82 TREATISE ON ALTERNATING CURRENTS. 



the same R.M.S. values, and having- a differ- 

 ence of phase equal to 0. 



55. We are now in a position to say that calculations based 

 on the assumption that the E.M.F.s and currents are simple sine 

 functions are perfectly legitimate, provided (1) that only K.M.S. 

 values are involved, (2) that the assumed sine values of the 

 E.M.F.s and currents have the same K.M.S. values as the actual 

 E.M.F.s and currents have, and (3) that only odd terms of 

 Fourier's Series are involved. 



We can, for instance, calculate the effects of hysteresis and 

 eddy currents on the assumption of equivalent simple periodic 

 values, but we cannot, on the same assumption, draw any conclu- 

 sion whatever respecting the amount of insulation necessary in any 

 particular case, since the maximum E.M.F., and not its K.M.S. 

 value, determines the insulation needed. 



PROBLEMS ON CHAPTER IX. 



1. What are the maxima values of the equivalent sine curves of the 

 following ? 



(i.) 1000 sin 750* + 100 sin 2250*. 

 (ii ) 100 sin 300* + 10 sin 900* + 5 sin 1500*. 

 (iii.) 250 sin 240* + 50 sin 720* + 10 sin 120 *. 



Answers, (i.) 1005; (ii.) 100'62; (iii.) 255-1. 



2. What are the equivalent phase differences between the following pairs of 

 curves? 



i = 100 sin 300* 

 (i) ' 



f i = luu sin duu* 



I e - 500 sin (300* - *W 50 sin ( ( JOO* - - 



;t = 100 sin 450* + 10 sin 1350* 

 e = 300 sin (450* - ) + 30 sin (l350* - "\ 



Answers, (i.) 30 30'. (ii.) 45. 



