinmetz wording, modern translation, and ether-field interpretation in separate labeled layers.