iii the Charging of a Condenser* 

 Kg. 8. 



393 





c 



IE 

 t II 



Pa 



— ^ . . 



charging battery, and R the resistance and L the coefficient 

 of self-induction of the circuit, we have 



and 



a+Lj-a-CPi-pj, . . . 



i 3(P,-P.) 



(1) 



(2) 



Differentiating equation (1) and combining the result with 

 equation (2), we obtain 



Gin ~di ;_dE 



or 



5? + L^ + LC 



(3) 



The integral of equation (3) for the case that R, L, and C 

 are constants is 



i=6 ~ k '{ A ^\/m-&- t+B Ww-S^- t }- 



A and B are integration-constants, and e the base of the 

 natural system of logarithms. 



For t=0 we have 2 = 0, and hence B = 0, 



and equation (4) reduces to 



'-^"^x/ro-n?-'- • • • (5) 



(4) 



