ELECTRIC CIRCUITS 109 



the impressed e.m.f. and its phase relation with the current. 

 (Fig. 78.) 



The impressed e.m.f. consists of two components; one is re- 

 quired to drive the current i (curve 1) through the resistance of 

 the circuit; it is CR = iR (curve 2), in phase with i; the other 

 component is the e.m.f. required at the terminals of the con- 

 denser or the e.m.f. consumed by the condensive reactance of 



the circuit; it is ex c = and was shown to lag 90 degrees behind 



the current. Art. 76 (curve 3). 



The total impressed e.m.f. is (curve 4) 



(156) 



RI sin 2 itft + ^ f/o sin (2 */) dt 



RI sin 2 irft - cos 



= I (R sin 2 irft X c cos 2 irft) 



(157) 



where Z = VR 2 +X C 2 is the impedance of the circuit in ohms, 

 and is the angle of lag of the impressed e.m.f. behind the cur- 



X 

 rent; ^4,=^==, cos = 



78. Resistance, Inductance and Capacity in Series. If a 



current i I sin 2 irft flows in a circuit consisting of a resistance 

 R, inductance L and capacity C connected in series, the impressed 

 e.m.f. is 



e = e R + ex + e Xe , ..... (158) 



