Method of Measuring Energy dissipated in Condensers. 

 Difficulty of the Method. 



We have seen that the presence of a resonance-coil in series 

 with the condenser (1) quenches, to a large extent at least, the 

 upper harmonics, (2) raises the voltage upon the condenser, 

 thus avoiding transforming up, (3) enables measurements to 

 be made more safely and more conveniently upon a low voltage, 

 and (4) transfers the wattmeter problem from the most un- 

 favourable case (where the angle of phase-difference is nearly 

 90°) to the most favourable case where the current and 

 electromotive force are nearly in phase. There is, however, 

 one serious difficulty in the method. If the resonance- coil is 

 made of small wire, it has a great resistance, and of the total 

 power measured only a small part is expended on the con- 

 denser. Thus the condenser loss is the difference between 

 two relatively large quantities, and cannot be determined as 

 accurately as would be desired. If, on the other hand, a 

 large coil of larger wire is used so that its resistance is small, 

 there will be eddy-currents in the copper of the coil, and the 

 power expended on the coil will be greater than 1V C . This 

 excess will go into the remainder as condenser loss, and may 

 give rise to a considerable error. If the wire is of large cross- 

 section, but stranded, so that its resistance is small and the 

 eddy-currents negligible, then a large coil will have a large 

 inductance, and no difficulty appears. The method is then 

 accurate as well as quick and convenient. 



The Resonance Ratio, 



As the condenser is alternately charged and discharged 

 energy is handed to and fro between the coil and the condenser. 

 When the condenser is charged to its maximum extent the 

 current is zero and all the energy is potential and residing in 

 the condenser. A quarter of a period later the condenser is 

 discharged and the current is a maximum ; the energy is now 

 kinetic, and resides in the magnetic field of the resonance- 

 coil. At other instants the energy is partly potential (in the 

 condenser) and partly kinetic (in the coil). As this transfer 

 of energy to and fro continues, the dynamo supplying the 

 current furnishes just enough energy to make good the losses, 

 that is, the heating effect in the wires and the dielectric of the 

 condenser. The losses due to electromagnetic radiation and 

 mechanical vibrations are usually negligible. 



For the condenser alone, 



i= E 



\A + <y 



cy 



