second order transient response

brickcitysaint

Joined Feb 12, 2009
1
Ok guys this is my first post so bear with me. Just needed some quick pointers or direction as to how to start the problem.

I started looking for t=$$\infty$$
first KVL of i(t) yields L di/dt + V(t) then KCL of i(t) yields i(t)=i$$_{r}$$+i$$_{c}$$+i$$_{L}$$ after all that i came up with v(t force) =0. then i solve for V(t) natural which yields k1e$$^{-2x10^{5}t}$$+k2e$$^{-8x10^{5}t}$$.
What do i do after this? I know i have to solve for i(0$$^{-}$$) and V(0$$^{-}$$) how do i solve for those V and i?

THanks!

guitarguy12387

Joined Apr 10, 2008
359
Imagine what the circuit looks like for t < 0. Way before t = 0, the capacitor will charge up and look like an open circuit (**hint hint**). Also, note that the inductor and other resistor are switched out of the circuit (when calculating initial conditions).

Then you may want to (depending on the formulas you're using) determine the final values of i_c, v_c, i_l, v_l for t >> 0.

To do that, simply notice that after a long time, the capacitor will again look like an open and the inductor will look like a short.

Then just plug into the formula! Good luck.