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Theory Section 18: Equivalent Sine Waves

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FieldValue
SourceTheoretical Elements of Electrical Engineering
Year1915
Section IDtheoretical-elements-electrical-engineering-section-18
Locationlines 7381-7736
Statuscandidate
Word Count962
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18. EQUIVALENT SINE WAVES 87. In the preceding chapters, alternating waves have been assumed and considered as sine waves. EQUIVALENT SINE WAVES 107 The general alternating wave is, however, never completely, frequently not even approximately, a sine wave. A sine wave having the same effective value, that is, the same square root of mean squares of instantaneous values, as a general alternating wave, is called its corresponding "equivalent sine wave." It represents the same effect as the general wave. With two alternating waves of different shapes, the phase relation or angle of lag is indefinite. Their equivalent sine waves, however, have a definite phase relation, that which gives the same effect as the general wave, that is, the same mean (ei). Hence if e = e.m.f. and i = current of a general alternating wave,
18. EQUIVALENT SINE WAVES 87. In the preceding chapters, alternating waves have been assumed and considered as sine waves. EQUIVALENT SINE WAVES 107 The general alternating wave is, however, never completely, frequently not even approximately, a sine wave. A sine ...
... rH 00 00 T-( c co" co"co"co'Nco>i-r ^^^ooooooo 1— «O ..» 00 00^2 ^ ^ ^ se ^ oo oo . < r-l CO ?CI> i-H QJ CO EQUIVALENT SINE WAVES 109 Fig. 41 and Table I, the number of primary turns is 500, the length of the magnetic circuit 50 cm., and its section shall be chosen so as to give a maximum density B = 15,000. At this density the hysteretic cycle is as shown in Fig. 42 and Table II. FIG. 41. — Wave-shape of e.m.f. in example 88. What is the shape ...
... of B' of column (6) are found as the relative instantaneous values of magnetic flux density. Since the maximum magnetic flux density is 15,000 the in- 15 000 stantaneous values are B = B' ' . , plotted in column (7). From the hysteresis cycle in Fig. 42 are taken the values of magnetizing force /, corresponding to magnetic flux density B. They are recorded in column (8), and in column (9) the instan- taneous values of m.m.f. F = If, where I = 50 = length of magnetic ...
... aves. Considering in the preceding the alternating currents as equiva- lent sine waves representing general alternating waves, the investigation becomes applicable to any alternating circuit irrespective of the wave shape. The use of the terms reactance, impedance, etc., implies that a wave is a sine wave or represented by an equivalent sine wave. Practically all measuring instruments of alternating waves (with exception of instantaneous methods) as ammsters, volt- meters, wattmeters, etc., g ...
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  • Waves / transmission lines: Map Steinmetz’s wave and line language onto modern distributed constants, propagation velocity, standing waves, and reflections.
  • Magnetism: Track flux, reluctance, permeability, magnetizing force, and loss language against modern magnetic-circuit terminology.
  • Hysteresis: Compare the passage with modern magnetic loss, B-H loop area, lag, material memory, and empirical loss laws.
  • Impedance / reactance: Translate historical opposition terms into modern impedance, admittance, conductance, susceptance, and complex-plane notation.
  • Alternating current: Compare Steinmetz’s AC language with modern sinusoidal steady-state analysis, RMS quantities, phase, and phasor notation.
  • Waves / transmission lines: Standing/traveling wave passages may support richer field interpretations; the page keeps those readings separate from verified Steinmetz wording.
  • Magnetism: Centrifugal/divergent magnetic-field readings are interpretive overlays, not automatic historical claims.
  • 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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