490 THE ELECTROMAGNETIC FIELD. [PT. III. CH. XII. 



Thus the tendency of the inductance and capacity is to neutralise 

 each other's effects, Exact neutralization is produced, so that 

 there is neither lag nor advance, when 



1 1 27T 



In this case the impedance is the smallest possible, and the 

 magnitude of the current is a maximum, being the same as would 

 be given by Ohm's Law for steady currents with a closed circuit. 

 The period of the electromotive force which gives this result is 

 exactly that of the free vibration which would be natural to the 

 system if there were no damping. Under these circumstances 

 the system is said to be in resonance with the force. The 

 magnitude of the current is inversely proportional to the resist- 

 ance, and if there were no damping would be infinite. For this 

 reason resonant oscillations, either mechanical or electrical, may 

 be very intense. By connecting two similar circuits with two 

 similar Ley den jars, Lodge has caused the oscillatory discharge of 

 one jar to produce such violent resonant oscillations in the other 

 circuit that a considerable spark-discharge is produced. The 

 phenomena of resonance have been demonstrated in a number of 

 interesting papers by Pupin*. 



In order to show how the resonance depends on the agreement 

 of the frequency of the impressed force with that of the free 

 vibration, we give in Fig. 95 a graphical representation of the 

 current as a function of the frequency. If we call a) m the value 

 of ft) which gives the maximum current, 



fc : -'= 3 1 



the amplitude of / is 



/ 

 A/ 



ft) ft) TO V 

 KR Z \co m w / 



In Fig. 95 are plotted the values of the factor of E /R as 

 ordinates, the abscissas being those of o)/a> m . The different 

 curves are, beginning at the outermost, for integral values of 



the ratio . /= / R from 1 to 10. The resonance is sharper the 

 larger this ratio. 



* Pupin, "Electrical Oscillations of Low Frequency and their Kesonance." 

 Am. Journ. Science, April, May, 1893. 



