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Transient analysis

$$\frac{V_c-V_2} {R_2} + C \cdot \frac{dV_c}{dt} + \frac{V_c} {R_3} = \frac{V_1-V_c}{R_1}$$ $$V_c(0) = V_2 $$

I have tried to solve this with the help of MATLAB, but the answer from the book is apparently different from my answer. What's wrong with my differential equation?

Here is the answer from the book.

$$v_C(t) = Ke^{−t/\tau} + \tau f (t)$$ $$v_C(0) = Ke^0 + V_T$$ $$K = v_C(0) − V_T = V_2 − V_T$$ $$v_C(t) = (V_2 − V_T )e^{−t/R_T C} + V_T$$

Null
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kile
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  • I can't speak for how you used matlab, but your initial statement is correct and your initial conditions are also correct. I started here: \$\frac{V_c}{R_1}+\frac{V_c}{R_2}+\frac{V_c}{R_3}+C\frac{\text{d}}{\text{d}t}V_c=\frac{V_1}{R_1}+\frac{V_2}{R_2}\$ and reached yours without trouble. – jonk Sep 11 '22 at 18:07
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    Show us how you tried to solve the equation, and what you got as a result. Also tell us what you believe is the correct solution. – Elliot Alderson Sep 11 '22 at 18:09
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    Kile, you also should be able to solve this using a variety of different techniques for the solution of 1st order diff-eq. For example, using methods such as these: *integrating factor* or *variation of parameters*. If you are not able to independently solve these kinds of problems without the use of Matlab then that's a problem you need to work on. Being crippled by a dependence upon tools you little understand isn't a good thing. It's about as bad is depending upon a calculator to perform addition and subtraction and not being able to do a simple problem of either, yourself. – jonk Sep 11 '22 at 18:20
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    Hi Kile: Matlab often provide solutions in strange forms. It may just look different from the book. Both may be correct. Perhaps all you need to do is manipulate the Matlab output to match the book. – RussellH Sep 11 '22 at 19:09
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    @kile It was more of a worry I was feeling, than advice. I'd like to see you write out a solution using an integrating factor and your known initial conditions or else using variation of parameters to work this out by hand. You should be able to achieve that. And if so, you will know who is right and who is wrong -- matlab or your book. (You've disclosed neither to us.) You correctly laid out the differential KCL and initial conditions. And I think that's the good news. I'm very glad you performed that so well. But it is the rest that I'm worried about, now. Can you solve this by hand? Or not? – jonk Sep 12 '22 at 04:48
  • The solution of the book you posted is missing something. 1) the time constant is expressed as RT*C, but what is RT? 2) K is expressed in term of VT, but there is no definition of VT. Are these the parameters of the Thévenin equivalent you are not supposed to use? – LorenzoDonati4Ukraine-OnStrike Sep 24 '22 at 15:53
  • @LorenzoDonatisupportUkraine See my answer, please. – Antonio51 Sep 24 '22 at 16:00
  • @Antonio51 OK, thanks, but I didn't ask because I needed to know how to calculate them. I was prompting the OP to improve his post by providing complete information. If he posts the solution of the book, then he should post the entire solution, complete with all the parameters. Probably I should have said that explicitly. Oh well, the question was closed rightfully since the OP doesn't seem to want to improve the post. – LorenzoDonati4Ukraine-OnStrike Sep 25 '22 at 13:39
  • No worries, Lorenzo. I give it to anyone who needs it. I think a direct solution is given with the use of EET. But I did not use that theorem ... although I read about it the presentation of @VerbalKint which is very clear. Useful https://electronics.stackexchange.com/questions/484502/analysis-of-unbalanced-bridge-circuit – Antonio51 Sep 25 '22 at 15:36
  • Any interest to these theorems https://cbasso.pagesperso-orange.fr/Downloads/PPTs/Chris%20Basso%20APEC%20seminar%202016.pdf – Antonio51 Sep 25 '22 at 15:47

1 Answers1

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What's wrong with my differential equation?

Unless EE&O. Best use of EET & FACTS...

You just have to do:

enter image description here

Nothing seems wrong with your equation.

When I have a doubt, I do always, if possible at least, two "checkings".
One is easy. Simulation. microcap v12.
The other is a calculation with something like a Maple sheet.

What "solution" was found in the book? Can you compare "result" numerically with this?

I did the simulation. The switch is closed at 10 ms until 20 ms.

enter image description here

And here is the result of the calculation with OP equation ...
Exactly the same behavior. So, until the "book equation" is known ...

enter image description here

enter image description here

Antonio51
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