# Homework Help: How long does it take for energy stored in the capacitor to reach its maximal value?

1. Oct 15, 2012

1. The problem statement, all variables and given/known data
An RC circuit has EMF=12.0V, R=15 kΩ and C=3.8 μF. How long does it take for energy stored in the capacitor to reach 65% of its maximal value?

2. Relevant equations
1) Q = Cε
2) Q X .65 = desired charge
3) q(t) = Q(1 - e-t/RC)

3. The attempt at a solution
This is fairly straightforward to be honest, but I just don't know how to isolate for t in formula 3.

1) Q = 12v X 3.8μf = 4.56 X 10-5 C
2) Q X .65 = 4.56 X 10-5 C X .65 = 2.964 X 10-5
3) q(t) = 2.964 X 10-5(1 - e-t/0.057)

First question: Is that how I have to write down the formula with the known values?
Second question: How do I isolate for t?

Thank you!

Edit: Here is what I found by browsing on the Internet:

0.65Q = Q(1 - e-t/RC, or 0.65 = 1 - e-t/RC
-.35 = -e-t/RC
.35 = e-t/RC
ln .35 = -t/RC
t = -ln(.35) * RC
t = 1.0498 * 0.057
t = 0.0598 seconds

Last edited: Oct 15, 2012
2. Oct 15, 2012

### CWatters

Re: How long does it take for energy stored in the capacitor to reach its maximal val

Deleted as you found the answer.