EXAMPLES OF REACTIVE CIRCUITS. 73 



(1) the equivalent resistance, (2) the equivalent self-induction, and (3) the impe- 

 dance of the combination, the frequency being 100 periods per second? 

 Answer. (1) 0-62175 ohms; (2) 0-0333 henry ; (3) 21 ohms. 



14. An inductance of 0'05 henry having negligible resistance, and a capacity 

 of 3 microfarads, are connected in parallel. A P.D. of 100 volts is applied 

 between their common terminals, and the frequency is 100 periods per second. 

 Find the current in each of the branches and in the main circuit respectively. 



Answer. Current in inductive branch = 3'1831 amperes. 



condenser = 0'1885 

 Total current = 2-9946 amperes. 



15. What capacity is necessary so that, when placed in parallel with an 

 induction of - 05 henry, there will be no current in the main circuit, the resist- 

 ances of the circuits being negligible, and the frequency being 75 periods per 

 second? 



Answer. 90 microfarads. 



16. Two circuits, one having a resistance of 10 ohms, and a self-induction of 

 0'125 henry, and the other having a resistance of 100 ohms, and a capacity of 

 25 microfarads, are placed in parallel between the terminals of an alternator 

 giving 1000 volts at a frequency of 50 periods per second : what are the currents 

 in the two branches, and in the main circuit ? 



Answer. Current in inductive branch = 24 94 amperes. 



condenser = 6'17 

 Total current = 21 '41 ,, 



17. What is the impedance of the combination in Question 16? 

 Answer. 46*7 ohms. 



18. What is the self-induction of a coil of negligible resistance such that, 

 when placed in series with a non-inductive apparatus taking 10 amperes at 

 40 volts, will allow of the arrangement being used on a 100-volt 50-frequency 

 circuit ? 



Answer. 0*029 henry. 



19. If in Problem 18 the apparatus had a resistance of 2 ohms, and a self- 

 induction of O'Oll henry, what should be the self-induction of the coil? 



Answer. 0-02015 henry. 



20. A coil whose self-induction is 0*04 henry is used in series with an arc 

 lamp which takes 7'5 amperes at 40 volts, the whole being in a 100-volt circuit : 

 what is the frequency of the current ? 



Answer. 43*3 periods per second. 



