78 TREATISE ON ALTERNATING CURRENTS. 



It may be that, in a transformer or other induction machine, 

 either the current or E.M.F. follows the simple sine law. The 

 presence of iron, however, causes one of them to deviate from the 

 sine law. If' a sine potential difference is applied between 

 the terminals of the primary of a transformer, the primary-current 

 wave will be compounded of a sine function and some of its higher 

 odd harmonics, and wjll consequently be distorted. 



If a sine current is produced, the applied potential difference is 

 distorted. 



52. Root Mean Square Value of a Curve 

 compounded of a Fundamental Sine Curve and 

 its Higher Odd Harmonics. 



Let 



y = a\ sin (pt 0i) 4- #3 sin (3pt 0s) + ... etc. 

 then 



if = a? sin 2 (pt - 0i) -f as 2 sin 2 (3pf - 8 ) 4- . . . etc. 

 4- 2ai 3 sin (pt - 0i) sin (3pt - 3 ) 4- ... etc. 

 4- 2a r a,, sin (rpt 0,.) sin (spt V ) 4- . . . etc. 



The mean square value of y is 



that is, the mean square value of y is the sum of a series of terms, 

 such as 



p f *> 



2~ a? r sii 



sin 2 (rpt - 9,.)dt 

 together with the sum of a series of terms, such as 



p 

 - 2a r a s sin (rpt 0,.) sin (spt O^dt 



where r and s are always QljJ integers. 

 Now 



2 



