Impedance
Steinmetz Usage
Section titled “Steinmetz Usage”Impedance is the alternating-current opposition that combines resistance and reactance. In the symbolic method, Steinmetz represents it as a complex quantity:
The OCR candidate in Chapter V places this directly after the discussion of current as a complex wave and the voltage required to overcome resistance and reactance.
Modern Equivalent
Section titled “Modern Equivalent”Modern notation usually writes:
where R is resistance, X is total reactance, and |Z| is impedance magnitude.
Physical Meaning
Section titled “Physical Meaning”Resistance is the power-consuming part. Reactance is the field-storage part. Impedance is the total relation between alternating voltage and alternating current when both effects are present.
Mathematical Layer
Section titled “Mathematical Layer”This is Ohm’s law restored for AC, but only after voltage, current, and opposition are treated as complex quantities with phase.
Ether-Field Interpretive Reading
Interpretive only: impedance can be read as the circuit-level expression of both dissipative opposition and field-storage opposition. Field-centered readers may emphasize the latter, but the source claim remains an engineering relation between voltage, current, resistance, and reactance.
Related Pages
Section titled “Related Pages”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 313 candidate hits across 28 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.
Terms And Aliases Tracked
Section titled “Terms And Aliases Tracked”impedance, impedances
Concordance Records
Section titled “Concordance Records”Source Distribution
Section titled “Source Distribution”| Source | Candidate Hits | Sections | Concepts represented |
|---|---|---|---|
| Theory and Calculation of Alternating Current Phenomena | 313 | 28 | Impedance |
| Theory and Calculation of Electric Apparatus | 255 | 12 | Impedance |
| Theory and Calculation of Alternating Current Phenomena | 243 | 23 | Impedance |
| Theory and Calculation of Alternating Current Phenomena | 170 | 19 | Impedance |
| Theoretical Elements of Electrical Engineering | 160 | 30 | Impedance |
| Theory and Calculation of Transient Electric Phenomena and Oscillations | 59 | 18 | Impedance |
| Theory and Calculation of Electric Circuits | 45 | 7 | Impedance |
| Engineering Mathematics: A Series of Lectures Delivered at Union College | 22 | 3 | Impedance |
Priority Passages To Read
Section titled “Priority Passages To Read”Chapter 17: The Alternating-Current Transformer - 45 candidate hits
Source: Theory and Calculation of Alternating Current Phenomena (1916)
Location: lines 16521-17716 - Tracked concepts: Impedance
Open source text - Open chapter workbench
... 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 secondary circuit are represented in the impedance by Zo = To + jxo, and Zi = ri + jxi. Within the limited range of variation of the magneti...... The resistance and reactance of the primary and the secondary circuit are represented in the impedance by Zo = To + jxo, and Zi = ri + jxi. Within the limited range of variation of the magnetic density in a constant-potential transformer, admittance and impedance can usually, and with sufficient exactness, be considered as constant. Let no = number of...Chapter 5: Single-Phase Induction Motor - 44 candidate hits
Source: Theory and Calculation of Electric Apparatus (1917)
Location: lines 8555-10582 - Tracked concepts: Impedance
Open source text - Open chapter workbench
... hus is proportional to the quadrature flux. At synchronism, the quadrature magnetic flux produced by the armature currents becomes equal to the main magnetic flux produced by the impressed single-phase voltage (approximately, in reality it is less by the impedance drop of the exciting current in the armature conductors) and the magnetic disposition of...... olt-ampere excitation of the single- phase motor thus is the same as in the polyphase motor at the same induced voltage, and decreases to half this value at stand- still, where only one of the two quadrature components of magnetic flux exists. The primary impedance of the motor is that of the circuits used. The secondary impedance varies from the join...Chapter 16: Induction Motor - 42 candidate hits
Source: Theory and Calculation of Alternating Current Phenomena (1900)
Location: lines 13649-16361 - Tracked concepts: Impedance
Open source text - Open chapter workbench
... em ; if r^ = secondary resistance per circuit, rt = a2 r{ = secondary resistance per circuit reduced to primary system ; if x± = secondary reactance per circuit, xt = a2 x\ = secondary reactance per circuit reduced to primary system ; if £/ = secondary impedance per circuit, z1 = azz\ = secondary impedance per circuit reduced to primary system ; that...... rt = a2 r{ = secondary resistance per circuit reduced to primary system ; if x± = secondary reactance per circuit, xt = a2 x\ = secondary reactance per circuit reduced to primary system ; if £/ = secondary impedance per circuit, z1 = azz\ = secondary impedance per circuit reduced to primary system ; that is, the number of secondary circuits and of tur...Chapter 19: Alternating- Current Motors In General - 39 candidate hits
Source: Theory and Calculation of Electric Apparatus (1917)
Location: lines 21713-23905 - Tracked concepts: Impedance
Open source text - Open chapter workbench
... it, r', consumes an e.n r'(, in phase with the current, and the total or effective resistance of the circuit is, therefore, r = r' + r", and the total e.m.f. consumed by the circuit, or the impressed e.m.f.. is: E = (r+jx)I = Z{, .where : Z = r + jx = impedance, in vector denotation, z = Vr* + i* = impedance, in absolute terms. If an electric circuit...... urrent, and the total or effective resistance of the circuit is, therefore, r = r' + r", and the total e.m.f. consumed by the circuit, or the impressed e.m.f.. is: E = (r+jx)I = Z{, .where : Z = r + jx = impedance, in vector denotation, z = Vr* + i* = impedance, in absolute terms. If an electric circuit is in inductive relation to another electa circu...Chapter 4: Induction Motor With Secondary Excitation - 37 candidate hits
Source: Theory and Calculation of Electric Apparatus (1917)
Location: lines 5555-8554 - Tracked concepts: Impedance
Open source text - Open chapter workbench
... As illustration is shown in Fig. 20 the load curve of a typical 100-hp. 60-cycle 80-polar induction motor (90 revolutions per minute) of the constants: Impressed voltage: ea = 500. Primary exciting admittance: Ya = 0.02 - 0.6 j. Primary self-inductive impedance: Zu = 0.1 + 0.3j. Secondary self-inductive impedance: Zi = 0.1 + 0.3 j. INDUCTION MOTOR 53...... typical 100-hp. 60-cycle 80-polar induction motor (90 revolutions per minute) of the constants: Impressed voltage: ea = 500. Primary exciting admittance: Ya = 0.02 - 0.6 j. Primary self-inductive impedance: Zu = 0.1 + 0.3j. Secondary self-inductive impedance: Zi = 0.1 + 0.3 j. INDUCTION MOTOR 53 As seen, at full-load of 75 kw. output, the efficiency i...Chapter 12: Frequency Converter Or General Alternating Current Transformer - 33 candidate hits
Source: Theory and Calculation of Electric Apparatus (1917)
Location: lines 14897-17124 - Tracked concepts: Impedance
Open source text - Open chapter workbench
... air gap in the magnetic circuit, to permit movability between primary and secondary, and thus they require a higher magnetizing current than the closed magnetic circuit stationary transformer, and this again results in general in a higher self- inductive impedance. Thus, the frequency converter and in- duction motor magnetically represent transformers...... magnetic circuit stationary transformer, and this again results in general in a higher self- inductive impedance. Thus, the frequency converter and in- duction motor magnetically represent transformers of high ex- citing admittance and high self-inductive impedance. 104. The mutual magnetic flux of the transformer is pro- duced by the resultant m.m.f....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.