30 TREATISE ON ALTERNATING CURRENTS. 



where 



e is the base of Naperian logarithms, and A is a constant. 

 The exponential term in (6) soon dies out, and the current soon 

 assumes the steady periodic state given by the equation 



This shows that the current leads before the E.M.F. by a time 

 t = -. An example of such current and E.M.F. curves is given in 



Fig. 7. 



FIG. 7. 



24. Electric Current in a Circuit containing 

 Resistance, Capacity, and Self-induction in 

 Series. Let the total resistance of the circuit be ?, the co- 

 efficient of self-induction L, the capacity C, the E.M.F. e = Esinpt, 

 and the resulting instantaneous value of the current *'. 



The E.M.F. c has to drive the current i against the resistance 

 r, and to balance the E.M.F.s due to self-induction and capacity. 

 Therefore 



L^ + ri + ^Zsinpt (8) 



where Q is the quantity of electricity on the condenser at any 

 instant. 



Differentiating equation (8) with respect to t, we get 



