ELECTRIC CIRCUITS 



111 



and 



therefore, 



R sin 4> =2 irfL cos < ^ _ fn cos <, 

 1 



tan (f> = 



sin <f> = 



cos = 



and from equation 162 

 T/ 7 7? 



IQ COS <f> 



= VR*+(X-X C ) Z = Z, . . (166) 



where 



is the impedance of the circuit. 

 y 



2 ,L - 





FIG. 79. Sine wave. 



The impressed e.m.f. is therefore a sine wave of maximum 

 value EQ = I Z = I VR 2 + ( X X c ) 2 , and leads the current 



V V 



wave by an angle = tan~ 



R 



If X c > X, < is negative and the impressed e.m.f. lags behind the 

 current. 



If X c = X, <j> = and the e.m.f. is in phase with the current, 

 and the impedance of the circuit is Z = R. 



79. Vector Representation of Harmonic Quantities. A sine 

 wave may be obtained from a circular locus as shown in Fig. 79. 



