(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I'm trying to use the Laplace transform to find the charging equation of a capacitor with an initial voltage already on the capacitor.

2. Relevant equations

[tex]V_i = RC\frac{dVc}{dt} + V_c[/tex]

The initial condition of Vc will be [tex]\lambda[/tex].

3. The attempt at a solution

[tex]V_i(s) = sRC*V_c(s) + V_c(s) - \lambda[/tex]

Vi will be a step function of magnitude V, so

[tex]\frac{V_i}{s} + \lambda = (sRC + 1)V_c(s)[/tex]

[tex]V_c(s) = \frac{V}{s(sRC+1)} + \frac{\lambda}{sRC+1} [/tex]

So using a table of Laplace transforms I get:

[tex]V_c(t) = V_i(1-e^{\frac{-t}{RC}}) + \frac{\lambda}{RC}(e^{\frac{-t}{RC}})[/tex]

The problem is that this doesn't seem to agree with the formula I've seen, it's close but lambda shouldn't be divided by RC. I'm wondering how I went wrong? Thanks for any advice.

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# Homework Help: Laplace transform IVP

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