•22 Messrs. E. B. Rosa and A. W. Smith on a Resonance 



energy expended in the resonance -coil and the fixed coil of 

 the wattmeter, I 2 (r c -\-r w ), subtracted from the total power 

 measured leaves the condenser loss. This remainder is found 

 to be also proportional to the square of the current. Hence 

 we may write it I 2 r s , and r s is the u equivalent resistance " of 

 the condenser, which it is desired to find. This does not 

 indicate the nature of the process by which energy is dissi- 

 pated in a condenser, but simply that for a given condenser 

 made of a given dielectric at a given temperature and fre- 

 quency, the heating effect is the same as though there were a 

 certain resistance r 8 in series with a perfect condenser of the 

 same capacity. For the same dielectric r s changes with 

 changes in the temperature or the frequency; and for another 

 dielectric with the same capacity, temperature, and frequency 

 r s would be different. 



If £ = 27r\/LO, there is complete resonance; t= , and 



1 . 1 n 



p = 27rn. Therefore - = n/LC, or 0=-^. That is, for 

 p p 2 h ' 



complete resonance the capacity is inversely proportional to 

 the square of the frequency for a given self-induction. If 





Fig. 2. 



(b) 

 B b 



A a 





a c D 



the frequency is fixed, either the capacity or the induct nee 

 may be varied until the current is a maximum ; but if the 

 frequency can be varied, the maximum resonance may be 

 attained without varying C or L. 



