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!