PROBLEMS. 3 8 5 



each alternator? Ans. (a) 1,628 volts ; (b) output of A 29,780 

 watts, output of B 146,470 watts. 



23. The electromotive force of alternator A, problem 22, is 

 135 ahead of the electromotive force of alternator B in phase. 

 A current of 1 20 amperes flows through both alternators, lagging 

 30 behind their resultant electromotive force. What is the out- 

 put of each alternator ? Ans. Output of A 30,800 watts nega- 

 tive, output of B 122,770 watts positive. . 



Note. Negative output means intake as a motor. 



24. Two coils A and B are connected in series across 1 1 o- 

 volt alternating-current mains. The voltage across A is 76 

 volts and the voltage across B is 80 volts. What is the phase 

 difference between the voltages across A and B, assuming all 

 of the voltages to be harmonic ? Ans. 89 39'. 



Note. It is impossible to determine from the data of this problem which of the 

 voltages, A or B, is ahead of the other in phase. 



25. A non-inductive rheostat of which the resistance is 60 

 ohms is connected in series with an alternating-current fan motor 

 to 1 1 o- volt alternating supply mains. The voltage across the 

 6o-ohm rheostat is 62} volts, and the voltage across the fan 

 motor is 64 volts. Find (a) the current flowing through the 

 circuit, (b) the phase difference between the current and the volt- 

 age across the fan motor, and (c) the power delivered to the fan 

 motor. Ans. (a) 1.04 amperes, (b) 59 10', (c) 34.17 watts. 



Note. It is impossible from the data of this problem to tell whether the voltage 

 across the 6o-ohm rheostat is ahead of or behind the voltage across the fan-motor in 

 phase. As a matter of fact, the voltage across the 6o-ohm rheostat is in phase with 

 the current, and the voltage across the fan-motor is ahead of the current in phase. 



26. An alternator delivers 200 amperes of current to glow 

 lamps, and 75 amperes to start an induction motor. The power 

 factor of the motor while starting is 0.3. Find the total current. 

 Ans. 233.7 amperes. 



27. A harmonic alternating current of which the effective value 

 is 15 amperes has a frequency of 133 cycles per second. (<?) 

 Find the rate at which the current changes at the instant it 



passes through zero value, and (b) find what value the current 

 26 



