Chapter 30: Balanced And Unbalanced Polyphase Systems

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

Field	Value
Source	Theory and Calculation of Alternating Current Phenomena
Year	1916
Section ID	`theory-calculation-alternating-current-phenomena-chapter-30`
Location	lines 35256-35691
Status	candidate
Word Count	1574
Equation Candidates In Section	0
Figure Candidates In Section	0
Quote Candidates In Section	0

Opening Source Excerpt

CHAPTER XXX BALANCED AND UNBALANCED POLYPHASE SYSTEMS 273. If an alternating e.m.f., e = E\/2 sin ^, produces a current, i = /V2 sin (/3 - &), where Q is the angle of lag, the power is p = ei = 2 EI sin (3 sin (/3 - d) = EI (cos 0 - cos (2 /3 - e)), and the average value of power, P = EI cos e. Substituting this, the instantaneous value of power is found as cos (2/3 - e)^ _ P A _ cos(2)£J- d)\ \ cos 0 / ' Hence the power, or the flow of energy, in an ordinary single- phase, alternating-current circuit is fluctuating, and varies with twice the frequency of e.m.f. and current, unlike the power of a continuous-current circuit, which is constant, p = ei.

Source-Located Theme Snippets

Alternating current

... ) = EI (cos 0 - cos (2 /3 - e)), and the average value of power, P = EI cos e. Substituting this, the instantaneous value of power is found as cos (2/3 - e)^ _ P A _ cos(2)£J- d)\ \ cos 0 / ' Hence the power, or the flow of energy, in an ordinary single- phase, alternating-current circuit is fluctuating, and varies with twice the frequency of e.m.f. and current, unlike the power of a continuous-current circuit, which is constant, p = ei. If the angle of lag, ^ = 9, it is, p - P(l - cos 2/3); hence the flow of energy varies between zero and 2 P, ...

Waves / transmission lines

... between zero and 2 P, where P is the average flow of energy or the effective power of the circuit. If the current lags or leads the e.m.f. by angle d, the power varies between P(l ^)andP(l +-^), \ cos 6/ \ cos 6/ that is, becomes negative for a certain part of each half-wave. That is, for a time during each half-wave, energy flows back into 405 406 ALTERNATING-CURRENT PHENOMENA the generator, while during the other part of the half-wave the generator sends out energy, and the difference between both is the effective power of the circuit. ...

Dielectricity / capacity

... nced system if the flow of energy varies periodically, as in the single-phase system; and the ratio of the minimum value to the maximum value of power is called the halance-J actor of the system. Hence in a single-phase system on non-inductive circuit, that is, at no-phase displacement, the balance-factor is zero; and it is negative in a single-phase system with lagging or leading current, and becomes equal to — 1 if the phase displace- ment is 90° — that is, the circuit is wattless. 275. Obviously, in a polyphase system the balance of the system is a fu ...

Radiation / light

... P = EI cos e. Substituting this, the instantaneous value of power is found as cos (2/3 - e)^ _ P A _ cos(2)£J- d)\ \ cos 0 / ' Hence the power, or the flow of energy, in an ordinary single- phase, alternating-current circuit is fluctuating, and varies with twice the frequency of e.m.f. and current, unlike the power of a continuous-current circuit, which is constant, p = ei. If the angle of lag, ^ = 9, it is, p - P(l - cos 2/3); hence the flow of energy varies between zero and 2 P, where P is the average flow of energy or the effective power ...

Chapter-Local Concept Hits

Concept Candidate	Hits In Section	Status
Frequency	3	seeded

Chapter-Local Glossary Hits

Term Candidate	Hits In Section	Status
No chapter-local term hits yet	-	-

Equation Candidates

Candidate ID	OCR / PDF-Text Candidate	Source Location
No chapter-local candidates yet	-	-

Figure Candidates

Candidate ID	OCR / PDF-Text Candidate	Source Location
No chapter-local candidates yet	-	-

Hidden-Gem Quote Candidates

Candidate ID	Candidate Passage	Source Location
No chapter-local candidates yet	-	-

Modern Engineering Reading Prompts

Alternating current: Compare Steinmetz’s AC language with modern sinusoidal steady-state analysis, RMS quantities, phase, and phasor 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.
Radiation / light: Compare the chapter’s radiation vocabulary with modern electromagnetic radiation, spectral frequency, wavelength, absorption, and illumination engineering.
Complex quantities: Track how Steinmetz preserves geometric rotation and quadrature while translating the same operation into symbolic form.

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.
Radiation / light: Radiation and wave language can invite ether-field comparison, but source wording, modern radiation theory, and speculative synthesis must stay separated.

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.