Alternate Current- Condensers. 103 



K the capacity, and t the time. Then 



and the power spent at any instant, 



EC=EK^. 

 at 



If e is the maximum electromotive force, the work done in 

 charging the condenser is thus 



Jo 



the ordinary expression. On discharging, the work absorbed 

 is 



K1 >( We or -4K* 2 . 



s. 



It is equally easy to show that no power is absorbed in the 

 case of an induction-coil with no hysteresis, without assuming 

 the pressure to vary harmonically. 



If C does not vary as the rate of increase or decrease of E, 

 but is greater on charging and less on discharging, power is 

 absorbed. A hysteresis curve, like those we are accustomed 

 to in iron, can be plotted in the case of a condenser. It has 

 no very close analogy with the case of iron, however. 



At first it might seem that absorption might be neglected 

 as too trifling to matter in commerci.nl work. This, however, 

 is not the case. Some condensers about a foot square and an 

 inch thick absorbed over half a horse-power, and soon rose 

 above the temperature of boiling water. 



According to Maxwell's theory, the absorption of power is 

 just as easily explained as the time-lag in discharge. Suppose 

 the dielectric is paper soaked in melted paraffin, and suppose 

 the fibres of paper do not insulate and that the paraffin does. 

 When the plates are charged, a fibre running part of the way 

 across the dielectric finds its ends at different potentials ; so 

 a current is set up to equalize them. This current means loss 

 of power by heat. It also increases the capacity of the con- 

 denser. An increase of the capacity of the condenser when 

 the pressure is increasing, or after it is applied, means in- 

 creased energy put into the condenser. If the capacity of 

 the condenser were constant, the current into it would be 

 proportional to the rate of increase of the electromotive force, 

 and no power would be absorbed in a period ; but if the 

 capacity is increased as the pressure rises and decreased as it 



