First, I hope this topic doesn't already exist. I've searched and searched and Google'd and compiled everything that seemed to make sense.
Just getting started on these, I don't know differential equations but I don't think first-order are that hard so I'm not too worried. What I do want to know is that the work and figuring that I have done is not in error.
My goal was to get a GENERAL equation. I don't know why it was so hard. My solution ended up as this:
y(t) = (y(0-) - y(∞))e^-at + y(∞)
Where y can be either current or voltage and a can be either the time constant for an RC or for an RL. From what I've found, this should work BUT I really don't know what I'm doing and maybe it's pure falsehood.
The only real problem I have "solving" these after I get this form set up is what to do with y(∞). There's a table in the textbook where if that value is a constant you just replace it with a different constant and a couple other if-else situations. The ones we did in class were super confusing with 800 more letters in them, so I'm not confident I should say (for a small circuit with a switch, a Vs, an R(4) and a C(.25) where Vc(0-) is 2) that the solution is:
Vc(t) = (2 - K)e^-t + K
I know that's probably hard to follow, but the general equation is what I'm really after for now.
Just getting started on these, I don't know differential equations but I don't think first-order are that hard so I'm not too worried. What I do want to know is that the work and figuring that I have done is not in error.
My goal was to get a GENERAL equation. I don't know why it was so hard. My solution ended up as this:
y(t) = (y(0-) - y(∞))e^-at + y(∞)
Where y can be either current or voltage and a can be either the time constant for an RC or for an RL. From what I've found, this should work BUT I really don't know what I'm doing and maybe it's pure falsehood.
The only real problem I have "solving" these after I get this form set up is what to do with y(∞). There's a table in the textbook where if that value is a constant you just replace it with a different constant and a couple other if-else situations. The ones we did in class were super confusing with 800 more letters in them, so I'm not confident I should say (for a small circuit with a switch, a Vs, an R(4) and a C(.25) where Vc(0-) is 2) that the solution is:
Vc(t) = (2 - K)e^-t + K
I know that's probably hard to follow, but the general equation is what I'm really after for now.