Admittance
Steinmetz Usage
Section titled “Steinmetz Usage”Admittance is introduced as the reciprocal form of impedance, useful especially when currents divide through parallel paths. The OCR candidate gives admittance as a complex quantity with conductance and susceptance components.
Conductance is the active or power component. Susceptance is the reactive or wattless component.
Modern Equivalent
Section titled “Modern Equivalent”Modern texts often write:
The sign convention differs by author and context. The archive should preserve Steinmetz’s notation and then translate it explicitly.
Mathematical Meaning
Section titled “Mathematical Meaning”If:
then admittance depends on both r and x. Conductance is not generally just 1/r, and susceptance is not generally just 1/x.
Why It Matters
Admittance is one of the places where old AC language can save readers from a common simplification. The reciprocal of a complex quantity is not the same as taking reciprocals of its parts.
Related Pages
Section titled “Related Pages”Reader Synthesis
Section titled “Reader Synthesis”What Steinmetz Is Doing Here
Admittance is the reciprocal language that makes parallel AC circuits tractable.
The current strongest source route is Theory and Calculation of Alternating Current Phenomena, with 136 candidate hits across 17 sections.
Modern Translation
Modern readers should map it to Y = G + jB, conductance, susceptance, and parallel network calculation.
This page currently tracks 481 candidate occurrences across 10 sources and 79 sections.
Mathematical And Visual Route
Focus on reciprocal impedance, conductance, susceptance, and vector addition of branch currents.
Use the math/visual bridge lower on this page to jump into formula families, source visual maps, and candidate figure leads.
Interpretive Boundary
Keep the interpretation modest: the page is mostly mathematical method and circuit bookkeeping.
Layer labels stay active: source claim, modern equivalent, mathematical reconstruction, historical note, and interpretive reading are not interchangeable.
Fast Reading Path For Admittance
Section titled “Fast Reading Path For Admittance”| Passage | Hits | Location | Open |
|---|---|---|---|
| Chapter 16: Induction Motor Theory and Calculation of Alternating Current Phenomena | 28 | lines 13649-16361 | read - research review |
| Chapter 20: Single-Phase Induction Motors Theory and Calculation of Alternating Current Phenomena | 23 | lines 21538-22301 | read - research review |
| Apparatus Section 3: Induction Machines: Single -phase Induction Motor Theoretical Elements of Electrical Engineering | 22 | lines 20428-21157 | read - research review |
| Chapter 17: The Alternating-Current Transformer Theory and Calculation of Alternating Current Phenomena | 21 | lines 16521-17716 | read - research review |
Research Position
Section titled “Research Position”- Tracked vocabulary: Admittance.
- Concordance: Admittance.
- Source discipline: the table above is for reading and navigation; exact quotation still requires scan verification.
- Editorial rule: expand this page by promoting scan-checked passages, equations, and diagrams from the linked workbench pages, not by adding unsourced generalizations.
Source-Grounded Dossier
Section titled “Source-Grounded Dossier”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.
Candidate occurrences tracked for this page.
Sources with at least one hit.
Sections, lectures, chapters, or report divisions to review.
What The Current Corpus Shows
Section titled “What The Current Corpus Shows”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 Alternating Current Phenomena with 136 candidate hits across 17 sections.
The dossier is meant to turn a concept page into a reading path: begin with Steinmetz’s source wording, then use the research links only when you need candidate counts, snippets, mathematical reconstruction, historical context, or interpretive layers.
