How Long Does It Take for Charge to Reach 1/e of Maximum in an RC Circuit?

[auslmar]

Homework Statement

A 1.47 micro F capacitor is charged through a 123 Ohm resistor and then discharged through the same resistor by short-circuiting the battery.

While the capacitor is being charged, find the time for the charge on its plates to reach 1/e of its maximum value.

Homework Equations

q = Q_final[1-e^(-t/RC)], (q)/(Q_final) = [1-e^(-t/RC)]

The Attempt at a Solution

Firstly, forgive my ignorance.

Well, I know that when charging an RC-circuit, the current decreases exponentially with time and the charge on the capacitor increases with time as the capacitor charges. Using the above equation, I assume we should be able to calculate a time constant, when t = RC, so that the charge would be 1-1/e of its final value. Though this will probably be straightforward to everyone else here, it's still not clear for me how to approach this. If I straightforwardly find the product of the capacitance and resistance, I'm only finding the aforementioned 1-1/e of the maximum value, correct? I'm beginning to become very muddled about this problem, and I can't tell if I'm fudging the the math (perhaps I just need an Algebra problem-solving review), or if my conception of the problem is way off. If anyone can provide a suggestions or hints as of how to approach this problem, I would greatly appreciate it. I apologize if this has been a waste of your time.

Thanks,

Austin

 

[chaoseverlasting]

First off, they're asking you to find 1/e of qmax. If you look at the equation you've typed out, the max value is when t is infinity (or a very large amount of time compared to the rest of the quantities). This gives you qmax.

Then replace q by qmax*1/e in the same equation and calculate the time required from that.

 

[auslmar]

First off, they're asking you to find 1/e of qmax. If you look at the equation you've typed out, the max value is when t is infinity (or a very large amount of time compared to the rest of the quantities). This gives you qmax.

Then replace q by qmax*1/e in the same equation and calculate the time required from that.

Okay. Would this mean that q_max and Q_final are equal? I'm inclined to say no because I keep reaching the same (wrong) calculation. I can't figure out any way to find them without eliminating them from both sides of the equation. I keep getting that t=RC, which I know is wrong. What am I not understanding?

 

[auslmar]

Thanks for your help, I finally figured it out. I think I was just miscalculating and making some stupid mistakes.