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Power Factor

Power factor measures how much of an AC voltage-current relation produces real power rather than wattless exchange. It belongs beside impedance, reactance, admittance, conductance, and susceptance.

power factor=cosϕ\text{power factor} = \cos \phi

where phi is the phase angle between voltage and current.

P=VIcosϕP = VI\cos\phi

Steinmetz’s AC language repeatedly distinguishes active or power components from wattless or reactive components. Power factor is the practical operating measure of that distinction.

The source work still needed here is exact: find the passages where Steinmetz uses “power factor,” “wattless,” and component language, then anchor them to scan-checked citations.

Power factor is where symbolic geometry becomes system economics. Low power factor can mean high current for the same useful power, larger conductors, larger losses, and more demanding apparatus ratings.

Ether-Field Interpretive Reading

Interpretive only: a field-centered reading may describe wattless current as energy moving into and out of field storage rather than being consumed. This is compatible with modern reactive power language, but any broader ether interpretation must remain labeled.

  • Extract Steinmetz’s exact power-factor wording from the AC source.
  • Link power factor to wattless current, reactance, admittance, and transformer excitation.
  • Add a worked numerical example.

Generated evidence layer: this dossier is built from the processed concept concordance. Counts and snippets are OCR/PDF-text aids, not final quotations. Verify against scans before making exact claims.

671

Candidate occurrences tracked for this page.

11

Sources with at least one hit.

101

Sections, lectures, chapters, or report divisions to review.

Read this concept page through the linked source passages first. Use the dossier to locate Steinmetz’s wording, then add modern, mathematical, historical, and interpretive layers only with labels.

The strongest current source concentration is Theory and Calculation of Electric Apparatus with 206 candidate hits across 14 sections.

The dossier is meant to turn a concept page into a research workbench: begin with Steinmetz’s source wording, then add modern interpretation, mathematical reconstruction, historical context, and any ether-field reading as separate layers.

power factor, power-factor, wattless component, wattless current

Power Factor

SourceCandidate HitsSectionsConcepts represented
Theory and Calculation of Electric Apparatus20614Power Factor
Theory and Calculation of Alternating Current Phenomena13318Power Factor
Theory and Calculation of Alternating Current Phenomena8914Power Factor
Theoretical Elements of Electrical Engineering8324Power Factor
Theory and Calculation of Electric Circuits545Power Factor
Theory and Calculation of Alternating Current Phenomena3912Power Factor
Theory and Calculation of Transient Electric Phenomena and Oscillations355Power Factor
Engineering Mathematics: A Series of Lectures Delivered at Union College182Power Factor
Chapter 20: Single-Phase Commutator Motors - 64 candidate hits

Source: Theory and Calculation of Electric Apparatus (1917)

Location: lines 23906-30087 - Tracked concepts: Power Factor

Open source text - Open chapter workbench

... resistance, which represents the power loss. In addition thereto, in the alternating-cur rent motor voltage is consumed by the inductance, which is wattless or reactive and therefore causes a lag of current behind the vol- tage, that is, a lowering of the power-factor. While in the direct- current motor good design requires the combination of a strong...
... While in the direct- current motor good design requires the combination of a strong field and a relatively weak armature, so as to reduce the armature reaction on the field to a minimum, in the design of the alter- iiatiiig-current motor considerations of power-factor predominate; that is, to secure low self-inductance and therewith a high power- fact...
Chapter 4: Induction Motor With Secondary Excitation - 50 candidate hits

Source: Theory and Calculation of Electric Apparatus (1917)

Location: lines 5555-8554 - Tracked concepts: Power Factor

Open source text - Open chapter workbench

... ating magnetizing current is a wattless reactive current, the result is, that the alternating-current input into the induction motor is always lagging, the more so, the larger a part of the total current is given by the magnetizing current. To secure good power-factor in an induction motor, the magnetizing current, that i«, the current which produces...
... erload capacity has to be met, etc. In such motors of necessity the exciting current or current at no-load - which is practically all magnetizing current - is a very large part of full-load current, and while fair efficiencies may nevertheless be secured, power-factor and apparent efficiency necessarily are very low. As illustration is shown in Fig. 2...
Chapter 14: Constant-Potential Constant-Current Trans Formation - 42 candidate hits

Source: Theory and Calculation of Electric Circuits (1917)