Terms And Aliases Tracked
Section titled “Terms And Aliases Tracked”admittance, admittances
Concordance Records
Section titled “Concordance Records”Source Distribution
Section titled “Source Distribution”Priority Passages To Read
Section titled “Priority Passages To Read”Chapter 16: Induction Motor - 28 candidate hits
Source: Theory and Calculation of Alternating Current Phenomena (1900)
Location: lines 13649-16361 - Tracked concepts: Admittance
... econdary frequency is s N, the secondary in- duced E.M.F. (reduced to primary system) is El = - se. Let I0 = exciting current, or current passing through the motor, per primary circuit, when doing no work (at synchronism), and K= g -j- j 'b = orimary admittance per circuit = - . We thus have, ge = magnetic energy current, ge* = loss of power oy hyster...... f (R = reluctance of magnetic circuit per pole, as dis- cussed in Chapter X., it is A^^ft*. * Complete discussion hereof, see Chapter XXV. INDUCTION MOTOR. 241 Thus, from the hysteretic loss, and the reluctance, the constants, g and b, and thus the admittance, Fare derived. Let rQ = resistance per primary circuit ; XQ = reactance per primary circuit ;...Chapter 20: Single-Phase Induction Motors - 23 candidate hits
Source: Theory and Calculation of Alternating Current Phenomena (1916)
Location: lines 21538-22301 - Tracked concepts: Admittance
... sity - the total volt-amperes excitation of the single-phase induction motor must be the same as of the same motor on polyphase circuit, it follows that by operating a quarter-phase motor from single-phase circuit on one primary coil, its primary exciting admittance is doubled. Operating a three-phase motor single-phase on one circuit its primary exci...... e same motor on polyphase circuit, it follows that by operating a quarter-phase motor from single-phase circuit on one primary coil, its primary exciting admittance is doubled. Operating a three-phase motor single-phase on one circuit its primary exciting admittance is trebled. The self-inductive primary impedance is the same single-phase as polyphase...Apparatus Section 3: Induction Machines: Single -phase Induction Motor - 22 candidate hits
Source: Theoretical Elements of Electrical Engineering (1915)
Location: lines 20428-21157 - Tracked concepts: Admittance
... admit- tance per circuit Y = g - jb and self-inductive impedances ZQ = rQ + jxQ and Zi = TI + jxi per circuit with the same motor operating as single-phase motor from one pair of termi- nals, the single-phase exciting admittance is Y' = 3 Y (so as to give, the same volt-amperes excitation 3 eF), the primary 330 ELEMENTS OF ELECTRICAL ENGINEERING self-...... by the armature magnetization equal to the main magnetic flux produced by the impressed e.m.f. If an accurate calculation of the motor at intermediate speed and at standstill is required, the changes of effective exciting admittance and of secondary impedance, due to the decrease of the quadrature flux, have to be considered. At synchronism the total...Chapter 17: The Alternating-Current Transformer - 21 candidate hits
Source: Theory and Calculation of Alternating Current Phenomena (1916)
Location: lines 16521-17716 - Tracked concepts: Admittance
... y much smaller. Symbolic Method 149. In symbolic representation by complex quantities the transformer problem appears as follows: The exciting current, /oo, of the transformer depends upon the primary e.m.f., which dependence can be represented by an admittance, the "primary admittance," Fo = g^i - jbo, of the transformer. The resistance and reactance...... c Method 149. In symbolic representation by complex quantities the transformer problem appears as follows: The exciting current, /oo, of the transformer depends upon the primary e.m.f., which dependence can be represented by an admittance, the "primary admittance," Fo = g^i - jbo, of the transformer. The resistance and reactance of the primary and the...Chapter 12: Effective Resistance And Reactance - 20 candidate hits
Source: Theory and Calculation of Alternating Current Phenomena (1916)
Location: lines 10718-13483 - Tracked concepts: Admittance
