THE ALTERNATOR. 31 



the case of the current which is produced by an alternating 

 electromotive force through a circuit which allows current 

 to pass in one direction but not in the other direction. The 

 mercury-arc and the aluminum-valve rectifiers are examples of 

 such circuits. 



The simple average of the positive (or negative) values of an 

 alternating electromotive force or current during half a cycle is 

 of course not zero. 



Effective values. Consider an alternating current of which the 

 value at a given instant is i. During a cycle, i passes through 

 a set of positive values and a similar set of negative values, 

 whereas i 2 is always positive. Therefore the average value of i 2 

 is not zero. The square root of the average value of i 2 , which is 

 called the effective value of the alternating current, is always used 

 in specifying an alternating current in amperes. Thus an alternat- 

 ing current of 10 amperes is an alternating current of which the 

 average value of i 2 is 100 amperes 2 . An alternating electromo- 

 tive force is also specified by giving its effective value. Thus an 

 alternating electromotive force of 1,000 volts is an alternating 

 electromotive force of which the average value of the square is 

 1,000,000 volts 2 . 



The principal reason for using effective values in the specifica- 

 tion of alternating electromotive forces and currents is that the 

 voltmeters and ammeters used in alternating-current measure- 

 ments always give effective values, as explained in Chapter II. 

 The term "effective value" originated as follows: Consider an 

 alternating current of which the instantaneous value is i. The 

 rate at which heat is generated at a given instant in a circuit 

 through which this current flows is Ri z , where R is the resist- 

 ance of the circuit, and the average rate at which heat is gener- 

 ated in the circuit is R times the average value of z 2 , or RP, 

 where / 2 is equal to the average value of i 2 , or where / is 

 equal to the square-root-of-the-average-value-of-z 2 . That is, to 

 calculate the rate at which heat is generated in a circuit by an 

 alternating current, the resistance is multiplied by the square of 



