ALTERNA TING-CURRENT CIRCl'ITS 



47 



That is, the vector sum of the three voltages is equal to the line 

 voltage, which condition exists in the circuit. 



-A resistance, an impedance coil and a condenser are all con- 

 : in scries. The voltage across the resistance is 80 volts; that across 

 the impedance coil is 70 volts; that across the condenser is 90 volts and the 

 line voltage is 120 volts. A current of 5 amp. flows in the circuit and the 

 condenser current leads its voltage by 90. Determine: (a) The cir- 

 cuit power-factor angle 0. (6) The resistance and reactance of the impe- 

 dance coil. 



The voltage polygon is shown in Fig. -\ \. 



120.5 volts 



(a) E' 



+ 80 2 = \ 1 I . 



tan a = 



90 



80 



1.125 a = 48. 



/ =5.0a 



cos 



(7=907. E c + E B = 120. 5V. 



1 \. Polygon of voltages for alternating-current scries circuit. 



Applying the law of cosines to triangle oab, 70 1 = 120.5 2 + 120 s - 

 2 X 120.5 X 120 cos ft. 



24,0nn 



28,900 

 ft = 33.8 



= a -ft = 4S- 33.8 = 14.2 

 cos 14.2 = 0.969 (curn-nt leads). 



(6) The distance ,.,! UO cos 6 = 120 X 0.969 = 116.4 volts, oc - 

 " is th< ii of oc on od and c'd is the projection of 



nl> on ofl and ab is equal and parallel to oc. 

 Tli> 



oc - od- 80-116.4 -80 -3<, 



3 ohms resistance in imp' .1. Ans. 



3 70> ~ '^ 

 ce - \ 580 - 59.8 volts. 



")'.> X 



1 I 'Hi ,, ; 'icr m impedance coil. An*. 