... z - where z is determined by the magnetic characteristic of the iron and the shape of the magnetic and electric circuits - the impedance is represented, in phase and intensity, by the symbolic expression, Z - r -{- jx =^ z '&\n a -\- jz cos a; and the admittance by, 1 ^ g - JO = - Bin a - J- cos a = y sm a - jy cos a. The quantities z, r, x, and y, g,...... REACTANCE 129 m.m.f., / - effective current, since I\/2 = maximum current, the magnetic flux, (R (R Substituting this in the equation of the counter e.m.f. of self- induction, E = V2 irfn^ 10"', we have „ 2 wnJI 10-« ^= ^ 5 hence, the absolute admittance of the circuit is y = ^^ -^^^E = 2^f^T where 10« , , a = ^ - 5, a constant. 2 Trrr Therefore, the...Chapter 10: Effective Resistance And Reactance - 18 candidate hits
Source: Theory and Calculation of Alternating Current Phenomena (1900)
Location: lines 6957-8383 - Tracked concepts: Admittance
... s, - where s is determined by the mag- netic characteristic of the iron, and the shape of the magnetic and electric circuits, - the impedance is repre- sented, in phase and intensity, by the symbolic expression, Z = r - jx = z sin a - jz cos a ; and the admittance by, Y = g + j b = - sin a -j- j - cos a = y sin a -f- jy cos a. z z The quantities, z, r...... (R = magnetic reluctance of a circuit, £FA = maximum M.M.F., I - effective current, since /V2 = maximum cur- rent, the magnetic flux, (R (R Substituting this in the equation of the counter E.M.F. of self-induction we have (R hence, the absolute admittance of the circuit is (RIO8 = a& E ~ 2 TT n*N ~ N ' 108 where a = , a constant. 2 TT n Therefore, the...Reading Layers To Build Out
Section titled “Reading Layers To Build Out”| Layer | What to add next |
|---|---|
| Steinmetz wording | Pull exact source passages only after scan verification; keep OCR text labeled until then. |
| Modern engineering reading | Translate the source usage into present electrical-engineering or physics language without erasing the older vocabulary. |
| Mathematical layer | Link equations, variables, diagrams, and worked examples when the concept has formula candidates. |
| Historical layer | Identify whether the term is still used, renamed, absorbed into modern theory, or historically obsolete. |
| Ether-field interpretation | Keep interpretive readings separate from Steinmetz’s explicit claim and from modern physics. |
| Open questions | Record places where the concordance suggests a lead but the scan or edition has not yet been checked. |
Next Editorial Actions
Section titled “Next Editorial Actions”- Open the highest-priority source-text passages above and verify the wording against scans.
- Promote exact definitions, equations, diagrams, and hidden-gem passages into this page with source references.
- Add related concept links, equation pages, and diagram pages once the evidence is scan checked.
- Keep speculative or Wheeler-style readings in explicitly labeled interpretation blocks.
Math And Visual Evidence Map
Section titled “Math And Visual Evidence Map”Generated bridge: this section crosslinks the concept page with the formula atlas, figure atlas, source visual maps, and source formula maps. It is a routing layer, not final interpretation.
Formula candidates routed to this concept.
Figure candidates routed to this concept.
Modern guide diagrams related to this concept.
Formula Families To Review
Section titled “Formula Families To Review”Impedance, Reactance, And Admittance - Symbolic AC And Complex Quantities
Source Maps For This Concept
Section titled “Source Maps For This Concept”theory-calculation-alternating-current-phenomena visuals - theory-calculation-alternating-current-phenomena formulas - theory-calculation-alternating-current-phenomena-1900 visuals - theory-calculation-alternating-current-phenomena-1900 formulas - theory-calculation-alternating-current-phenomena-1897 visuals - theory-calculation-alternating-current-phenomena-1897 formulas - theory-calculation-electric-apparatus visuals - theory-calculation-electric-apparatus formulas - theoretical-elements-electrical-engineering visuals - theoretical-elements-electrical-engineering formulas - theory-calculation-electric-circuits visuals - theory-calculation-electric-circuits formulas
Related Modern Guide Diagrams
Section titled “Related Modern Guide Diagrams”Modern reading aid for induction-machine field language in AC and Theoretical Elements sources.
symbolic-method, magnetism, phase, induction-motor
Modern reading aid for conductance, susceptance, and reciprocal impedance.
