# Homework Help: RC Circuit Discharge

1. Jul 1, 2008

### purduegirl

1. The problem statement, all variables and given/known data

A circuit consists of 3 components connected between 2 terminals: A 6 V source, a 60 ohms resistor and a 0.02 F capacitor. The capacitor is initially uncharged. The voltage source is turned on. What is the current flowing through the above capacitor after a very long time?

2. Relevant equations

I(t) = E/R *e^(-t/time constant)
time constant = (R)(C)

3. The attempt at a solution
time constant = 1.2 s

Because the time is a long time, I thought that I wouldn't have to enter anything in for time. I then used the I= E/R*e^(-1/time constant) to solve for the current. I got I = (6 V/60 ohms)*e^(-1/1.2s) = 4.35E-1. I'm pretty sure I'm wrong here so any help to tell me what I am doing wrong would be greatly appreciated.

2. Jul 1, 2008

### alphysicist

Hi purduegirl,

But you did enter something here for time--you entered 1, so you found the current at 1 second.

When they say the time is a very long time, what does that mean? Or alternatively, what is $e^{-t/(\mbox{time constant})}$ for very large t (if you plot it, for example)?

3. Jul 1, 2008

### purduegirl

They didn't give a specified time for " a long time". That's why I'm not sure what they want here.

4. Jul 1, 2008

### alphysicist

No, there's not a specified number; that's not what they want here.

But try answering my second question; the problem is understanding the behavior of the exponential function, which is important for understanding RC circuits. Make a plot of $\exp(-t/1.2)$. What happens to the value of that as t gets larger and larger?

Once you know what happens to the exponential function, you'll know what happens to the current, since it's just a constant multiplied by the exponential function.

5. Jul 1, 2008

### Gear300

If this is a series circuit, remember that capacitors are technically breaks in the circuit. After a long time, the circuit is in steady state, and the current across branches involving capacitors can set to 0A. When referring to a long time, take the limit as t approaches infinite.

6. Jul 2, 2008

### purduegirl

So from what I just read in my textbook, long after the switch is closed, the potential difference across the capacitor is nearly equal to the emf and the current is small. Looking at a graph of current as a function of time, I can see that the longer the circuit is flowing, the smaller the current gets.

7. Jul 2, 2008

### purduegirl

Unforunatly, the only exponential examples my book gives are for finding the voltage across the capacitor (0.632*Voltage of Battery) and for finding the current when the time equals the time constant (0.368*(Voltage of Battery/Resisitivity). I tried the last equation to no avail.

8. Jul 2, 2008

### alphysicist

That's right; and as t gets larger and larger (goes to infinity), what would you say the current is? That is the answer they are looking for here.

9. Jul 2, 2008

### Dick

What could they mean by 'after a very long time'? There's no number to put in corresponding to a 'very long time' is there? I think you've just stated the answer, metaphorically.

10. Jul 2, 2008

### purduegirl

Thanks to all! My prof gave us homework on RC circuits, but never lectured over it. Thanks so much for the help!