468 ALTERNATING CURRENTS 



13. Define a scalar quantity; a vector quantity. How are vectors repre- 

 sented'/ I low are they added? What is meant by the parallelogram of 

 forces? The triangle of forces? How are vectors subtracted from one 

 another? 



14. What is meant by a current and a voltage being in phase with each 

 other? In what terms is phase difference expressed? A certain wave 

 crosses the zero axis in a positive direction to the right of another wave. 

 Is the first wave lagging or leading the other? Explain. 



15. If two current waves are plotted, how can the sum of the currents 

 be determined? If two currents are in phase how is their sum found? . 



16. Is the sum of two current waves necessarily equal to their algebraic 

 sum? Explain. How may this be proved? 



17. Explain how a sine wave is produced by a rotating vector. How 

 is the value of the wave determined at any instant? What is the relation 

 of the speed of the rotating vector to the circuit frequency? 



18. If two current waves differ in phase by a certain angle, what is the 

 relation existing between the vectors which produce these waves? Illus- 

 trate with sketches. 



19. What is the fundamental method of adding two currents? How is 

 the resultant current determined? 



20. What relation exists between the resultant wave and the vector sum 

 of the rotating vectors? Does this suggest a ready method of adding 

 alternating currents or voltages? Why may vectors representing effective 

 values be used as well as vectors representing maximum values? 



PROBLEMS ON CHAPTER I 



1. An alternating current has an effective value of 28.3 amp., making its 

 maximum value 40 amp. Draw this wave to scale by the method of Fig. 

 2, page 4 and also construct this wave from a table of sines. (See page 

 5.) Indicate the effective and average values of this wave. 



2. Find the instantaneous values of the current in problem 1 for angles of 

 30, 60, 270, 290, using a table of sines. If. the frequency of this wave is 

 25 cycles per second, to what values of time do the above angles correspond 

 assuming that the time is zero when the wave crosses the axis in a positive 

 direction ? 



3. An alternating voltage, following a sine law, has a maximum value of 

 155 volts and a frequency of 60 cycles per second. What is the value of 

 this voltage 0.001, 0.004 and 0.01 sec. after crossing the zero axis in a positive 

 direction? 



4. A 60-cycle water-wheel generator has a speed of 120 r.p.m. How 

 many poles has this generator? How many electrical space-degrees corre- 

 spond to one actual space-degree? 



6. What is the speed in r.p.m. of a 60-cycle, 10-pole, turbo-driven alter- 

 nator? How many electrical space-degrees correspond to one actual 

 space-degree ? 



6. What is the frequency of a 750 r.p.m. four-pole alternator? Of a 

 500 r.p.m. four-pole alternator? 



