Chapter 32: Quarter-Phase System
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Source Metadata
Section titled “Source Metadata”| Field | Value |
|---|---|
| Source | Theory and Calculation of Alternating Current Phenomena |
| Year | 1900 |
| Section ID | theory-calculation-alternating-current-phenomena-1900-chapter-32 |
| Location | lines 25904-27405 |
| Status | candidate |
| Word Count | 4310 |
| Equation Candidates In Section | 0 |
| Figure Candidates In Section | 2 |
| Quote Candidates In Section | 0 |
Opening Source Excerpt
Section titled “Opening Source Excerpt”CHAPTER XXXII. QUARTER-PHASE SYSTEM. 294. In a three-wire quarter-phase system, or quarter- phase system with common return wire of both phases, let the two outside terminals and wires be denoted by 1 and 2> the middle wire or common return by 0. It is then : EI = E = E.M.F. between 0 and 1 in the generator. Ez=jE = E.M.F. between 0 and 2 in the generator. Let: ./i and 72 = currents in 1 and in 2, 70 = current in 0, Z-L and Zz = impedances of lines 1 and 2, Z0 = impedance of line 0. Yl and Y2 = admittances of circuits 0 to 1, and 0 to 2, // and //= currents in circuits 0 to 1, and 0 to 2, Eia.-ndE2'= potential differences at circuit 0 to 1,Source-Located Theme Snippets
Section titled “Source-Located Theme Snippets”Complex quantities
Section titled “Complex quantities”... In a three-wire quarter-phase system, or quarter- phase system with common return wire of both phases, let the two outside terminals and wires be denoted by 1 and 2> the middle wire or common return by 0. It is then : EI = E = E.M.F. between 0 and 1 in the generator. Ez=jE = E.M.F. between 0 and 2 in the generator. Let: ./i and 72 = currents in 1 and in 2, 70 = current in 0, Z-L and Zz = impedances of lines 1 and 2, Z0 = impedance of line 0. Yl and Y2 = admittances of circuits 0 to 1, and 0 to 2, // and //= currents in circuits 0 to 1, a ...Impedance / reactance
Section titled “Impedance / reactance”... erminals and wires be denoted by 1 and 2> the middle wire or common return by 0. It is then : EI = E = E.M.F. between 0 and 1 in the generator. Ez=jE = E.M.F. between 0 and 2 in the generator. Let: ./i and 72 = currents in 1 and in 2, 70 = current in 0, Z-L and Zz = impedances of lines 1 and 2, Z0 = impedance of line 0. Yl and Y2 = admittances of circuits 0 to 1, and 0 to 2, // and //= currents in circuits 0 to 1, and 0 to 2, Eia.-ndE2'= potential differences at circuit 0 to 1, and 0 to 2. it is then, 7, -f 78 + 70 = 0 ) «v or, I0 =-(/; + 7 ...Waves / transmission lines
Section titled “Waves / transmission lines”... constant maximum and minimum values, — that is, in equal time intervals repeating the same values, — is called an alternating current if the arithmetic mean value equals zero ; and is called a pulsating current if the arithmetic mean value differs from zero. Assuming the wave as a sine curve, or replacing it by the equivalent sine wave, the alternating current is charac- terized by the period or the time of one complete cyclic change, and the amplitude or the maximum value of the current. Period and amplitude are constant in the alter- nating cu ...Dielectricity / capacity
Section titled “Dielectricity / capacity”... 414 F2Z2 Hence, the balanced quarter-phase system with common return is unbalanced with regard to voltage and phase rela- tion, or in other words, even if in a quarter-phase system with common return both branches or phases are loaded equally, with a load of the same phase displacement, nevertheless the system becomes unbalanced, and the two E.M.Fs. at the end of the line are neither equal in magnitude, nor in quadrature with each other. QUARTER-PHASE SYSTEM. B. One branch loaded, one unloaded. 485 a.) b.) Substituting these values in (4), giv ...Chapter-Local Concept Hits
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Chapter-Local Glossary Hits
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Equation Candidates
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Figure Candidates
Section titled “Figure Candidates”| Candidate ID | OCR / PDF-Text Candidate | Source Location |
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theory-calculation-alternating-current-phenomena-1900-fig-209 | which is characterized by a constant angle of intersection Fig. 209. Fig. 210. | line 26776 |
theory-calculation-alternating-current-phenomena-1900-fig-210 | Fig. 209. Fig. 210. with all concentric circles or all radii vectores.” The oscil- | line 26779 |
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Modern Engineering Reading Prompts
Section titled “Modern Engineering Reading Prompts”- 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.
- Waves / transmission lines: Map Steinmetz’s wave and line language onto modern distributed constants, propagation velocity, standing waves, and reflections.
- Dielectricity / capacity: Check whether the passage treats capacity, condensers, displacement, or dielectric stress as field storage rather than only circuit algebra.
- Transients / damping: Separate the temporary term from the final steady-state term and compare with differential-equation response language.
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.
- Transients / damping: Transient collapse, impulse, and surge behavior can be compared with alternative field language, but only as a clearly marked reading.
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