# Find voltage by using Laplace transform

Hi I've been trying to solve this problem on finding the voltage out by using the Laplace transform. I know it's pretty basic but I can't get the solution after trying many times. I'm starting now to study this, and I'm a bit confused because it's a bit different to the way I'm used to solve this kind of circuits.

This is the problem: Solution: $$v_{o}(t) = (20e^{-2000t} - 10e^{-1000t})u(t)$$

I have tried to associate Ls and R in parallel and then associating (R||Ls)+(1/Cs) but I don't get to the solution I should obtain. Can someone help me and tell me what should I do to solve this kind of circuit? (I don't want you to solve it, just need you to give me a hint on what's the operation I should do to obtain Vo(s) ) Thank you very much.

EDIT: So this is what I have to develop?

$$V_{o}(s) = \frac{10}{s} \cdot \frac{\frac{RLs}{R+Ls}}{\frac{1}{Cs}+\frac{RLs}{R+Ls}}$$

## 1 Answer

You are right about combining Ls & R in parallel. Next do a voltage divider with that combination and 1/Cs to divide 10/s to Vo.

• I don't get the same solution as given either. – Austin Mar 16 '15 at 19:32
• Whoops, I do get the right answer, just read my calculator wrong. It's a little off but it rounds to what you gave. – Austin Mar 16 '15 at 19:48
• Thanks @austin. Can you look at my edit to see if I understood right what you told me? Thanks sir. – user3780731 Mar 16 '15 at 19:54
• @user3780731 Yes, your edit is correct. I got most of the way doing the algebra on paper but gave up and used a TI-89. – Austin Mar 16 '15 at 20:01