CURRENTS IN INDUCTIVE CIRCUITS. 25 



The equation from which to determine the current is then, 

 by 15 and 16 



..... (8) 



The complete solution of this equation is (see Appendix) 

 ._gsin(^-0) .,< (9) 



where given by tan 6 = .......... (10) 



A is a constant 

 and c is the base of TSTaperian logarithms, and equals 27 nearly. 



After a very short time i~zr becomes negligibly small, and 

 the current attains a steady periodic state represented by the 

 equation 



- 0) 



TT 



If we write / for , equation (10) takes the form 



i = Ism(pt-B) (12) 



I is therefore the maximum value of the current. 



Equation (8) shows that the P.D. is zero when t = 0, and 

 equation (12) shows that the resulting current is zero, and in- 

 creasing in the same direction when 



t - B 



ii ~, 



that is, the current is a sine function of the time, and has its zero 

 and maximum values later in point of time than, or lags behind, 



n 



the P.D. by an amount -. 

 P 

 The E.M.F. of self-induction is given by 



di 

 - L m = - P L1 cos (P* - 0) 



