CHAPTER V 

 INDUCTIVE .CIRCUITS IN SERIES AND PARALLEL 



(Solve all problems graphically and give results in numbers. 

 Angles may be defined by their tangents.) 



1. Two circuits having resistances of 2 and 10 ohms respectively 

 and T\J and ^fa henries are in series on a circuit having , 300; 

 find the e.m.f. around each of these and across the outside ter- 

 minals with 200 amperes flowing. What is the frequency? (5 ;/ 



2. An induction coil is to be used for cutting down the light of 

 a 100-volt lamp; the voltage is to be reduced to 50, with which 

 the current through the lamp is 0.2 ampere. If the coil ha\ 

 ohms resistance, determine what will be the e.m.f. induced in it, 

 and what will be its terminal e.m.f. What per cent of the energy 

 used will be consumed in the coil? What is the power factor? 

 (4 min.) 



3. Two inductive circuits in series are designated by r\ t r, X| t 

 x 2 , Ei, 2, E and I. In general, if five of these are given tin- other 

 three can be determined graphically from the trhingle diagram. 

 Draw and letter this diagram and then state briefly but compl 

 the geometrical construction for the cases win-re the following are 

 the unknown quantities: (a) n, r 2 , x 2 ; (b) r 2 , xj, E; (c) rj, I 



(d) x 2 , E!, Ez; (e) x 2 , E, I; (f) EI, 2, I. (30 min.) 



4. Given the resistances and reactances of three circuit* in 

 series, and the line e.m.f. Show how to determine* the current and 

 the e.m.f. for each circuit. (5 min.) 



5. Given two circuits having TI, 5; LI, 0.01 ; rj, 20; and L, 0.02; 

 if an alternating current of 500 amperes with w, 600, be put through 

 these two circuits in series, what e.m.f. must be used and what will 

 be the drop and lag for each? (8 min.) 



6. Three circuits, A, B and C, are in series and have n*i 



0.1, 0.01 and henry and 5, 15 and 12 ohms. With 5 amperes 

 at 60 periods find the drop around A and B, B and C, and A, B 

 and C. (7 min.) 



7. Circuits A, B and C in series have inductances of 1.2, and 

 0.3 and resistances of 0, 50 and 100; also a 100-period current ghrea 



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