Given the differential equation below, find the solution using Laplace transformation. The parameters
R,L
,
and
I_(s)
are constants that are related to the resistance and the inductance in an RL circuit, and current
I_(s)
is applied at time
t=0
to the circuit in series.
I_(L)
is the function you have to solve for and it corresponds
to the current in the inductor. Initially
I_(L)(0)=0
.
L(dI_(L))/(dt)+RI_(L)(t)=RI_(s)
(a) Give an expression for
I_(L)(s)
, where
L{I_(L)(t)}=I_(L)(s)
,
(b) Give an expression for
I_(L)(t)
; the solution to the differential equation