128 PROBLEMS IN ALTERNATING CURRENT MACHINERY 



what are the equations for the line voltages on the three-phase 4 

 side? 



12. In problem 10 there are impressed on the two-phase side 

 equal electromotive forces which contain a third and a fifth har- 

 monic. The effective value of these electromotive forces is 

 1100 volts and the harmonics are respectively 0.3 and 0.2 of the 

 fundamental. What are the effective values of the three-phase 

 line voltages? What per cents, of the fundamental components 

 are each of the harmonics in these line voltages? 



13. The line voltage and the voltage to neutral of a balanced 

 three-phase circuit are respectively 230 volts and 139 volts. The 

 voltage to neutral contains a fundamental and a third harmonic 

 only. Three equal resistance units of 10 ohms each are connected 

 in Y across the lines of this circuit. 



(a) What is the line current? What are the line and neutral 

 currents when the neutral point of the resistance units is connected 

 to the neutral of the circuit. 



(b) If the power is measured by the two-wattmeter method 

 what would be the indicated power before and after the connection 

 to the neutral is made? If a wattmeter were connected in the 

 circuit with its current coil in the neutral and its potential coil 

 between the neutral and one of the lines, what would this watt- 

 meter indicate in the second case? 



14. The voltage to neutral of a balanced three-phase circuit 

 is 134 volts, and it contains a fundamental and a fifth harmonic 

 which is 0.2 of the fundamental. Three equal resistance units of 

 10 ohms each are connected in Y across the lines of this circuit. 

 What is the line current? If the neutral point of the resistance 

 units and the neutral of the circuit are connected what is the cur- 

 rent in the neutral conductor? What is the total power supplied 

 in each case? 



15. The line voltage and the voltage to neutral of a balanced 

 three-phase, 60-cycle circuit are respectively 230 volts and 139 

 volts. The voltage to neutral contains a fundamental and a 

 third harmonic only. Three equal air-core reactors, each having a 

 resistance of 5 ohms and an inductance of 0.015 henry, are con- 

 nected in Y across the lines of this circuit. 



(a) What is the line current? What are the line and neutral 

 currents when the neutral point of the reactors is connected to 

 the neutral of the circuit? 



(b) If the power is measured by the two-wattmeter method 



