200 ELECTRICAL MACHINERY 



of the two currents in heating a certain resistance. Or we 

 may say that an alternating current has an effective value of 

 one ampere when it produces heat in a certain resistance at 

 the same rate as heat is produced in the same resistance by 

 one ampere of continuous current. 



Virtual Value of a Sine Wave. It may be proved 

 experimentally or by the calculus, that if the alternating 

 current is a simple sine wave (i.e., no upper harmonics 

 present) as shown in Fig. 117, the virtual value in amperes, 

 is equal to the maximum value in amperes, divided by 

 \/2. That is, if we have an alternating current of the form 



i = /sin(o; (38) 



where ^ = the instantaneous value of the current; 

 7 OT = the maximum value of the current; 

 w = 2x times the frequency; 



then /, the virtual value of such a current is given by the 

 relation 



I=I m /V2=I m X.7Q7 (39) 



Virtual Value of a Complex Wave. When the curve 

 of current is not a simple sine wave the relation between 

 the virtual and maximum values can not be represented 

 by a simple expression. But, in any case, we have the rule 

 that the virtual value of any alternating current is equal 

 to the square root of the average square of the instantaneous 

 values. This is expressed in some texts by the letters 

 R.M.S., meaning "root mean square." 



What has been said in regard to current waves holds 

 good also for voltage waves so we have, when e = E m sin tot, 



E=E m /V2=EmX.7Q7 .... (40) 



where e = the instantaneous value of the voltage; 

 E m = the maximum value of the voltage; 

 E = the virtual value of the voltage. 



