108 PROBLEMS IN ALTERNATING CURRENT MACHINERY 



21. Three impedance units whose values are represented by 

 the expressions, Zi = 2.Q+j 1.0, z 2 =1.5-{-j 0.5, and z 3 = 2.5+ 

 j 1.0, are connected in delta at the end of a three-phase transmis- 

 sion line each conductor of which has a resistance of 0.1 ohm and 

 a reactance of 0.15 ohm. If the line voltages at the generating 

 station are each 11,000 volts, (a) what are the line currents? 

 (b) What are the line voltages at the load? (c) What is the effi- 

 ciency of transmission? 



22. The power supplied to a three-phase induction motor is 

 measured by the two-wattmeter method. One wattmeter indi- 

 cates 5770 watts and the other 2930 watts. What is the power 

 supplied? At what power factor is the motor operating? 



23. The only instrument available for measuring the power 

 taken by a three-phase, 230-volt induction motor is a wattmeter 

 of suitable range. Measurements are made as follows: The 

 current coil of the wattmeter is inserted in main 1 and the poten- 

 tial coil, first between mains 1 and 2 and then between mains 

 1 and 3. If the two wattmeter readings thus obtained are 5760 

 and 3380 watts respectively what is the power supplied to the 

 motor? If the line voltage is 230 volts what is the line current? 

 At what power factor is this motor operating? 



24. The power taken by a balanced three-phase load is meas- 

 ured by two wattmeters. The current coils of the wattmeters are 

 connected to current transformers which are in lines 1 and 2 

 respectively. The potential coils are connected to potential 

 transformers which are across lines 2 and 3 and lines 1 and 3 

 respectively. The line voltages are each 230 volts and the line 

 currents are each 150 amperes. The wattmeters each indicate 19.6 

 kw. What is the power supplied? What is the power factor? 



25. The power taken by an unbalanced three-phase load is 

 measured by two wattmeters. The current coils of the watt- 

 meters are connected to current transformers which are in lines 

 1 and 2 respectively, and the potential coils are connected to 

 potential transformers which are across lines 2 and 3 and lines 1 

 and 3 respectively. The line voltages are each 230 volts. The 

 currents in lines 1 and 2 are 150 amperes and 200 amperes re- 

 spectively. The first wattmeter indicates 21. 2 kilowatts and the 

 second indicates 18.1 kilowatts. What is the power supplied to 

 the load? 



26. A 3-phase, 500-volt, Y-connected alternating-current 

 generator with equal line voltages and a grounded neutral supplies 



