21 S POLYPHASE CURRENTS. [Exp. 



Suppose, for example, 7 is 173 and ID is 105 instead of 100 (an 



increase of 5 per cent); then H = 



In the laboratory measure / and ID and calculate H. Compute H 

 as per cent, of / -f- \/3 > also compute the per cent, increase in ID over 

 /H-V3- Although noticeable at no load, the percentage difference 

 practically disappears under load, for H remains constant and hence 

 is relatively smaller when / and ID become large. 



43. Third Harmonic in Star-connection. If the transformer pri- 

 maries are y-connected, the third harmonic caused by hysteresis 

 will be in the same phase in the three transformers and will tend to 

 flow to or from the neutral simultaneously in the three. The star 

 voltage Es will thus be more than the line voltage E divided by \/3> 

 thus Es = V(-^ V3) 2 + n 2 , where EH is voltage due to hystere- 

 sis. If the neutral is insulated no current due to these harmonics 

 can flow. If there is a return circuit from the neutral, through 

 ground or a fourth wire, a current of triple frequency will flow; but 

 no current of fundamental frequency will flow in the neutral if the 

 line voltages are symmetrical. 



44. The third harmonic in the neutral can be prettily shown in 

 the laboratory by means of a telephone, which should be protected 

 by a resistance in series, or in shunt, or both, or by connecting through 

 a transformer. Connect to a 3-phase supply three transformers or 

 other coils* with iron; the more nearly similar these are the better. 

 Let 0' be the neutral of the three coils and let O be the neutral of 

 the supply system. (If the supply system has no neutral, one may be 

 obtained by three F-connected resistances.) Connect the telephone 

 between and 0'. If the coils are well balanced, the fundamental 

 will be perhaps scarcely discernible ; the third harmonic will sound 

 very clearly an octave and a fifth (do to sol} above the fundamental; 

 the ninth, if discernible, is the same interval above the third. On 

 a 64-cycle circuit, the fundamental is C with harmonics g, d", b", etc. 



If there is any question as to what is the fundamental, it can 

 usually be told by listening to various apparatus in the laboratory; 

 or by connecting the telephone, with a series resistance, to the supply 

 circuit. 



by measuring the total and separate voltages when two sources are put 

 in series. Do not short circuit one source on the other. 

 * Shunt choking-coils used for series lighting are suitable for this. 



