CHAP. V] EXCITING AMPERE-TURNS 83 



rent is limited to a certain percentage of the full-load current. In 

 practice, such curves are sometimes plotted directly from the 

 results of tests on previously built transformers. These experi- 

 mental curves are the most secure guide for predicting the exciting 

 current in transformers; formula (42) shows their rational basis. 



Prob. 1. Prove that if there were no core loss the exciting current 

 would l>e purely reactive, that is to say, in a lagging phase quadrature 

 with the induced voltage. 



Prob. 2. The core of a 22-kv. 25-cycle transformer, like the one 

 shown in Fig. 12, has a gross cross-section of 4500 sq.cm.; the inr.-m 

 path of the lines of force is 420 cm.; the material is silicon steel: the 

 maximum flux is 36 megalines. The expected reluctance of each of the 

 four butt joints is estimated to be equivalent to an 0.08 mm. air-gap. 

 What are the two components of the exciting current, and what is the 

 total no-load current? Ans. 1.8; 0.4; 1.85. 



Prob. 3. In what respects does the calculation of the magnetizing 

 current in a shell-type or cruciform-type transformer differ from that 

 in a core-type transformer? 



Prob. 4. Show that for flux densities up to 10 kl./sq.cm. the mag- 

 netizing volt-amperes per kilogram of carbon steel at 60 cycles are 

 approximately equal to 7.3(# m /10) J . 



Prob. 5. Show that the influence of the joints can be taken into 

 a< 'count in formula (42) by adding to the actual volume of the iron 

 the volume of the air-gaps multiplied by the relative permeability of 

 the iron. 



Prob. 6. A shell-type 1000-kva., 60-cycle transformer is to have a 

 core made of silicon-steel punchings of a width ?r = 17 cm. (Fig. 13); 

 the average length of the magnetic path in iron is 180 cm.; the reactive 

 component of the no-load current must not exceed 2 per cent of the 

 full-load current. Draw curves of the require* 1 height of the core |xr 

 link, and of the total core loss in per cent of the rated kva., for flux 

 densities up to 10 kl./sq.cm. 



Ans. B'A-5200; at 5-9, P-0.51 per cent. 



34. The Exciting Current in a Transformer with a Saturated 

 Core. In the preceding article the flux density in the .iv is 

 supposed to lx wit! i in the range of the straight part of the satura- 

 tion curves (Fig. 3), so that, when the flux varies according to the 

 sine law, the iiiai:ncli/.iiiL r current also follows n sine wave. We 

 slmll now consider the case when the flu\ <1< -nsity rises to a value 

 on or beyond the knee of the magnet i/.at ion curve. Such high flux 

 ties are used with silicon steel cores, especially at low fre<juen- 

 cies. In this case the magnet i/.ini: current dors not vary according 

 to the sine law, but is a peaked wave, because at the moments when 



