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



I and E being the square root of the mean square values as 

 indicated by an electrodynamometer and electrometer. 

 For the combined circuit 



1 = 



\/(r w + r e + r s y+(p^-^j 



where e is the small impressed electromotive force and the 

 denominator is the combined impedance of the circuit. 

 For complete resonance, 



jt)L= p-, and hence 1= 



Cp' r w + r e + r a 



Hence 



/TTj~ 



E V c C 2 p 2 Impedance of the condenser ^ 



— = — = — - — rfn—i rr =±tesonance ratio. 



e r c + r s + r w 1 otal resistance 



In one case e was 50 volts and E was 2250, giving a reso- 

 nance ratio of 45. The impedance was 51 ohms, r +r w 



51 



was *38, r s was '72. Hence ' =46*4, agreeing very 



nearly with the ratio of the voltages. In this case the coil 

 was of large wire (No. 5 B & S) , and had considerable eddy- 

 current loss. Hence the value '72 for r s was too large, and 

 the degree of resonance was lower than it would have been in 

 the absence of eddy-currents. In another case, using a coil of 

 No. 10 wire, the impressed electromotive force was 29*5 volts, 

 the voltage on the coil or the condenser was 1808, and the 



E 

 resonance ratio — was therefore 61*9. 

 e 



The Resonance- Coll in Parallel. 



A second arrangement of the resonance-coil is to put it in 

 parallel with the condenser (fig. 5), and impress upon both a 

 high electromotive force. Each of the two parallel circuits 

 from B to C takes its own current, independently of the 

 other, but being nearly opposite in phase they nearly cancel 

 each other in the supply wires. Hence a small transformer 

 is sufficient to supply the small current needed, although 

 without the resonance-coil a large transformer would be 

 necessary. If, as before, 



pL= k' 



