Natural and step response RLC find iL(t)

[pokie_panda]

Homework Statement

The switch in the circuit in the figure has been open a long time before closing at t=0.
Find iL(t) t>0
Express your answer in terms of t, where t is in milliseconds.

https://www.flickr.com/photos/84781786@N03/8899251427/

The Attempt at a Solution

We simplify to circuit to get

4A current , 2kohms,62.5H,2.5uF (All in parallel with each other).

iL(0-)= -15/3000 =-5mA ,
Vc(0-)=0,
iL(∞)= 4mA,

wo^2= 1/LC=10^6/62.5*.5 =6400
wo=80 rad/s

a= 1/2RC =10^6/4000*2.5 =100

s1,s2=-100±√100^2-80^2=-100±60
s1=-40 , s2=-160

iL=If+A'1e^-40t + A'2e^-160t

iL(∞)=If=4mA
iL(0)=A'1+A'2+If=-5mA

so A'1+A'2=-9mA

diL/dt(0) =0=-40A1 - 160A'2

A'1=12mA A'2=3mA

iL=4-12e^-40t+3e^-160t t≥0

 

[gneill]

Your diagram doesn't appear to match your problem statement.

 

[rude man]

What switch?