Method of Measuring Energy dissipated in Condensers, 23 



In fig. 2, let Aa = i*c, the ohmic resistance of the coil; 



aB = pL, the reactance of the coil ; 



Bb=r s , the equivalent resistance of the con- 



-* denser ; 



bG = -7s, the condensance of the condenser ; 

 pyj 



CD = r w , the resistance of the fixed coil of the 

 wattmeter, its induction being ne- 

 gligible ; 



AD = the resultant impedance of the circuit. 



Then if pL= p-, the reactance is equal and opposite to the 



condensance (fig. 2 c) , the resonance is complete, and the 

 impressed electromotive force e is expended in overcoming 



the resultant resistance AD=r c + r s +r. and 1= — - - — . 



r c + r s + r w 



lines represent 



In fig. 3, similar to fig. 2 c, the several 

 electromotive forces. Aa = Ir c = e c = that part 

 of the electromotive force expended in over- 

 coming the ohmic resistance of the coil ; simi- 

 larly, B# = e s , OD = e w . Ba is the electromo- 

 tive force (due to resonance) which overcomes 

 the reactance, and bG is the electromotive force 

 which overcomes the condensance. The po- 

 tential of the point B varies through a wide 

 range; whereas the points A, C, and D, and 

 the instruments suffer only small changes of 

 potential. 



Fig. 3. 

 B 



/ 



Advantages of the Method. 



Herein lies one of the chief advantages of 

 the method, that voltages below a hundred 

 have to be dealt with at the instruments, 

 whereas upon the condenser there may be an 

 active electromotive force of several thousand 

 volts. The noninductive resistance E, is at 

 most a few hundred ohms. On the contrary, if the shunt- 

 resistance were applied directly at the terminals of the con- 

 denser, it would necessarily be several thousands of ohms, it 

 must be capable of carrying the entire shunt-current of the 

 wattmeter, it must be strictly non-inductive, and be of 

 known value — conditions difficult to fulfil. In the resonance 

 method a small inductance in the shunt-resistance or the 

 movable coil of the wattmeter produces no appreciable error; 

 whereas in the simple wattmeter method it produces a large 

 error. 



