Theory Section 14: Rectangular Coordinates
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Source Metadata
Section titled “Source Metadata”| Field | Value |
|---|---|
| Source | Theoretical Elements of Electrical Engineering |
| Year | 1915 |
| Section ID | theoretical-elements-electrical-engineering-section-14 |
| Location | lines 5264-5831 |
| Status | candidate |
| Word Count | 1710 |
| Equation Candidates In Section | 0 |
| Figure Candidates In Section | 0 |
| Quote Candidates In Section | 0 |
Opening Source Excerpt
Section titled “Opening Source Excerpt”14. RECTANGULAR COORDINATES 64. The vector diagram of sine waves gives the best insight into the mutual relations of alternating currents and e.m.fs. For numerical calculation from the vector diagram either the trigonometric method or the method of rectangular components is used. The method of rectangular components, as explained in the above paragraphs, is usually simpler and more convenient than the trigonometric method. In the method of rectangular components it is desirable to distinguish the two components from each other and from the resultant or total value by their notation. To distinguish the components from the resultant, small letters are used for the components, capitals for the resultant. Thus in the transformer diagram of Section 13 the secondary current I\ has the horizontal component ii = — I\ cos 0i, and the vertical component i'\Source-Located Theme Snippets
Section titled “Source-Located Theme Snippets”Complex quantities
Section titled “Complex quantities”... mponents undesirable, since indices are reserved for distinguishing different e.m.fs., currents, etc., from each other. Thus the most convenient way is the addition of a prefix or coefficient to one of the components, and as such the letter j is commonly used with the vertical component. Thus the secondary current in the transformer diagram, Section 13, can be written i\ + ji* = Ii cos 0i + jli sin 0i. (1) This method offers the further advantage that the two com- ponents c ...Impedance / reactance
Section titled “Impedance / reactance”... urrent is J0 = I' + J00 = (aii + h) -j (aiz + g). (9) The e.m.f. consumed by primary resistance rQ is r0Jo = TQ (aii + h) - jr0 (aiz + 0). (10) The horizontal component of primary current (aii + h) gives as e.m.f. consumed by reactance XQ a negative vertical com- ponent, denoted by JXQ (aii + h). The vertical component of primary current j (aiz + g) gives as e.m.f. consumed by react- ance XQ a positive horizontal component, denoted by XQ (aiz + (/)• Thus the total e.m ...Waves / transmission lines
Section titled “Waves / transmission lines”14. RECTANGULAR COORDINATES 64. The vector diagram of sine waves gives the best insight into the mutual relations of alternating currents and e.m.fs. For numerical calculation from the vector diagram either the trigonometric method or the method of rectangular components is used. The method of rectangula ...Alternating current
Section titled “Alternating current”... The method of rectangular components, as explained in the above paragraphs, is usually simpler and more convenient than the trigonometric method. In the method of rectangular components it is desirable to distinguish the two components from each other and from the resultant or total value by their notation. To distinguish the components from the resultant, small letters are used for the components, capitals for the resultant. Thus in the transformer diagram of Section 13 the second ...Chapter-Local Concept Hits
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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.
- Alternating current: Compare Steinmetz’s AC language with modern sinusoidal steady-state analysis, RMS quantities, phase, and phasor notation.
- Hysteresis: Compare the passage with modern magnetic loss, B-H loop area, lag, material memory, and empirical loss laws.
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.
- Hysteresis: An interpretive reading can treat hysteresis as field lag or memory, but the historical claim must remain Steinmetz’s actual magnetic-loss treatment.
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