90 .CURRENT VALUE. 



The average value of their squares is 

 1 4. 4 4. 9 4. 16 30 

 4 : 4 



The square root of this = = = 2-73. 



2 2 



Consequently we see that the current which has the same 

 heating effect as a direct current is not the current whose 

 average value is the same as the direct current, but the 

 current whose average value of the squares of its instantaneous 

 values is the same as the square of the direct current. 



The student should convince himself by actual trial of 

 the difference between the average value and the root of 

 the mean of values squared. For this purpose he should draw 

 a curve - such as that shown in Fig. 4, and measure 

 the length of a number of equi-distant ordinates. By adding 

 these lengths together and dividing by the number of 

 ordinates taken, he will obtain the average value of the current 

 represented bv the curve. By squaring each ordinate, adding 

 the o^dis^8together, dividing by the number of ordinates, 

 and then extracting the square root, he will obtain the value 

 of the alternating current which is the equivalent as regards 

 heating of a direct current of that number of amperes. 



It can be proved mathematically that the average ordinate 



2 

 of a sine curve is = 635 of the maximum ordinate, whereas 



7T 



V the average value of the squares of the ordinate = 



= or -707 of the height of the maximum ordinate. 

 V ^ 



It is important always to remember that the average 

 value of an alternating current is never employed, since it 

 would not be equivalent to a direct current of the same 

 number of amperes. 



The value of the alternating current which is equivalent 

 to a direct current as regards heating effect is called the 

 virtual, effective, or R.M.S. (root of mean squares) value, and 

 it is this which is recorded on an ammeter and is generally 

 understood when an alternating current of a given number 

 of amperes is spoken of. 



The virtual value of an alternating current of regular 



wave form is therefore -= or -707 of its maximum value. 



