106 ELECTRICAL ENGINEERING 



This is a sine wave 90 degrees ahead of the current wave, with a 

 maximum value IQX and is the e.m.f. consumed by the reactance 

 in the circuit. 



The instantaneous value of the impressed e.m.f. (curve 5) is 

 the sum of the instantaneous values of e R and e x , thus 



........ (151) 



= 7o R sin 2 nft + I X sin (2 irft + 90) 



= I Q (R sin B + X cos 6) 



t / R X \ 



= In VR 2 +X 2 / Sm H ,- COS 



\\/7?2 I ya \/R 2 -l-Jf 2 / 

 = 7 Z sin ((9 4- 0), . - . . . (152) 



where Z = VR 2 +X 2 is called the impedance of the circuit and 

 is expressed in ohms and <f> is the angle of lead of the impressed 

 e.m.f. relative to the current. 



X R 



sin </> = -7===- and cos = 



The impressed e.m.f. is therefore a sine wave leading the cur- 

 rent by an angle <j>. Its maximum value is 



Eo = Jo VR*+X 2 = 7oZ, .... (153) 

 and its effective value is 



i 7= ~-= , 



V2 V2 



where / is the effective value of the current. 



The component of E in phase with the current is 



and the component of E 90 degrees ahead or in quadrature ahead 

 of the current is 



