ELECTRIC CIRCUITS 



113 



of the eoin.f . e = E Q sin 6, and 01 



I = ~= is the effective 



Vz 



value of the current i = I sin (0 $). The vector 01 is be- 

 hind the vector OE by angle < and so indicates the relative phase 

 of the two quantities. The counter-clockwise direction is taken 

 as the direction of advance in phase since it was adopted at the 

 International Electrotechnical Congress at Turin and is now 

 standard. 



80. Power and Power Factor. In continuous current cir- 

 cuits the power consumed is the product of the impressed e.m.f. 

 and the current, and is 



P = EI watts (167) 



In alternating-current circuits the power varies with time; its 

 instantaneous value is 



p = ei watts, (168) 



where e and i are the instantaneous values of the e.m.f. and 

 current in the circuit. 



FIG. 81. Power in a non-inductive circuit. 



Two cases will be considered, first, when the current and e.m.f. 

 are in phase and, second, when the current lags behind the e.m.f. 



Case I. If an e.m.f. e = E sin 6 is impressed on the terminals 

 of a circuit of resistance R a current i = J sin 6 will flow in 

 phase with the e.m.f. 



The instantaneous power in the circuit is 



, p = ei = E Q 7 sin 2 = ^ (1 - cos20). . . (169) 

 The values of e, i and p for a complete cycle are plotted in Fig. 81. 



