CHAPTER IV 

 FUNDAMENTAL PROBLEMS 



27. The current-voltage relation. To determine the electromotive 

 force required to maintain a given harmonic current in a circuit 

 having resistance and inductance and containing a condenser. 



A coil of resistance R and inductance L, and a condenser 

 of capacity C are connected in series across alternating current 

 mains as shown in Fig. 57. An alternating current flows back 



Supply main 



Supply main 



Fig. 57. 



Fig. 58. 



and forth through the coil and charges the condenser first in one 

 direction and then in the reverse direction repeatedly. The prob- 

 lem of finding the relation between the current in the coil and the 

 electromotive force between the mains is reduced to its simplest' 

 form as follows : 



To determine the electromotive force necessary to make the charge 

 q on the condenser vary harmonically, so tliat 



q = Q sin u>t (a] 



in which t is the elapsed time, &>/ is an angle increasing at a 

 constant rate, and Q is the maximum charge on the condenser. 

 This varying charge may be represented by the rotating line Q 



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