Timeline for System of First Order ODEs for a Parallel RLC Circuit
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 21, 2023 at 23:28 | vote | accept | Sterling Saini | ||
| Aug 20, 2023 at 11:20 | comment | added | periblepsis | I'll write one more time. That's it. There are many choices you can make. But the usual case is the energy of the inductor (propto its current) and the energy of the capacitor (propto its voltage difference.) So \$i_{_\text{L}}\$ and \$v_{_\text{C}}\$, where \$\dot{i_{_\text{L}}}=\frac1{L}v_{_\text{C}}\$ and \$-\dot{v_{_\text{C}}}=i_{_\text{L}}+\frac1{R}v_{_\text{C}}\$ (from KCL.) You will need the initial states for \$i_{_\text{L}}\$ and \$v_{_\text{C}}\$ at \$t=0\$, as there's no driving function. You need to tell me what your problem is with this. I'm flummoxed about your confusion. | |
| Aug 15, 2023 at 22:14 | answer | added | user319836 | timeline score: 1 | |
| Aug 15, 2023 at 4:54 | comment | added | periblepsis | In your case, the usual approach is to consider the current through the inductor as one state and the voltage across the capacitor as another state. So that's two states. This is usually done this way because the initial conditions (current in inductor and voltage across capacitor) are direct items of interest/knowledge. (This is the same thing, though, as knowing Q and d/dt Q.) Anyway, can you refine the question? I don't see anything to grab ahold of and run with. I could say what I think. But that may not help. Depends on your perspective, not mine. | |
| Aug 15, 2023 at 0:42 | comment | added | periblepsis | Yeah, then you are looking for a state-space approach. The linked page already has more than enough detail to move you almost to completion. But no, it doesn't hand you a state-space result, boxed up and neatly tied with a bow. | |
| Aug 15, 2023 at 0:07 | comment | added | Sterling Saini | @periblepsis I thank you for your response. I think this might be state-space kind of thing, though I haven't come across that terminology before. In regards to the similar answer - and this may be due to my own incompetence rather than anything else - I am simply looking for a way to reduce the 2nd order ODE to a system of First Order ODEs - this doesn't seem to be covered in the supplied article (though I will keep it for a later case). This is less about solving the question any which way and more - can it be solved this way? | |
| Aug 14, 2023 at 14:23 | comment | added | periblepsis | Also, just to be clear... is your question a state-space kind of thing? Sounds like it to me, looking back on this. But what do I know? | |
| Aug 14, 2023 at 13:41 | comment | added | periblepsis | I think an answer (or close enough that you should be readily able to do whatever else you feel is needed) is already here at EESE. | |
| S Aug 14, 2023 at 5:15 | review | First questions | |||
| Aug 14, 2023 at 6:01 | |||||
| S Aug 14, 2023 at 5:15 | history | asked | Sterling Saini | CC BY-SA 4.0 |