admittance, conductance, susceptance, symbolic-method
Modern reading aid for number, direction, and symbolic calculation in Engineering Mathematics.
complex-quantities, number, symbolic-method
Modern redraw sheet for rectangular components, resultant addition, and quarter-period j rotation.
symbolic-method, complex-quantities, phasor, operator-j
Modern reading aid for vector and complex-number representation of alternating quantities.
symbolic-method, complex-quantities, phase, phasor
Modern guide for resistance, reactance, impedance, phase angle, and symbolic quantities.
impedance, reactance, power-factor, symbolic-method
Highest-Priority Formula Leads
Section titled “Highest-Priority Formula Leads”| Candidate | Family | OCR/PDF text | Routes |
|---|---|---|---|
theoretical-elements-electrical-engineering-eq-candidate-0102strong-formula-candidate | symbolic-ac | e = 2 7r/n$ sin r the instantaneous generated e.m.f. | source research review |
theory-calculation-alternating-current-phenomena-1900-eq-candidate-0240strong-formula-candidate | symbolic-ac | is r - j (x -f x0} = r = .6, x + x0 = 0, and tan S>0 = 0 ; | source research review |
theory-calculation-alternating-current-phenomena-eq-candidate-0167strong-formula-candidate | symbolic-ac | B = 6’ + jh” = 6(cos 13 + j sin /3) | source research review |
theory-calculation-alternating-current-phenomena-eq-candidate-0294strong-formula-candidate | symbolic-ac | is r - j {x + Xo) = r = 0.6, x -{- Xo = 0, and tan do = 0; that | source research review |
theory-calculation-electric-apparatus-eq-candidate-0028strong-formula-candidate | symbolic-ac | = - J = (tan a - j) (7) | source research review |
theory-calculation-alternating-current-phenomena-1900-eq-candidate-0001strong-formula-candidate | symbolic-ac | 1.) Ohm’s law : i = e j r, where r, the resistance, is a | source research review |
theory-calculation-alternating-current-phenomena-1900-eq-candidate-0131strong-formula-candidate | symbolic-ac | or, if E = e -\-je’ is the impressed E.M.F., and 7 = i ’ -\- ji’ | source research review |
theory-calculation-alternating-current-phenomena-eq-candidate-0206strong-formula-candidate | symbolic-ac | /, upon the e.m.f., or by IE cos d, where 9 = angle of time- | source research review |
Highest-Priority Figure Leads
Section titled “Highest-Priority Figure Leads”| Candidate | Caption lead | Section | Routes |
|---|---|---|---|
theory-calculation-alternating-current-phenomena-fig-049Fig. 49 | 7 1.8 Fig. 49. The sign in the complex expression of admittance is always opposite to that of impedance; this is obvious, since if the cur- | Chapter 8: Admittance, Conductance, Susceptance | source research review |
theory-calculation-alternating-current-phenomena-1900-fig-108Fig. 108 | 211 Fig. 108. admittance Y0) the exciting current, the other branches of the impedances ZJ + Z7, ZJ1 + Zn, … 2f + Zx, the latter | Chapter 14: The Alternating-Current Transformer | source research review |
theory-calculation-alternating-current-phenomena-fig-117Fig. 117 | of admittance Yq. Thus, double transformation will be represented by diagram. Fig. 117. With this the discussion of the alternate-current transformer ends, by becoming identical with that of a divided circuit con- | Chapter 17: The Alternating-Current Transformer | source research review |
theory-calculation-alternating-current-phenomena-fig-144Fig. 144 | nal admittance of the second machine. Fig. 144. Then, er + e’r = al^• | Chapter 23: Synchronizing Alternators | source research review |
theory-calculation-alternating-current-phenomena-fig-173Fig. 173 | 180 Fig. 173. magnetic reluctance, or its reciprocal, the magnetic reactance of the circuit. In consequence thereof the magnetism per field- | Chapter 25: Distortion Of Wave-Shape And Its Causes | source research review |