330 PRACTICAL MATHEMATICS 



Fig. 112 shows the curves obtained by plotting the values of 

 s horizontally and the values of y vertically. 



168. If the voltage in an electric circuit is v volts, the current 

 is C amperes, the resistance R ohms, the self-inductance L henries, 



then v = RC + L -r- where t is time in seconds. 

 at 



(1) To express C in terms of / when v is constant. 



/7P 



Now v = RC + 



v - RC = l 

 at 



R" C = R^ 



r dC Rf 



and I = y- \ at + Const 



JL_C 

 Integrating, logJ^ C ) = y t + Const. 



at 





 i / Li 



(a) Let the initial condition be C = when t = 0. 



v 

 Then log e = Const 



ix 



/u \ . v ~Rt 

 Hence log, (^ - C J - log, ^ = - -j- 



R ~ C 



"R 



and 



_Kt 



It should be noticed that as t becomes large e L becomes small, 



and therefore C tends to the value ^. 



Jx 



(b) Let the initial condition be C = C when t = 



Then - log/5 - C ) = ? + Const 



\rt / Lt 



