ALTERNATING-CURRENT C71H UIT8 25 



13. Circuit Containing Resistance Only. Figure 22 shows an 

 alternating-current circuit containing resistance only. A poten- 

 tial difference of K volts is impressed across the resistance R. 

 In virtue of this voltaic a current having the equation i = I max 

 sin ut flows, where to is the angular velocity of the rotating vector 

 in radians per second. (See page 11, par. 6, equation (3).) Asone 

 revolution of the rotating vector corresponds 



- radians, the vector must complete 2irf - 

 radians per second, where / is the frequency. 

 Hence u = 27T/. (For 60 cycles, w = 377; 

 for 2.~> cycles, o> = 1.Y7.) 



From the definition of an alternating- 

 current volt (Par. 8), - 



e = Ri = RI m , u t. FlG '. 22 --9 ircuit 



containing resistance 



The current and the voltage are in phase. <>"ly. 

 They have the same frequency and when t = 

 u, sin u>< = 0, and both the current and voltage waves are 

 ;iir the zero axis simultaneously and increasing positively, 

 as shown in Fig. 23 



If effective values are used. /,' = 1 1\. Figure 23 (6) shows the 

 vector diagram for this circuit, using effective values. The IR 



(a) 



! ph.-ix-. :unl 



drop is in phase with the current / and is equal to the voltage E, 



no other vol' i he circuit. 



As the current and the voltage are in phase, the power 



/' A7 (7) 



shown r AJio 



P = / /,' 



