210 



ELEMENTS OF ELECTRICAL ENGINEERING. 



or, substituting the effective value '(='/ 1/2), and solving 

 for 4> we have 



in which E f is the effective value in abvolts of a harmonic volt- 

 age acting on the primary coil of a transformer, N f is the num- 

 ber of turns of wire in the coil, to is the frequency in radians per 

 second (= 2?r times frequency in cycles per second), and <I> 

 is the maximum positive and negative value between which the 

 core flux pulsates. 



The maximum flux density & reached in the transformer 

 core is of course equal to <I> divided by the area of the cross- 

 section of the core in square centimeters. 



102. Curve of magnetizing current, primary voltage being harmonic, (a) 



On the assumption that the magnetic reluctance of the core is constant. In this case 

 the value m of the magnetizing current at each instant would be proportional to the 

 value 4> of the core flux at that instant, and therefore the magnetizing current would 

 be a harmonic current 90 behind the primary voltage in phase. 



(6) When the hysteresis loop of the transformer core is given for that range of 

 flux which is produced by the given primary voltage (eddy currents ignored). Let 

 ordinates of the dotted curve, Fig. 177, represent the values of core flux 4> and let 



b! 



Fig. 177. 



*he abscissas of the dotted curve represent the corresponding values of steady current 

 m in the primary coil. Let the sine curve 4* represent the harmonically varying core 

 flux corresponding to the given primary voltage. From a point s on the flux-time 

 curve draw the lines sv and sp. Then lay off vu equal to pq. Proceeding in this 

 way the entire current-time curve may be constructed, it being remembered that the 

 branch a of the flux-current curve corresponds to increasing flux and branch b to 

 decreasing flux. 



