536 BELL SYSTEM TECHNICAL JOURNAL 



The discharge current for incomplete charge is given by 



— I)^ F, F, 



^^ 47r AttCoR AttCoR 



Or if 



+ i^^)^^'""" - (\^) '-'"""'"' (20) 



- i) 



= - Qd = I. 



+ y^Eie-''"^ - 7x£ie-^'^+'''^/^ (20a) 



Equation (20) or (20a) is an example of the superposition principle 

 for the residual currents in a dielectric having a single absorptive 

 polarization with a relaxation-time t. It is evident that in the early 

 stages of the charging process the electronic or instantaneous polariza- 

 tions responsible for €„ have the same external effect as an absorptive 

 polarization because of the fact that the current by which they are 

 formed must flow through the lead resistance R. Thus the condenser 

 acts as though it contained a polarization yielding a dielectric constant 

 with a relaxation-time e^CoR. 



As the time-constant e^^CoR is generally small, the first two terms on 

 the right of (20a) may usually be neglected and we have 



Id = -y^E^e-'^i' - 7«£ie-('^+''^)^ (21) 



The first term on the right of (21) is the discharge current correspond- 

 ing to the discharge of the condenser after the residual polarizations 

 have been fully formed. The second term gives the value which the 

 charging current would have if the charging process were continued 

 for the interval of time tc + td instead of being discontinued after tc 

 seconds. When the charging time is large as compared with r the 

 second term may be neglected and the magnitude of the discharge 

 current is the same function of the discharge time as is the charging 

 current of the charging time; the charging curve and discharge curve 

 can then be superimposed on one another if we disregard the direction 

 of the current. There is only one complete charging current curve and 

 only one discharging current curve corresponding to complete polarization 

 of the dielectric at any given applied potential. There is, however, an 

 infinite number of discharge curves corresponding to incomplete polariza- 

 tion of the dielectric, that is, to any time of charging which is shorter 

 than that necessary for complete polarization. 



f 



