enter image description here

I want to make equation that describe relation between vi and vc. I did it like this. Is this right way?

enter image description here


2 Answers 2


EE&O ...
To help a little (check results of differential equations), here are pictures of the inductor current and the voltage across the capacitor ...
Values : L:= 1e-3 H: C:= 1e-6 F: r1:= 1 ohm : r2:= 100 Ohm: Vin:=step 1 V.

enter image description here


Well, using Laplace transform we can see that:


Where \$\alpha\space\text{||}\space\beta:=\frac{\alpha\beta}{\alpha+\beta}\$.

So, when we simplify we can write:


So, we get:


  • \$\begingroup\$ thx for fast answer but i don't know Laplace transform... what is that jw thing?? \$\endgroup\$
    – moonjy1120
    May 27, 2022 at 10:11
  • \$\begingroup\$ j is i, sqrt(-1). It's an engineer thing. w is lowercase omega, angular frequency, f/2pi, basically f but more convenient to avoid pis popping up everywhere. Laplace transform is a way of solving many differential equ'ns by transforming your functions into others where doing differentiation maps to a simple algerbraic operation . A tool a bit like the way it makes more sense to think of response in terms of frequency than time-axis response in AC circuits (which is effectively looking at the Fourier transform). Doing the similar but different Laplace is useful for analysing filters. \$\endgroup\$
    – Dannie
    May 27, 2022 at 10:39
  • \$\begingroup\$ thanks for nice explanation @Dannie, in this circuit the input is not AC but DC square wave.... is it apply to both ac and dc? \$\endgroup\$
    – moonjy1120
    May 27, 2022 at 11:26
  • \$\begingroup\$ "what is that jw thing??" Somewhat out of place here as this is a Laplace domain expression. It should be s, the complex frequency variable used in place of f or ω in Laplace expressions, so should read \$\frac{1}{sC}\$ \$\endgroup\$
    – Graham Nye
    May 27, 2022 at 14:27

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.