130 PROBLEMS IN ALTERNATING CURRENT MACHINERY 



a third harmonic which is 0.3 of the fundamental component. The 

 resistances of the lamp loads are 5, 8, and 10 ohms. What are 

 the line currents, the neutral current, and the total power 

 supplied? 



20. Three equal lamp loads are connected in Y across the lines 

 of a balanced three-phase circuit. The line voltages are 230 

 volts and the voltage from line to neutral is 139 volts. The latter 

 voltage is known to contain harmonics. The resistance of each of 

 the lamp loads is 5.0 ohms. What will be the effect on the line 

 current if the neutral point of the load is connected through 

 a resistance of 2 ohms to the neutral of the circuit? By what 

 amount is the power supplied to the lamps increased? What is 

 the loss in the 2-ohm resistance? 



21. The voltages from the lines to the neutral conductor of a 

 balanced three-phase circuit are each 140 volts. Three equal 

 resistance units of 10 ohms each are connected in Y across this 

 circuit. A voltmeter connected between the neutral point of 

 this load and the neutral conductor indicates 40 volts. What 

 power will these resistance units take if the neutral point of the 

 load is directly connected to the neutral conductor? What will 

 be the current in the neutral conductor? 



22. The line voltages of a three-phase circuit are equal and 

 maintained constant. The voltages from the lines to the neutral 

 conductor, which are known to contain third harmonics, are also 

 maintained constant and are each equal to 140 volts. Three 

 equal resistance units of 10 ohms each are connected in Y across 

 this circuit. The measured voltage from the neutral of this 

 load to the neutral conductor is 40 volts. What current will 

 exist in the neutral conductor if a resistance unit of 5 ohms is 

 connected between these two points? What is the effective 

 voltage across each of the equal resistance units before and after 

 this additional resistance is inserted in the circuit? 



23. Three hypothetical impedance units, a resistance, a re- 

 actor, and a condenser are so constructed that at 60 cycles the 

 values of their impedances may be represented in the complex 

 notation by: 0i = 10+jO, z 2 = 0+jlO and z 2 = 0-.7lO. These 

 impedance units are connected between the mains and neutral 

 of a balanced three phase, 60-cycle circuit The line voltages are 

 each 230 volts, and the voltages between the lines and the neutral 

 are equal and consist of a fundamental and a third harmonic 

 which is 0.3 of the fundamental component. The first impedance 



