ALTKRNATINQ-CURRRNT CIRCUITS 41 



The current taken by the resistance 



120 

 IK = -r^r = 12 amp. in phase witli K. 



IL = - - =15 amp. in quadrature with E and lagging. 



o 



/ = -r=- = 8 amp. in quadrature with E and leading, 

 lo 



.rronts are shown vectorially in Fig. 39 (b). 



Thf voltaic is tho same for all three blanches of the circuit and is laid 

 off as tho horizontal vector. The resistance current / is in phase with 

 the voltage K. The inductive current lags the voltage by 90 and the 

 condensive current leads the voltage by 90. As the inductive current and 

 condensive current are in exact opposition, they subtract from each 

 other, leaving 7 amp. lagging by 90. The resultant current /o is the 

 vector sum of the 7 amp. and the 12 amp. 



(a) / = \/12 8 + 7 s = 13.9 amp. lagging. AUK. 



(b) Obviously the cosine of the angle 6 between the voltage and the 



current is 



cos e = y* = T^ = 0.864 = P.P. Ans. 

 lo lo.9 



(c) P = EI R = 120 X 12 = 1,440 watts. Ans. 



Also P = EIo cos 6 = 120 X 13.9 X 0.864 = 1,440 watts. Ans. 



For convenience the following equations are given for the 



parallel circuit. 

 R and L in parallel 



R and C in parallel 



R, L. anil ( in p nallel 



z _ __ 1 



/ - 



the total current :m( | /; i< the circuit v.. It age. 



22. Resonance in a Parallel Circuit.- Resonance in a parallel 

 circuit exiMs when tin- resultant mrrent and the line voltage are 



