AN ELECTRICAL EXAMPLE 881 



and - lo - C = Const 



--C 



log, 5__ 

 1 c L 



R~ 



_r 



R ~ a 



^^"T 



--C 



T 



H 



_ jTT 



R 



(2) To express C in terms of t when t> = v sin pi. 

 Then RC + L-j- = v sin p/ 



dC R n 



and -T- + =^C = ^ 



(ft L L 



Now T"!^ = T" 



M 

 The integrating factor is therefore e L 



and Ce 1 ' = -Y\e^ sinpt dt+ Const 



^R . 



, 



( y sin pi p cos 2><J + Const 



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

 Then = ^2 + Const 