Location: lines 24023-27995 - Tracked concepts: Power Factor

Open source text - Open chapter workbench

... n series with this circuit. The impedance of this circuit then is Z = r + jxof and, absolute, and thus the current, / = ^* = -^ (1) ^ r + jxo and the absolute value is eo Co the phase angle of the supply circuit is given by (2) and the power factor. tan ^0 = - (3) T cos ^0 = -• (4) z ^ ^ If in this case, r is small compared with Xq, it is ,-^£o _-l (5...
... l theorem. V • • • \xj hence, : (6) 6o I = - Xo 2xo2^8xo* -r . . . that is, for small values of r, the current, z, is approximately constant, and is 6o I = - Xo CONSTANT-CURRENT TRANSFORMATION 247 For small values of r, the power-factor cosfl - - is very low, however. Allowing a variation of current of 10 per cent, from short- circuit or no-load, r =...
Chapter 16: Induction Motor - 28 candidate hits

Source: Theory and Calculation of Alternating Current Phenomena (1900)

Location: lines 13649-16361 - Tracked concepts: Power Factor

Open source text - Open chapter workbench

... e the motor is in operation. 256 ALTERNATING-CURRENT PHENOMENA. Since, necessarily, ri<*, ''<•< and since the starting current is, approximately, 7 =f , we have, Ta < would be the theoretical torque developed at 100 per cent efficiency and power factor, by E.M.F., E0, and current, /, at synchronous speed. Thus, T0<T00, and the ratio between the starti...
... in absolute units, = = N (f* + r22) W where N= frequency. The power output is torque times speed, thus : The power input is, ^•l2 + The voltampere input, o2 ( Vi + V,) /o2 ( Vi - V8) hence, efficiency, J\ _ a, (I - s) J? Vi + V2 power factor, apparent efficiency, <2o torque efficiency, * a. ./V Vi + V. * That 5s the ratio of actual torque to torque wh...
Chapter 23: Review - 24 candidate hits

Source: Theory and Calculation of Electric Apparatus (1917)

Location: lines 32138-32819 - Tracked concepts: Power Factor

Open source text - Open chapter workbench

... change of the inductivity of the load, hasmade njGfl compounding unsuitahie for the modern high-power altcrnu- ton. Condenser Motor. - 77. Single-phase induction motor with condenser in tertiary circuit on stator, for producing shirting torque and high power-factor. The space angle between pri- mary and tertiary stator circuit usually is 45° to 60°, a...
... r-factor. The space angle between pri- mary and tertiary stator circuit usually is 45° to 60°, and often a three-phase motor is used, with single-phase supply on one phase. and condenser on a Becond phase. With the small amount of capacity, sufficient for power-factor compensation, usually the starting torque is small, unless a starting resistance is...
Chapter 14: Dielectric Losses - 20 candidate hits

Source: Theory and Calculation of Alternating Current Phenomena (1916)

Location: lines 14334-15409 - Tracked concepts: Power Factor

Open source text - Open chapter workbench

... dielectric fields, but is so small, that it usually is overshadowed by the other losses. In alternating dielectric fields in solid materials, such as in condensers, coil insulation, etc., a loss is commonly observed which gives an approximately constant power-factor of the elec- tric energizing circuit, over a wide range of voltage and of fre- quency,...
... rved which gives an approximately constant power-factor of the elec- tric energizing circuit, over a wide range of voltage and of fre- quency, from less than a fraction of 1 per cent, up to a few per cent. 150 DIELECTRIC LOSSES 151 Constancy of the power-factor with the frequency, means that the loss is proportional to the frequency, as the current i,...
LayerWhat to add next
Steinmetz wordingPull exact source passages only after scan verification; keep OCR text labeled until then.
Modern engineering readingTranslate the source usage into present electrical-engineering or physics language without erasing the older vocabulary.
Mathematical layerLink equations, variables, diagrams, and worked examples when the concept has formula candidates.
Historical layerIdentify whether the term is still used, renamed, absorbed into modern theory, or historically obsolete.
Ether-field interpretationKeep interpretive readings separate from Steinmetz’s explicit claim and from modern physics.
Open questionsRecord places where the concordance suggests a lead but the scan or edition has not yet been checked.
  1. Open the highest-priority source-text passages above and verify the wording against scans.
  2. Promote exact definitions, equations, diagrams, and hidden-gem passages into this page with source references.
  3. Add related concept links, equation pages, and diagram pages once the evidence is scan checked.
  4. Keep speculative or Wheeler-style readings in explicitly labeled interpretation blocks.