# Capacitor Discharge problem

1. Oct 11, 2008

### haxxorboi

1. The problem statement, all variables and given/known data
A capacitor is charged to 1 coulomb; the capacitance is 8.00×10-5 farads. Then a switch is closed which puts the capacitor in a closed circuit with a resistor; the resistance is 8.60×101 ohms. Calculate the charge on the capacitor after 4.00 milliseconds. (1 ms = 0.001 s)

2. Relevant equations
I=V/R
C=Q/V

3. The attempt at a solution
C=Q/V=8E-5 F=1/V V=12500 V

I=V/R=12500/86=145.348 A

145.348 C/S = .145348 C/mS

.145348*4=.5814 C transferred in that 4 milliseconds

1-.5814=.4186 C left

So the answer would be .4186 C I think but I'm getting an "Incorrect Answer" apparently

2. Oct 12, 2008

### LowlyPion

This is a time varying current flow. You will want to consider the Charge as a function of time.

$$Q_{(t)} = Q_o*e^{\frac{-t}{RC}}$$

3. Oct 12, 2008

### haxxorboi

I've never seen that equation before and I can't find it in our chapter.

Let me see if I understand this equation...

Final charge=1 Coulomb * 1.602E-19-.004/(86*8E-5)

Does that seem right or am I misinterpreting part of the equation.

Thanks

4. Oct 12, 2008

### Phrak

"e" is the natural base = 2.71828..., rather than the charge of the electron, in this case. Just write it as "e", and use the exponental function on your calculator.

5. Oct 12, 2008

### LowlyPion

This is correct. Not e the charge of an electron. e the natural log

It's typically used to express the decay in RC networks.

6. Oct 12, 2008

### haxxorboi

SWEET! The answer ended up being .5591 C which was correct with the system.

Thanks so much for the help guys, I feel stupid with not recognizing which "e" that was seeing as this is an exponential decay. I'm not sure how we were supposed to know how to do this problem though as I can't even find this equation in our course pack I have no idea how my Prof expected our Phy101 class to know this without going for help.

Thanks again guys for the help!

7. Oct 16, 2009

### Wizardofwaz

I have the same problem but with these numbers
A capacitor is charged to 1 coulomb; the capacitance is 6.00×10-5 farads. Then a switch is closed which puts the capacitor in a closed circuit with a resistor; the resistance is 9.20×101 ohms. Calculate the charge on the capacitor after 4.00 milliseconds. (1 ms = 0.001 s)

what kind of formula do I use to solve this