204 THE MAGNETIC CIRCUIT [ART. 62 



the distance between A and B be equal to 6 and the distance 

 U'tween A and C be equal to 26. If the wire B were moved to 

 coincide with C, the inductance of A would be the same as if it 

 belonged to a single-phase loop with a spacing 26. If C were 

 moved to coincide with B, the inductance of A would be that of a 

 wire in a single-phase loop with a spacing 6. Thus, the inductance 

 < >f. 1 corresponds in reality to a spacing intermediate between 6 and 

 26. The inductance of the middle wire B is the same as that of a 

 wire in a single-phase loop with the spacing 6, as is proved above. 

 Thus, the inductance of either A or C is larger than that of B. 



An inspection of a table of the inductances or reactances of 

 transmission lines will show that the inductance increases much 

 more slowly than the spacing. For instance, according to the 

 Standard Handbook, the reactance per mile of No. 0000 wire, at 

 25 cycles, is 0.303 ohm with a spacing of 72 inch, and is 0.340 ohm 

 with a spacing of 150 inch. Therefore, in practical calculations, 

 when the spacing is semi-symmetrical, the values of inductance are 

 taken the same for all the three wires, for an average spacing 

 between the three, or, in order to be on the safe side, for the maxi- 

 mum spacing. In the most unfavorable case, even if an error of 

 say 10 per cent be made in the estimated value of the inductance, 

 and if the inductive drop is say 20 per cent of the load voltage, the 

 error in the calculated value of voltage drop is only 2 per cent of 

 the load voltage, and that at zero power factor. At power factors 

 nearer unity, when the vector of the inductive drop is added at 

 an angle to the line voltage, the error is much smaller. 



Prob. 25. Show that the instantaneous electromagnetic energy 

 stored per kilometer of a three-phase line with symmetrical spacing is 

 equal to W/(W+W'Mfl millijoules per kilometer, where L' has the 

 value given by eq. (125). If this is true, then each wire may be con- 

 sidered as if it were subjected to no inductive action from the other 

 wires and had an inductance L' expressed by eq. (125). This is another 

 way of proving eq. (129), and the statement printed in italics above. 

 Solution: Consider each wire, with a concentric cylinder at infinity, 

 as a component system. Determine the linkages of the field created 

 by the system A with the currents in A, B, and C, as in Art. 61. The 

 result is equal to \L'i?. Similar expressions are then written by analogy 

 for the fluxes due to the systems B and C. 



Prob. 26. Show graphically that, when the distances A-B and 

 \-C are equal, the equivalent flux linking with A is independent of 

 the spacing B-C, and is the same as if B and C coincided. Thiit is, 

 prove that the inductance of A is the same as if it belonged to a single- 



