ALTEK\.\ TING-CV&REN T < BISCUITS 23 



It will bo noted that this power curve is a sine wave having 

 double the frequency of either the voltage or the current. For 

 every cycle of either voltage or current . the power wave touches 

 tin- y.ero axis twice, so that in such a circuit the power is zero 

 twice during each cycle. Since the peaks of the voltage and 

 current waves occur at the same instant, the corresponding peak 

 of the power cur\ 



(VM) (V2I) = 2EI 

 where E and 7 are the effective values of voltage and current. 



This power wave has its horizontal axis of symmetry at a dis- 

 tance El above the zero axis. Consequently, A7 must be the 

 average value of the power, since the upper half waves will just 

 fill the shaded valleys below the axis of symmetry of the power 

 wave. When the current and the voltage are in phase the aver- 

 age power is their product, as with direct currents. 



//>/<. An incandescent-lamp load takes 30 amp. from 115-volt, 

 60-cycle mains. (In this type of load the current and voltage are sub- 

 stantially in phase.) How much power do the lamps consume'.' 



P = El = 115 X 30 = 3,450 watts. Ans. 

 ire 20 shows the current and voltage 90 out of pha- 

 in quadrature, the voltage leading. Let it be required to deter- 

 mine the power curve for this E 

 condition. At points a, 6, c, d 

 and i , either the current or the 

 volt a i:e i- BCTOj and the power 

 must he zero at each of tl 

 points. Between a and 6 the 

 voltage is positive and the cur- 

 rent LB negative, and they are 

 therefore acting in opposition. 

 The product of a positive anda r,, wi . r curve; ramaf 



IV,. miantitv j~ negative, ;u " 1 x " lt:i ^' in |ua.lr:itun-. rurn-nt 



,, /* , e begin* 



Hence the power between 



points a and h must be negative, This means that the circuit 



io the source of supply. Hi -tween points h and 



c both the curn-nt :md the voltage are positive and therefore 



the power between theee two points must be positive. He- 



r and // the eiirrent is positive, but the voltage is no\\ 



again negative between these two 



