Chapter 5: Symbouc Mbthod
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Source Metadata
Section titled “Source Metadata”| Field | Value |
|---|---|
| Source | Theory and Calculation of Alternating Current Phenomena |
| Year | 1897 |
| Section ID | theory-calculation-alternating-current-phenomena-1897-chapter-05 |
| Location | lines 2744-3229 |
| Status | candidate |
| Word Count | 2030 |
| Equation Candidates In Section | 31 |
| Figure Candidates In Section | 0 |
| Quote Candidates In Section | 0 |
Opening Source Excerpt
Section titled “Opening Source Excerpt”CHAPTER V. SYMBOUC MBTHOD. 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 numerical calculation, however, the graphical method is frequently not well suited, owing to the widely •different magnitudes of the alternating sine waves repre- sented in the same diagram, which make an exact diagram- matic determination impossible. For instance, in the trans- former diagrams (cf. Figs. 18-20), the different magnitudes •will have numerical values in practice, somewhat like E-^ = 100 volts, and /j = 75 amperes, for a non-inductive secon- dary load, as of incandescent lamps. Thus the only reac- tance of the secondary circuit is that of the secondary coil, or,Source-Located Theme Snippets
Section titled “Source-Located Theme Snippets”Waves / transmission lines
Section titled “Waves / transmission lines”CHAPTER V. SYMBOUC MBTHOD. 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 numerical calculation, however, the graphical method is frequently not well suited, owing to the widely •different magnitudes of the alternating sine waves repre- sented in the same diagram, which make an exact diagram- matic determination im ...Complex quantities
Section titled “Complex quantities”... ng sine waves repre- sented in the same diagram, which make an exact diagram- matic determination impossible. For instance, in the trans- former diagrams (cf. Figs. 18-20), the different magnitudes •will have numerical values in practice, somewhat like E-^ = 100 volts, and /j = 75 amperes, for a non-inductive secon- dary load, as of incandescent lamps. Thus the only reac- tance of the secondary circuit is that of the secondary coil, or, x\ = .08 ohms, giving a lag of eSj = 3.6^. We have also, fty = 30 turns. Uf, = 300 turns. (Fi = 2250 amper ...Impedance / reactance
Section titled “Impedance / reactance”... . If /= / +ji' is a sine wave of alternating current, and r is the resistance, the E.M.F. consumed by the re- sistance is in phase with the current, and equal to the prod- uct of the current and resistance. Or — r/= ri '\' jri\ If L is the inductance, and j: = 2 tt NL the reactance, the E.M.F. produced by the reactance, or the counter §20] SYMBOLIC METHOD. 39' E.M.F. of self-inductance, is the product of the current and reactance, and lags 90° behind the current; it is, therefore, represented by the expression — jxl =jxi — xi\ The E.M.F. requir ...Dielectricity / capacity
Section titled “Dielectricity / capacity”... — 7 ^ (^+J^(^+Jx) ^ er — /x , . /r + <f j: . or, if ^= ^? +yV' is the impressed E.M.F., and / = i +ji^ the current flowing in the circuit, its impedance is — Z^^ =^+J^ ^ (f +J^(' -Jn ^ ^i + ^i' I /i' - ^i' 40 ALTERNATING-CURRENT PHENOMENA, [§§ 30, 31 30. If C is the capacity of a condenser in series in a circuit of current 7=1 +/**', the E.M.F. impressed upon the terminals of the condenser is -£" = ~ , 90° behind the current ; and may be represented by —-^ — — - , or jx^ /, where x^^ = — • is the capacity reaciatice or condensance of the co ...Chapter-Local Concept Hits
Section titled “Chapter-Local Concept Hits”| Concept Candidate | Hits In Section | Status |
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| Frequency | 1 | seeded |
Chapter-Local Glossary Hits
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| No chapter-local term hits yet | - | - |
Equation Candidates
Section titled “Equation Candidates”| Candidate ID | OCR / PDF-Text Candidate | Source Location |
|---|---|---|
theory-calculation-alternating-current-phenomena-1897-eq-candidate-0077 | 100 volts, and /j = 75 amperes, for a non-inductive secon- | line 2759 |
theory-calculation-alternating-current-phenomena-1897-eq-candidate-0078 | or, x\ = .08 ohms, giving a lag of eSj = 3.6^. We have | line 2762 |
theory-calculation-alternating-current-phenomena-1897-eq-candidate-0079 | fty = 30 turns. | line 2766 |
theory-calculation-alternating-current-phenomena-1897-eq-candidate-0080 | Uf, = 300 turns. | line 2768 |
theory-calculation-alternating-current-phenomena-1897-eq-candidate-0081 | (Fi = 2250 ampere-turns. | line 2770 |
theory-calculation-alternating-current-phenomena-1897-eq-candidate-0082 | $f = 100 ampere- turns. | line 2772 |
theory-calculation-alternating-current-phenomena-1897-eq-candidate-0083 | Er = 10 volts. | line 2774 |
theory-calculation-alternating-current-phenomena-1897-eq-candidate-0084 | £^ = 60 volts. | line 2776 |
Figure Candidates
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Hidden-Gem Quote Candidates
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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.
- Dielectricity / capacity: Check whether the passage treats capacity, condensers, displacement, or dielectric stress as field storage rather than only circuit algebra.
- Alternating current: Compare Steinmetz’s AC language with modern sinusoidal steady-state analysis, RMS quantities, phase, and phasor notation.
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
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