How Long Does It Take for a Capacitor to Reach 80% Charge in an RC Circuit?

[blackbyron]

Homework Statement

A 4.1e-6 capacitor is connected in series with a 36V battery and a 851 ohlms resistor. At t= 0 the capacitor is uncharged. At what time will the capacitor have 80% of its maximum charge?

Homework Equations

I = V/R
Q = CV
I = Q/t

The Attempt at a Solution

I didn't learn RC circuit much in class since my teacher ran out of time.
But anyway,

So the first thing I did is I found the current which is,

I = .0423 A

Now I'm stuck on this one.

I = Q/t I need to find t, I tried to use .0423 = Q* (.8) / t but the problem is Q is unknown. Any ideas?

 

[MrNerd]

You're missing an important fact. The current will constant change as the capacitor charging, approaching zero. Is the 4.1e-6 supposed to be the farad value for it? You can use that in one of the equations you have to find the maximum Q. The equation you are missing is Q = Q_{max}[1 - e^{(-t/RC)}], I believe. Try getting the [1 - e^{(-t/RC)}] to get to the amount of the maximum charge you need.

 

[blackbyron]

You're missing an important fact. The current will constant change as the capacitor charging, approaching zero. Is the 4.1e-6 supposed to be the farad value for it? You can use that in one of the equations you have to find the maximum Q. The equation you are missing is Q = Q_{max}[1 - e^{(-t/RC)}], I believe. Try getting the [1 - e^{(-t/RC)}] to get to the amount of the maximum charge you need.

Thanks for your reply
But how do I find out out the max Q if q and t is unknown?

 

[MrNerd]

I think you misunderstood what I meant by max Q. The maximum Q is the highest charge the capacitor can hold with a given voltage. t is just the time, right? So you simply need to solve for t. I don't know if you already did this, but the inverse function of e is a natural log, shown as ln. So the natural log of e^x would give you x, and e^(lnx) would give you x as well. Remember, you want 80% of the maximum charge. The left q(the one by itself and equaling the other things) is the one you want at time t.

 

[WatermelonPig]

Solve for t as a function of R and C.