196 TREATISE ON ALTERNATING CURRENTS. 



5. If a non-inductive resistance r, a resistanceless inductance L, and a resist- 

 anceless capacity (7, are placed in parallel on a circuit of frequency n, what is 

 (1) the equivalent resistance, (2) the equivalent reactance, (3) the impedance of 

 the arrangement ? 



Answers. (1) Equivalent resistances = 



r * 



(2) Equivalent reactance = ? . 



1 



(3) Impedance . . . = 



where p = 2vn, n being the frequency. 



6. Find the current in each branch of the arrangement in Question 15, and 



also in the main circuit if pC = =.. and if n = 100, r = 10 ohms, L = 0-05 



pL 



henry, and if the applied P.O. is 50 volts. 



Answer. Current in non-inductive branch = 5 amperes. 



Current in inductive branch = 1*5915 amperes. 

 Current in condenser branch = 1 '59 15 amperes. 

 Current in main circuit 5 amperes. 



7. An inductive resistance r 1? whose self-induction is L, is placed in series 

 with a condenser of resistance r 2 and capacity C in a circuit of frequency n. 

 Find the condition that the P.D. between the condenser terminals may be 

 double of that between the terminals of the inductance. 



Answer. 4/V* - r* = j*L* - 2 



where p = 2im. 



8. A non-inductive resistance r 15 an inductive resistance r 2 , whose self- 

 induction is L, and a condenser circuit whose resistance is" r s , and capacity C 

 are connected (1) in series, and (2) in parallel. What is the power absorbed in 

 the two cases when an alternating P.D. of e volts is applied between the ter- 

 minals of the arrangements, the frequency being n periods per second ? 



Answers. (1) Power given to series arrangement 



<*fa + r a + r,) 



(2) Power given to parallel arrangement 



where_p = 



