132 PROBLEMS IN ALTERNATING CURRENT MACHINERY 



28. In problem 27 if the cyclic order of the line voltages is such 

 that the fundamental component of Vn lags V^ by 120 degrees 

 what are the line currents? 



29. Three equal resistance units of 50 ohms each are connected in 

 Y across the mains of a balanced three-phase, 230-volt circuit. An 

 air-core reactor which has a resistance of 0.5 ohm and an induc- 

 tance of 5 millihenrys is connected from neutral point of this 

 load through a switch to the neutral conductor of the circuit. The 

 voltage across the open switch is 40 volts. There is no higher 

 harmonic than a third present. 



(a) With the switch open what is the line current? What is 

 the total power supplied? 



(b) With the switch closed what is the line current? What is 

 the neutral current? What is the total power supplied? What 

 are the voltages across the resistance units before and after the 

 switch is closed? What is the voltage across the reactor after 

 the switch is closed? 



30. In problem 29 if the air-core reactor is replaced by a con- 

 denser which has a capacity of 50 microfarads what are the line 

 currents before and after the switch is closed? What is the 

 neutral current after the switch is closed? What is the total 

 power supplied with the switch open? With the switch closed? 

 What are the voltages across the resistance units before and after 

 the switch is closed? What is the voltage across the condenser 

 after the switch is closed? 



31. The voltages between the lines and neutral conductor of a 

 balanced three-phase, 60-cycle circuit are each 140 volts. Three 

 equal condensers each of 5 microfarads' capacity are connected 

 in Y across the lines of this circuit, and from their common junc- 

 tion a non-inductive resistance unit of 10 ohms' resistance is con- 

 nected through a switch to the neutral conductor. The voltage 

 across the open switch is 45 volts. There is no higher harmonic 

 than a third present, (a) With the switch open what is the line 

 current? What is the total power supplied? (b) With the switch 

 closed what is the line current? What is the neutral current? 

 What is the total power supplied? 



32. In problem 31 if the non-inductive resistance unit is 

 replaced by an air-core reactor which has a resistance of 0.5 

 ohm and an inductance of 5 millihenrys what are the line cur- 

 rents before and after the switch is closed? What is the neutral 

 current after the switch is closed? What is the total power sup- 



