How Do You Calculate Time in a Charging Capacitor Equation?

AI Thread Summary
To calculate the time for a charging capacitor to reach a specific voltage, the equation V = V0*[1 - e^(-t/RC)] is used. The user attempted to rearrange it to t = -RC*ln(V/V0), but encountered issues with the logarithmic steps. Feedback indicated a misunderstanding of logarithmic properties, specifically regarding ln(1+x) and ln(1-x). The discussion suggests that the lecturer may prefer an intuitive approach rather than a strict mathematical solution. Ultimately, the user decided to postpone the problem for now, appreciating the guidance received.
MidlandSoul
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Homework Statement


Solving the equation: V = V0*[1 - e^(-t/RC)]

Homework Equations


Need to solve this equation for time to calculate the time at which a charging capacitor achieves a certain voltage across it's plates.

The Attempt at a Solution


I solve it as: t = -RC*ln(V/V0) but this doesn't seem to work. Help!
 
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it looks like you might have done a step like this: ln(1+x) = ln(x) But this is not true.

Edit: Oh, welcome to physicsforums by the way!
 
Show your work step by step & we'll show you where you went wrong.
 
BruceW said:
it looks like you might have done a step like this: ln(1+x) = ln(x)
Or rather, ln(1-x) = ln(x)
 
Thanks guys. I think our lecturer intends for us to sort of 'have a guess' by inspection and using time constant ratios than actually solve this, so I can leave it for another day, phew!
Thank you for the feedback nonetheless.
 

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