ELECTRIC CIRCUITS 

 From the vector diagram 



123 



and leads E by an angle </>, where 



l/X e -l/X 



The impedance of the circuit is 



1 t/I + /l_JL 



VjR* + U X c ) 



(9) Find the magnitudes of the currents in the various parts 

 of the circuit in Fig. 94 and their phase relations with the im- 

 pressed e.m.f. 



I 



H ii 



:Ri R 2 



Xi 



X 2 



FIG. 94. 



E 



angle <i, where tan <i = 77 ; 



HI 



E 



and lags behind the impressed e.m.f. by an 

 X, 



and leads the e.m.f. by an angle $2, where 



/ = /! 2 -f- 7 2 2 -f 2 /i/ 2 cos (0! + $2) (see vector diagram) and 

 lags behind the e.m.f. by an angle 0, where 



1 1 sin <f>i - 7 2 sin <fe 

 tan 9 = ^ ; ^ - . 



/I COS 4>i + /2 COS 02 



The power consumed in the circuit is 

 P = El cos 



= /i 2 ^ + 7 2 2 #2 watts. 



