I'm really stuck on this simply RLC circuit problem:

If I have a series RLC circuit with the Vs(t) source how do I find \(i_{l}(t)\) (current through the inductor)?

I have the following parameters:
Vs(t) = \(5sin(10^{4}t)\) at t>0;
R=1250Ω
L=1.25mH
C = 5nF.

After doing KVL's, I keep ending with an equation for Vc(t), and not inductor current. I know that there is some trick that I'm not thinking of, but right now I can't figure it out. Help Please
Thank you.

 

Are the components in series or parallel?

Either way you can find the impedance of the network and then apply Ohm's law, i=v/Z

 

hi
u have w=10^4
so .. u can fiend impedance z=R+Xl+Xc
Xl=2*pi*w*L
Xc=1/2*pi*w*C
then fiend the total current
the total current = the current through the inductor !! because the impedance are connected on series
the current in series is
It=IR=IXl=IXc