Chapter 9: Divided Circuit
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Source Metadata
Section titled “Source Metadata”| Field | Value |
|---|---|
| Source | Theory and Calculation of Transient Electric Phenomena and Oscillations |
| Year | 1909 |
| Section ID | theory-calculation-transient-electric-phenomena-oscillations-chapter-31 |
| Location | lines 9228-10474 |
| Status | candidate |
| Word Count | 3576 |
| Equation Candidates In Section | 0 |
| Figure Candidates In Section | 0 |
| Quote Candidates In Section | 0 |
Opening Source Excerpt
Section titled “Opening Source Excerpt”CHAPTER IX. DIVIDED CIRCUIT. 72. A circuit consisting of two branches or multiple circuits 1 and 2 may be supplied, over a line or circuit 3, with an impressed e.m.f., e0. Let, in such a circuit, shown diagrammatically in Fig 31, rv Lv Cl and r2, L2, Cz — resistance, inductance, and capacity, respectively, of the two branch circuits 1 and 2; r0, L0, C0 = Co Fig. 31. Divided circuit. resistance, inductance, and capacity of the undivided part of the circuit, 3. Furthermore let e = potential difference at terminals of branch circuits 1 and 2, it and i2 respectively = currents in branch circuits 1 and 2, and i3 = current in undivided part of circuit, 3. Then ia = il + i2 and e.m.f. at the terminals of circuit 1 is ofSource-Located Theme Snippets
Section titled “Source-Located Theme Snippets”Dielectricity / capacity
Section titled “Dielectricity / capacity”... DIVIDED CIRCUIT. 72. A circuit consisting of two branches or multiple circuits 1 and 2 may be supplied, over a line or circuit 3, with an impressed e.m.f., e0. Let, in such a circuit, shown diagrammatically in Fig 31, rv Lv Cl and r2, L2, Cz — resistance, inductance, and capacity, respectively, of the two branch circuits 1 and 2; r0, L0, C0 = Co Fig. 31. Divided circuit. resistance, inductance, and capacity of the undivided part of the circuit, 3. Furthermore let e = potential difference at terminals of branch circuits 1 and 2, it and i2 respec ...Impedance / reactance
Section titled “Impedance / reactance”... e.m.f. at the terminals of circuit 1 is of circuit 2 is e = di 121 (2) (3) 122 TRANSIENT PHENOMENA and of circuit 3 is (4) Instead of the inductances, L, and capacities, C, it is usually preferable, even in direct-current circuits, to introduce the reactances, x = 2 nfL = inductive reactance, xc = = con- 2 7T/G densive reactance, referred to a standard frequency, such as / = 60 cycles per second. Instead of the time t, then, an angle 0 = 2 nft (5) is introduced, and then we have di x di dd di ^ * (6) i/iift - 2 Kfo f ...Transients / damping
Section titled “Transients / damping”... terminals of branch circuits 1 and 2, it and i2 respectively = currents in branch circuits 1 and 2, and i3 = current in undivided part of circuit, 3. Then ia = il + i2 and e.m.f. at the terminals of circuit 1 is of circuit 2 is e = di 121 (2) (3) 122 TRANSIENT PHENOMENA and of circuit 3 is (4) Instead of the inductances, L, and capacities, C, it is usually preferable, even in direct-current circuits, to introduce the reactances, x = 2 nfL = inductive reactance, xc = = con- 2 7T/G densive reactance, referred to a standard ...Complex quantities
Section titled “Complex quantities”... 3 the engineer who is mainly familiar with the effect of inductance in alternating-current circuits. Substituting therefore (5) and (6) in equations (2), (3), (4), gives the e.m.f. in circuit 1 as dL e = rli1 + xl -r1 + a in circuit 2 as dL ' C * = r** + **-fi + *ctJi,M', (8) in circuit 3 as e = e a. r { 4. x -h. _j_ x I { ^. /Q\ 0 03 ' 0 J/j ' CQ I 3 J v*^/ tZC7 «/ hence, the potential differences at the condenser terminals are /di< i,dd = e-r1i1- xt— S (10) e2= <J *i dd = e- r2i2 -*,-^> (11) and e3 = xco I i3dd = e0- e - r0i ...Chapter-Local Concept Hits
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| Frequency | 7 | seeded |
| Light | 1 | seeded |
Chapter-Local Glossary Hits
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Modern Engineering Reading Prompts
Section titled “Modern Engineering Reading Prompts”- Dielectricity / capacity: Check whether the passage treats capacity, condensers, displacement, or dielectric stress as field storage rather than only circuit algebra.
- Impedance / reactance: Translate historical opposition terms into modern impedance, admittance, conductance, susceptance, and complex-plane notation.
- Transients / damping: Separate the temporary term from the final steady-state term and compare with differential-equation response language.
- Complex quantities: Track how Steinmetz preserves geometric rotation and quadrature while translating the same operation into symbolic form.
- Radiation / light: Compare the chapter’s radiation vocabulary with modern electromagnetic radiation, spectral frequency, wavelength, absorption, and illumination engineering.
Ether-Field Interpretive Boundary
Section titled “Ether-Field Interpretive Boundary”- 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.
- Transients / damping: Transient collapse, impulse, and surge behavior can be compared with alternative field language, but only as a clearly marked reading.
- Radiation / light: Radiation and wave language can invite ether-field comparison, but source wording, modern radiation theory, and speculative synthesis must stay separated.
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