Theory and Calculation of Alternating Current Phenomena by Charles Proteus Steinmetz

By Charles Proteus Steinmetz

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A wave of equal intensity, but lagging 90, or onequarter period, behind a -f jb, has (Fig. 24) the horizontal SYMBOLIC METHOD. component, b, and the vertical 37 component, a, resented symbolically by the expression, ja Multiplying, however, a therefore, j, if we + jb and is rep- b, by/, we get : define the heretofore meaningless symbol, by the condition, y 2 =- i, we have hence /(*+/*) =ja 1>; : Multiplying the symbolic expression, a -\- jb, of a sine wave by j means rotating the wave through 90, or one-quarter period ; tJiat is, retarding the wave through one-quarter period.

Which is induction r7V7 10- 8 is VOltS. F. we have volts. given by, sine waves. 8 volts, formula of alternating-current AL TERNA TING-CURRENT PHENOMENA, 18 13. If, of n turns, the in a circuit inclosed by the circuit is magnetic flux, produced by the current flowing , in the circuit, the ratio X number flux of turns current is X 10~ 8 . called the inductance, L, of the circuit, in henrys. F. of self-inductance is: E = V2 =' 2 The product, x = and is 2 TT NLI vNL, is volts. F. F. lags 90 behind the magnetic flux.

Calculate the numerical values Usually, howtrigonometrically by means of the diagram. ever, this becomes too complicated, as will be seen by trying Fig. 21. F. is given by the of transformation. equation : = Vfr + S^ + 20^ sin Wi, 2 ffo 2 an expression not well suited as a starting-point for further calculation. A method exactness of is therefore desirable which combines the analytical calculation with the clearness of the graphical representation. Fig. 22. 25. We have seen that the alternating sine wave is represented in intensity, as well as phase, by a vector, Of, which is determined analytically by two numerical quantithe length, Of, or intensity ; and the amplitude, AOf, or phase <3, of the wave, /.

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