68 ELECTRICAL ENGINEERING PROBLEMS 



resistance must be in order that the current shall be brought into 

 phase with the e.m.f. so as to produce resonance. (6 min.) 



18. In problem 17 if the resistance of the condenser circuit be 

 eliminated, what will the necessary capacity become? (2 min.) 



19. In problem 18 if the resistance in the first circuit be reduced 

 to 2, what will the necessary capacity become? (4 min.) 



20. Given an enclosed arc lamp taking 75 volts at the arc 

 and 7 amperes, and used on a 100-volt circuit; required the 

 capacity that would have to be used in parallel to make the 

 power factor equal to 1 ; also the current under these conditions. 

 (4 min.) 



21. An induction-motor current of 25 amperes has a power 

 factor of 80%; the e.m.f. is 947 and the frequency 60. If the 

 wattless current required were to be supplied by a condenser in 

 parallel, its circuit having no resistance, what would be its capacity? 

 (3 min.) 



Note. If the wattless current is supplied by a condenser, the 

 power factor becomes unity. 



22. If, in the above, the frequency were doubled, what would 

 be the capacity needed? Also if the e.m.f. were halved with the 

 frequency at 60? (1 min.) 



23. A generator giving 4000 volts feeds a 5-microfarad con- 

 denser through an inductive circuit in which r is 10, L is 1.25 and 

 co is 400. Required the e.m.f. on the condenser. (2 min.) 



24. 100 volts at 96 periods is applied to a system consisting of 

 two parallel circuits having respectively 0.008 and 0.02 henry, 

 and 10 ohms and capacities of 125 microfarads and infinity re- 

 spectively. In series with these is another circuit having 0.005 

 henry and 5 ohms; required the currents, unknown e.m.f. 's and 

 lag for the system. (12 min.) 



25. What must be the capacity of a condenser to be placed in 

 parallel with the inductance coil of problem 13 in order to give 

 resonance on a circuit with to = 400, and what line current would 

 have to be supplied to obtain 40 amperes maximum through the 

 inductance coil? What would be the maximum impressed e.m.f.? 

 Check the results as obtained graphically by the proper formula. 

 (8 min.) 



26. Construct the sine curves which are represented by the 

 vectors of problem 25 and prove the numerical relation of their 

 ordinates for three points. (20 min.) 



