. Theory and calculation of alternating current phenomena . f thefunction represented by the curve. Thus we have / = rro + X(s-\/z^ — r^ is a maximum or minimum, if 2r) = 0; ro\/z^ — r^ — XqT = VoX — Xor = 0,or, r -7- X ^ ro -T- Xo. That is, the drop of potential is a maximum, if the reactance X Xn factor, -, of the receiver circuit equals the reactance factor, —, of the series impedance. 60. As an example. Fig. 61 shows the , E, at the receiverterminals, at a constant impressed , Eo = 100, a constant dr Differentiating, we get ,1 Xo ^ ^« + 2 V.^ - r^^ or, expanded. CIRCUITS CONTAI
. Theory and calculation of alternating current phenomena . f thefunction represented by the curve. Thus we have / = rro + X(s-\/z^ — r^ is a maximum or minimum, if 2r) = 0; ro\/z^ — r^ — XqT = VoX — Xor = 0,or, r -7- X ^ ro -T- Xo. That is, the drop of potential is a maximum, if the reactance X Xn factor, -, of the receiver circuit equals the reactance factor, —, of the series impedance. 60. As an example. Fig. 61 shows the , E, at the receiverterminals, at a constant impressed , Eo = 100, a constant dr Differentiating, we get ,1 Xo ^ ^« + 2 V.^ - r^^ or, expanded. CIRCUITS CONTAINING RESISTANCE 71 impedance of the receiver circuit, z = , and constant series impedances, Zo = + j (Curve I) Zo = +j (Curve II) as functions of the reactance, x, of the receiver circuit. 150 140 130 120 110 100 90 80 70 / / 1 / / / / A / ,.-- ^ Zo __ c +.4 j^ / 605040 / ^ / :+-! Ri . ^ -^ ^ lo — 302010 1. .9 .8 .7 .6 .5 ,4 .3 .2 .1 0 —^ Fig. 61. E // Uo / /> Uo // / f I 0 ] r tro. Fig. 62. Fig. 63. 72 ALTERNATING-CURRENT PHENOMENA Figs. 62 to 64, give the vector diagram for ^o = 100, x = ,X =. 0,x = - , and Zo = + j.
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