. Theory and calculation of alternating current phenomena . - xo^ , or, approximately, / Eo Xq This potential control, however, causes the current takenfrom the mains to lag greatly behind the , and therebyrequires a much larger current than corresponds to the powerconsumed in the receiver circuit. Since a condenser draws from the mains a current in leadingphase, a condenser shunted across such a circuit carrying cur-rent in lagging phase compensates for the lag, the leading andthe lagging current combining to form a resultant current more CIRCUITS CONTAINING RESISTANCE 73 or less in pha
. Theory and calculation of alternating current phenomena . - xo^ , or, approximately, / Eo Xq This potential control, however, causes the current takenfrom the mains to lag greatly behind the , and therebyrequires a much larger current than corresponds to the powerconsumed in the receiver circuit. Since a condenser draws from the mains a current in leadingphase, a condenser shunted across such a circuit carrying cur-rent in lagging phase compensates for the lag, the leading andthe lagging current combining to form a resultant current more CIRCUITS CONTAINING RESISTANCE 73 or less in phase with the , and therefore proportional tothe power expended. In a circuit shown diagrammatically in Fig. 65, let the non-inductive receiver circuit of resistance, r, be connected in serieswith the inductive reactance, Xo, and the whole shunted by acondenser C of condensive reactance, Xc, entailing but a negligibleloss of Fig. 65. Then, if Eo = impressed ,the current in receiver circuit is T Eo I = . r—> r + jxothe current in condenser circuit isy Eo li = :—y JXc and the total current is /o = / + /, = £;« ^ = Ed I = Eo Vr2 + Xo /i ^0. r + jxo J. jx Xo or, in absolute terms, /o = Eq ir^ + xo^ xj\ \ \r2 + xoV ^ V Xo while the at receiver terminals is r E = Ir = Eo E = xj Eor r + jxo Vr^ + xo^ 62. The main current, 7o, is in phase with the , Eo, or the lagging current is coznpletely balanced, orsupplied by, the condensive reactance, if the imaginary term inthe expression of 7o disappears; that is, if Xo 1 r^ + .ro^ = 0. 74 ALTERNATING-CURRENT PHENOMENA This gives, expanded, r^ + xo^ Xq 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
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