Theory and calculation of alternating current phenomena . V2 + .To2 .T,/r y ^ \r2 + a-o^ xj while the at receiver terminals is r E = Ir = Ec E = Eor • r + j^o Vr2 + Xo- 62. The main current, /o, is in phase with the , £0, or the lagging current is completely balanced, orsupplied by, the condensive reactance, if the imaginary term inthe expression of h disappears; that is, if a-o 1 r^ + Xo~ = 0. 74 ALTERNATING-CURRENT PHENOMENA This gives, expanded, Xo Hence the capacity required to compensate for the laggingcurrent produced by the insertion of inductive reactance inseries
Theory and calculation of alternating current phenomena . V2 + .To2 .T,/r y ^ \r2 + a-o^ xj while the at receiver terminals is r E = Ir = Ec E = Eor • r + j^o Vr2 + Xo- 62. The main current, /o, is in phase with the , £0, or the lagging current is completely balanced, orsupplied by, the condensive reactance, if the imaginary term inthe expression of h disappears; that is, if a-o 1 r^ + Xo~ = 0. 74 ALTERNATING-CURRENT PHENOMENA This gives, expanded, Xo Hence the capacity required to compensate for the laggingcurrent produced by the insertion of inductive reactance inseries with a non-inductive circuit depends upon the resistanceand the inductive reactance of the circuit. Xo being constant,with increasing resistance, r, the condensive reactance has to beincreased, or the capacity decreased, to keep the balance. Substituting r- + a-Q- Xc = Xq we get, as the equations of the inductive circuit balanced bycondensive reactance, Eo(r — jxo) I = £jo r + jXo T = jEoXo i 1 /•2 + Xo /o = Eor r2 + .To^^ 77- Eor r^ + Xo^ h =. r + jxo -vr^ + Xo and for the power expended in the receiver circuit, _ ^oV _ that is, the main current is proportional to the expenditure ofpower. For r = 0, we have Xc = Xo, as the condition of balance. Complete balance of the lagging component of current byshunted capacity thus requires that the condensive reactance Xcbe varied with the resistance, r; that is, with the varying loadon the receiver circuit. In Fig. 66 are shown, for a constant impressed , Eo =1000 volts, and a constant series reactance, Xo = 100 ohms, valuesfor the balanced circuit of current in receiver circuit (Curve I),current in condenser circuit (Curve II),current in main circuit (Curve III), at receiver terminals (Curve IV), CIRCUITS CONTAINING RESISTANCE 75 with the vahies the resistance, r, of the receiver circuit asabscissas. 63. If, however, the condensive reactance is left unchanged,Xc = Xo at the no-load value, the circuit is Ijalanced
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