CURRENT VALUE. 95 



Average Power in a Circuit. In the example which has just 

 been given, it was shown that the average value of C'*R in an 

 alternating circuit is half the maximum value. In a non- 

 inductive circuit C 2 R = C E, since the voltage E is equal to 

 the product C R of current resistance. Thus the average 

 value of the power developed in a non-inductive circuit is 

 half the maximum value of the power. In the case of measure- 

 ment of power, it is the average value which is required for 

 all purposes of comparison, since the total work done by 

 the current in the circuit is the sum of all products of the 

 form (power at any moment x time during which it is 

 developed), this is equivalent to (average power x time con- 

 sidered}. The work done in a circuit in five minutes, 

 for instance, is (average value of watts x 5 x 60 sees.) 



The maximum value of the watts in a non-inductive 

 circuit = maximum amperes x maximum volts, hence 



average watts = -~ (maximum amperes x maximum volts) 

 maximum amperes x -^~ maximum volts. 



/ 



\ 



= virtual amperes x virtual volts. 

 Hence we have the important relation for a non-inductive 

 circuit. 



Average power in circuit = product of virtual amperes 

 and virtual volts. 



The relation just obtained may be extended to an inductive 

 circuit if we substitute the energy voltage for the total voltage. 

 This is permissible, since the energy voltage is in phase with 

 the current, and is the only part of the voltage which 

 influences the power of the circuit. 



The energy voltage = e cos. <t> , and consequently in an 

 inductive circuit 

 average watts = virtual amperes x virtual volts x cos. <P. 



The above relations may be summarised in symbols as 

 follows, capital letters representing maximum values, and 

 small letters virtual values. 



For non-inductive circuits 



w = c.e. 



