6 PROBLEMS IN ALTERNATING CURRENT MACHINERY 



Assume that the core losses vary as the 1.7 power of the flux 

 density. 



27. The high-tension winding of a transformer consists of 

 two coils which may be connected in series or in parallel. When 

 these coils are connected in parallel across 22,000 volts at 60 

 cycles the no-load current is 0.077 amperes and the power is 371 

 watts, 28 per cent, of which is eddy current loss. What are the 

 no-load current and power when the coils are connected in series 

 across 22,000 volts at 30 cycles? 



28. At no load, with 460 volts impressed on the primary of a 

 transformer, the current is 0.94 ampere and the power is 122 

 watts. Another transformer is similar to this one except that 

 the primary winding has twice as many turns and the cross-sec- 

 tion of the magnetic circuit is one-half as great. What no-load 

 current and power will this transformer take with 460 volts im- 

 pressed on its primary winding? 



29. In a transformer having a ratio of transformation of Ni: N 2 

 the windings are so designed that the current densities in the 

 primary and secondary are the same. What is the ratio of pri- 

 mary to secondary resistance if both windings have the same 

 mean length per turn? What is this ratio if the mean length 

 per turn of the primary is 15 per cent, greater than that of the 

 secondary? (b) If the current density in the primary had been 

 15 per cent, greater than in the secondary what would have 

 been this ratio of the resistances if the windings had the same 

 mean length per turn? 



30. In a transformer having a ratio of transformation of NI : N 2 

 the windings are so designed that the heating losses in the pri- 

 mary and secondary are the same. What is the ratio of primary 

 to secondary resistance if both windings have the same mean 

 length per turn? What is this ratio if the mean length per turn 

 of the primary winding is 15 per cent, greater than that of the 

 secondary? (b) If the heating loss in the primary had been 15 

 per cent, greater than in the secondary what would have been 

 this ratio if both windings had the same mean length per turn? 



31. What effect will be produced on the iron losses of a trans- 

 former and on the kilowatt rating, on the basis of the same total 

 losses, by doubling the number of turns in the primary and secon- 

 dary windings and halving the cross-section of the wires: first, 

 when the impressed voltage is doubled; and second, when the 

 impressed voltage is unchanged and the cross-section of the mag- 



