CAPACITY AND INDUCTIVE CIRCUITS, RESONANCE 67 



when connected through a line of 1.1 ohms r< -.i-tance to a 400-volt 

 generator? (8 min.) 



Note. An over-excited synchronous motor or converter acts 

 like a circuit with resistance and capacity; that is, it has a leading 

 current. 



10. Upon a circuit having co = 400 (frequency = 63.7), two 

 circuits in series have respectively 19 ohms and 0.007 henry, and 

 5 ohms and 125 microfarads, what e.m.f. will be necessary to send 

 11 amperes through the combination? What change in frequency 

 would give unity power factor or resonance? (5 min.) 



11. Upon the same circuit as above, two circuits an- connected 

 in series, one of which has 7.2 ohms and 0.22 henry, and the other 

 5 ohms and 32 microfarads. What line e.m.f. will give 1000 volts 

 on the condenser? What will be the current and the voltage on 

 the inductive circuit? (5 min.) 



12. In problem 11 what capacity would be needed to give a 

 leading current with 90% power factor? Also to give unity power 

 factor or resonance? Check the graphical solution by the formula 

 for series resonance. (4 min.) 



13. An induction coil has a resistance of 25 ohms, and when 

 placed on a 1000-volt circuit with o> = 400, passes 2 amperes. 

 What must be the capacity of a condenser in series with this 

 circuit to give resonance? If the same line voltage were main- 

 tained, what current would flow, and what would be the voltage 

 around the induction coil and also that at the terminals of the 

 condenser? Give the graphical solution and check analytically. 

 (6 min.) 



14. Construct the sine curves of e.m.f. around the condenser 

 and the inductance coil in problem 13, and from them derive the 

 curve of impressed e.m.f. Compare the result with that obtained 

 in problem 13. (15 min.) 



15. In problem 10, if the circuits are placed in parallel, find the 

 necessary e.m.f. (6 min.) 



16. Three circuits in parallel have respectively 8, 12 and 3 

 ohms, 0, 0.06 and henries and 200, infinity and 300 microfarads 

 capacity; co is 500. If 200 volts are applied, required the current . 

 the phase angle and the power factor. (10 min.) 



17. Two circuits are in parallel on a 100-volt, 60-period system; 

 one has 10 ohms resistance and 3 ohms reactance; the other has 

 resistance and 60-degree lead. Determine what its capacity and 



