462 



Iransformers. 



[May 12, 



results which seem to be in accordance with snch experimental 

 observations as have yet been made. 



The effective current C (if V is the effective voltage) with 

 constant permeability is Y'j^ak ; with hysteresis (or with no 

 hysteresis but some saturation of the iron) but no eddy currents, 

 0' = r02V'/N 2 ff&, taking b as 0*2 ; with eddy currents and hysteresis, 

 C = VV(l , 04 + 2esin/+e 8 )/N 2 fffc. 



The average power given to the choking coil or average value of 



VC is V'C — e + sin f — neglecting the small terms due to b and m. 

 l-f-e 2 + 2esm/ ° ° 



Probably, in transformers there are always traces of the term in 

 Sht and the higher harmonics in both Y and I, but they certainly 

 must exist in either Y or I, whether the transformer is loaded or 

 unloaded. In the loaded transformer, magnetic leakage causes con- 

 siderable diminution in the higher harmonics of I, and this may 

 increase them in Y. 



It seems that in a choking coil with a finely-divided iron core, we 

 have found what has been long looked for, a method of increasing 

 frequency by mere magnetic means. A condenser shunting a non- 

 inductive part of the circuit would receive currents in which the 

 higher harmonics would be greatly magnified in importance. To 

 show the magnitude of the terms in (4) I will take the above-men- 

 tioned 1500- watt transformer, in which q = 7783. Taking / = or 

 no hysteresis, the power wasted in eddy currents being rfV 2 /2r'N 1 2 , 

 let this be 40 watts ; then n 2 jr = 2'1168 when Y = 2828. The eddy 

 current coil therefore which would replace all the eddy current 

 circuits is a coil of two turns whose resistance is about 1*9 ohms, 

 short circuited on itself. 



e = 0'38 if k = 600. Assuming constant permeability and no 

 eddy currents and no hysteresis C L = 0-07398 sin (Jit— 90°), with some 

 saturation and eddy currents but no hysteresis 



d = 0-07911 sin (&£—69°-2)— 0*014796 COS 3 Art — 0*003695 COS blct. 

 I have taken b = 0'2 and m = 0-05. 



The primary potential difference Y is never a simple sine function of 

 the time. Besides the important term in sin let there are small terms 

 of h ; gher frequency, and at least one term of lower frequency equal 

 to the number of turns of the armature per second. The tendency of 

 the forces acting on coils in series on an armature is to produce 

 greater dissonance at greater loads, but it may be assumed that in 

 good machines the fastenings are sufficiently rigid, and the coils 

 and pole pieces so nearly alike, that there is always very little dis- 

 sonance. 



The primary potential difference, instead of being 2828 sin 600 1 in 

 the above case, may be 



Y = 100 sin 20 1 + 2823 sin 600 1 + 200 sin 1800 1 , 



