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## Homework Statement

What is the voltage across a capacitor after a time of two constants when charging from zero voltage. When discharging from a fully charged condition?

## Homework Equations

V

_{Capacitor}= V

_{Battery}(1 - e

^{-t/2T})

V

_{Capacitor}= V

_{Maximum}* e

^{-t/2T}

## The Attempt at a Solution

I'm confused at how to start. I can do the algebra...

Charging from zero voltage - so would I set V

_{Maximum}to 0? Wouldn't I need to know V

_{Battery}? That wouldn't make sense to me. If I can get an idea of how to approach this problem, I should be able to solve it no problem. Thanks!

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## Homework Statement

With V = V

_{o}*e

^{-t/RC}, it mathematically takes an infinite time for a capacitor in an RC circuit to discharge. Practically, how many time constants does it take for a capacitor to discharge to less than 1% of its initial voltage?

## Homework Equations

V = V

_{o}*e

^{-t/RC}

## The Attempt at a Solution

0.01*V

_{o}= V

_{o}*e

^{-t/RC}

0.01 = e

^{-t/RC}

100 = e

^{t/RC}

ln(100) = t/RC

2*ln(10)*RC = t

So, I'm saying that it takes approximately 4.61 time constants.

Would this be correct? Thanks!