200 TKEATISE ON ALTERNATING CURRENTS. 



Substituting the value of C given by (4) in equation (3) we get 



f(i-r; 



which gives the value of i at every instant of time. 



APPENDIX B. 



Solution of the equation (see 21, Chap. III.) 

 di 



(1) 



Writing the equation in the form 



di r .? e , 



we get 



. * e f r* 



W = 2J * L sm P*to .... (2) 



To determine the integral in equation (2) we proceed as follows 

 Since 



cos pt + k sin pt = *'" 



where k = \/ 1, we have 

 / *(cos pt 4- k sin 



where C is a constant 



r 

 L 



-t L (cos pt -f- k sin ^;) 4- C 



