How Do You Calculate Time in a Charging Capacitor Equation?

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SUMMARY

The discussion focuses on solving the charging capacitor equation, V = V0*[1 - e^(-t/RC)], specifically for the variable time (t). The user initially attempted to rearrange the equation to t = -RC*ln(V/V0) but encountered issues with logarithmic properties. Feedback from other forum members highlighted a misunderstanding of logarithmic identities, particularly ln(1+x) and ln(1-x). Ultimately, the user concluded that their lecturer may prefer an intuitive approach using time constant ratios rather than a strict algebraic solution.

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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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