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## Homework Statement

Basically, I'm just trying to verify that I can do basic algebraic manipulation correctly. The objective: solve the charging equation of a simple RC circuit for (C), capacitance.

## Homework Equations

[tex] v\left(t\right)={v}_{s}\left(1-{e}^{{-t}/{RC}}\right) [/tex]

## The Attempt at a Solution

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I ended up with the following.

[tex] C=\frac{-t}{R\mathrm{ln}\left(\frac{{v}_{s}-{v}_{\left(t\right)}}{{v}_{s}}\right)} [/tex]

Is this correct? Also, I have a suspicion that the log in the denominator can somehow be simplified more than just putting [tex] \mathrm{ln}\left(1-\frac{v\left(t\right)}{{v}_{s}}\right) [/tex] but I can't think of how. Thanks in advance!