Message Boards Message Boards

0
|
3129 Views
|
0 Replies
|
0 Total Likes
View groups...
Share
Share this post:

RC first order system - solving DEs with laplace transform

Posted 9 years ago

Hello.

I am just starting with Laplace transforms and don't know how to solve that basic problem. I'm pretty sure I did something wrong because when I put the final equation into wolfram alpha, it gives me a completely wrong graph and an inverse transform solution that has no constants to calculate with initial condition i(0)=0.

given:

U=50V

R=4?

C=1mF

i(0)=0

R di/dt+i/C=U

RC di/dt+i=CU

Constants:

T=RC=4×10^(-3)

Gain=CU=50×10^(-3)

Solving differential equation for I(s) using laplace:

sRCI(s)+I(s)=CU(s)

I(s)×[sRC+1]=CU(s)

I(s)=(CU(s))/(sRC+1)

As voltage is a step function,

U(s)=U/s

I(s)=(CU/RC)/s×1/(s+1/RC)=12.5/s×1/(s+250)

So, where is the error and how to solve that? Thanks in advance!

edit: well, I just noticed there's something wrong with my equation as V=IR so V cant be Rdi/dt, but I got this equation from my lecture notes... totally confused now!

POSTED BY: Pawel Wozniak
Reply to this discussion
Community posts can be styled and formatted using the Markdown syntax.
Reply Preview
Attachments
Remove
or Discard

Group Abstract Group Abstract