ELECTRIC OSCILLATIONS AND ELECTRIC WAVES. 195 



113. The electric oscillator. The arrangement shown in Fig. 

 133 of Art. 112, consisting of an inductance L and a condenser 

 C connected as shown, is called an electric oscillator. This type 

 of oscillator does not radiate energy in the 

 form of electric waves to any appreciable ex- 

 tent, whereas the open oscillator which is 

 shown in Fig. 134 does radiate energy. 



Equation (21) of Art. 1 12 is true only 

 when the resistance of the circuit in Fig. 133 

 is negligibly small and when no appreciable 

 energy is radiated in the form of electric 

 waves. Under these conditions the differential equation* of 

 "motion" of the arrangement in Fig. 133 is: 



to terminals of 



high voltage 



induction coil 



Fig. 134. 



The complete solutionf of this equation is : 



q = Q sin (at - 6) 

 where Q and are constants of integration and 



VLC 



(2) 



(3) 



The period or time of one complete oscillation is the time required 

 for the angle co/ to increase from zero to 2ir. That is cor = 2T, 

 so that: 



r = 2irVTC (3) 



which is the same as equation (21) of Art. 112. 



When the circuit in Fig. 133 of Art. 112 has an appreciable 

 resistance, the differential equation of its "motion" is: 



* See derivation of equation (4) below. 



t See Franklin, MacNutt and Charles's Calculus, pages 181-185, published by 

 the authors, South Bethlehem, Pa., 1913. 



