16 PROBLEMS IN ALTERNATING CURRENT MACHINERY 



all of the coils are connected to form a regular transformer with a 

 ratio of transformation of 2:1, and in the second case they are 

 connected to form an auto-transformer with the same ratio of 

 transformation. When connected as a regular transformer with 

 the low-tension winding short circuited the current, voltage and 

 power, measured on the high-tension side are 8 amperes, 52 volts, 

 and 59 watts respectively. On open circuit with 220 volts 

 impressed on the high-tension side the core loss is 26 watts. 

 Assume that the paths of the leakage flux are the same for each 

 connection. Compare (a) the regulations and (b) the effi- 

 ciencies of this transformer for the two cases given above for a 

 load of 1.5 kw. at 0.9 power factor and 110 volts on the low-tension 

 side. 



78. Two transformers, one connected as a regular and the 

 other as an auto-transformer, have identical magnetic cores and 

 the same amount of copper in their windings. Each of the trans- 

 formers gives a ratio of transformation of 330:220 volts, and the 

 windings are so designed that the core losses in each are 122 watts 

 when 330 volts is impressed on their primaries. The primary and 

 secondary resistances of the regular transformer are 0.097 ohm 

 and 0.0431 ohm respectively. The resistance of the auto- 

 transformer measured on the low-tension side is also 0.0431 ohm. 

 The leakage reactance of the primary winding of the regular 

 transformer is 0.37 ohm. Assume that all of the windings have 

 the same mean length per turn, and that the leakage reactance of 

 the coils vary as the square of the number of turns, (a) On the 

 basis of the same total heating losses, what is the ratio of the out- 

 puts of these two transformers? (b) What is the regulation and 

 efficiency of each transformer for a load of 10 kw. at 0.87 power 

 factor and 220 volts? 



79. Two transformers, one connected as a regular and the 

 other as an auto-transformer, have identical magnetic cores and 

 the same amount of copper in their windings. Each of these 

 transformers gives a ratio of transformation of 330:110 volts and 

 the windings are so designed that the core losses of each are 371 

 watts when 330 volts is impressed on their primaries. The pri- 

 mary and secondary resistances of the regular transformer are 

 0.0306 ohm and 0.0034 ohm respectively. The resistances of the 

 auto-transformer measured on the high- and low-tension sides are 

 0.017 and 0.0034 ohm respectively. The equivalent leakage 

 reactance of the regular transformer referred to the high-tension 



