FUNDAMENTAL PROBLEMS. 



73 



32. The decaying oscillatory current. When a charged condenser is short- 

 circuited by a circuit containing resistance and inductance, a current surges back and 

 forth through the circuit, each surge of current being less in value than the pre- 

 ceding surge, until the surges cease. Such a decreasing or decaying oscillatory cur- 

 rent is represented graphically in Fig. 64.* 



Fig. 64. 



33. The effects which are produced immediately after a harmonic alterna- 

 ting electromotive force is connected to a circuit, (a) When the circuit contains 

 resistance and inductance. The dotted curve e Fig. 65 represents a given harmonic 

 alternating electromotive force, and the curve m represents the harmonic current 

 which would be maintained by e in a given inductive circuit. The relation between 

 e and m is given by equations (n) and (12) Art. 28. If the harmonic electro- 

 motive force is connected to the circuit at any instant / at which the maintained cur- 

 rent m would be zero, then the maintained current starts off at once without any 

 complications. If, however, the harmonic electromotive force is connected to the 

 circuit at any instant t' at which the maintained m would not be zero, then, since 

 the actual current must be zero at the instant that e is connected to the circuit, the 

 result is complicated. The current which starts is the maintained current m plus 

 a decaying current d, the decaying current being such that ( m -j- d} is zero at the 

 instant /'. After a very short time the decaying current d disappears, and the 

 maintained current m alone exists. 



* The differential equation of the decaying oscillatory current is 



in which q is the varying charge on the condenser. The integration of this equation 

 is discussed in Bedell and Crehore's Alternating Currents, 2d edition, Chap. VI, 

 pages 105-108. 



