By Charles Proteus Steinmetz

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Induced in the 8 volts, independent of the num- E = 4;z3>^V10~ ber of poles, or series or multiple connection of the armature, whether of the ring, drum, or other type. In an alternator or transformer, if n is the number of turns in series, <$ the maximum flux inclosed per turn, and the frequency, this formula gives, = 4 n$> JV10 - 8 volts. F. is ^max. we have ^ma*. F. avg. E, N 10 ~ is 8 VOltS. AT 10 ~8 volts, fundamental formula of alternating-current induction by sine waves. AL TERNA TING-CURRENT PHENOMENA 18 13.

29. F. consumed by the rein phase with the current, and equal to the prod- is uct of the current and resistance. rl = ri -\- Or jri' . F. produced by the reactance, If the L of alternating current, is the reactance, the counter or SYMBOLIC METHOD. F. F. r . ), and represented by the expression jx j~= jxi + xi'. F. required to overcome the resistance, and the reactance, x, is r, (r-jx)Ithat is Z= r jx is the expression of the impedance of the cir- cuit, in complex quantities. F. , and the current flowing in the circuit, its impedance or, if z= _ -\-je' is / = / r -f- is = ' |* 4- /' ji AL TERNA TING-CURRENT PHENOMENA.

And current ; or conversely, at a given primary Fig. 20. , v will be smaller with an inductive, and larger with a condenser , (leading current) load, than with a non-inductive load. At the same time we see that a difference of phase 'existing in the secondary circuit of a transformer reappears ALTERNATING-CURRENT PHENOMENA. 32 in the primary circuit, somewhat decreased Later we if [22 leading, and see that lagging. slightly increased hysteresis reduces the displacement in the primary circuit, so that, with an excessive lag in the secondary circuit, the if shall lag in the primary circuit may be less than in the secondary.