

M/rVRNATlKd (' I 'It RENTS 



negative, this energy is being given back again to the source. 

 Although the net power is zero, there is a continual transfer of 

 cnorgy from the source to the condenser and back again to the 

 source. 



16. Circuit Containing Resistance and Inductance in Series. 

 Figure 31 shows a circuit consisting of a resistance R and an 

 inductive reactance X L connected in series 

 across an alternating circuit whose frequency 

 is / cycles per second. The voltage impressed 

 across the circuit is E and a current / flows, 

 it be required to determine the relations 

 31. Cirtmit among /, E, R, and X L . 



Figure 32 (a) shows a vector diagram for 

 tm 's circuit. As the current / is the same in 

 both X L and R, it is laid off horizontally to 

 scale. The position of the current vector / is arbitrary. (It 

 is given the position shown merely for convenience.) From Fig. 

 23 (6), page 25, the voltage E R across the resistance R is in phase 

 with the current. Therefore, it is laid off along the current vector. 

 From Fig. 27, page 28, the voltage E L across the inductance 

 leads the current / by 90 and is equal to IX L . 



FIG. 



containing resistance 

 and inductance in 



(a) 



Fio. 32. Vector diagram for a series circuit containing resistance and 

 inductance. 



The line voltage E must be the vector sum of these two volt- 

 ages, so the parallelogram is completed and the diagonal is the 

 voltage E. The same result is obtained if IX L is laid off per- 

 pendicular to / at the end of the vector IR, using a triangle 

 rather than a parallelogram, as shown in Fig. 32 (b). 



As a right triangle is formed by these three voltages, the 

 hypotenuse 



E 



V(7R)* + (1XLY* 

 Vl*(W + AV) = 



XL* 



