ALTERNATING-CURRENT 



45 



(o) The value of the resistance. / (6) The circuit power-factor angle and 

 the power-factor, (c) The impedance-coil power-factor angle <f> and the 

 corresponding power-factor. (/' The circuit power. (V) The impedance- 

 coil power. (/) The impedance-coil resistance, (g) The impedance-coil 

 reactance. 



(a) R = E R /I = 60/4 = 15 ohms. An*. 



(b) Applying the law of cosines, page 457, to Fig. 42 (6), 

 80 s = 110 2 + GO 2 - 2 X 110 X 60 cos 



9,300 



COS = 



13,200 

 45.2. 



= 0.704. An*. 



.1 nx. 



O) 



=W V. 



C*) 



7=4. Oa 



'_'. Triangle of voltages for circuit having resistance and inductive im- 

 pedance in series. 



(c) By the law of sines, page 457, 

 sin/3 = 

 sin 6 80 



60 



sin = sin 45.2 



oU 



0.710 " : = 0.533 

 u 80 



/3 = 32.2 

 the exterior angle < is equal to the sum of the interior angles 6 and 



1. that is 



= 0+0 



<t> = 45.2 + 32.2 = 77.4. An*, 

 cos </> = cos 77.4 = 0.218. An*. 



The en-cult power 



/' 1 10 X 4 X cos = 440 X 0.704 = 310 watts.- Ans. 



(e) Tin- impcdance-eoil power 

 /' I: '/' X / X COS 



- 80 X 4 X 0.218 = 69.8 watts. 

 (/) I*R f = <i" 



j-.n w 



' ||p I.Uinhms. Xrw. 



(^) Th<- reactaOOe vtltau- in the impedaiK-e coil 

 - 80 X 0.976 - 78.1 volts. 



7s 1 



\ ''' ' : 



