TIme needed for a capacitor to reach a fraction of its final charge

[guyvsdcsniper]

Homework Statement

how much time elapses for the capicitor to reach 2/3 of its final charge?

Relevant Equations

e^-t/Tau

I am a little lost on the last step of this problem. I get that we want to know how much time elapses for the capacitor to reach 2/3 of its final charge. That is why 2/3Qf is equal to Qf(1-e^-t/RC).

I don't understand how we make the jump to e^-t/Tau is equal to 1/3? and then somehow e^-t/Tau is positive.

Could someone explain these steps to me?

 

[bob012345]

Homework Statement:: how much time elapses for the capicitor to reach 2/3 of its final charge?
Relevant Equations:: e^-t/Tau

View attachment 291407

I am a little lost on the last step of this problem. I get that we want to know how much time elapses for the capacitor to reach 2/3 of its final charge. That is why 2/3Qf is equal to Qf(1-e^-t/RC).

I don't understand how we make the jump to e^-t/Tau is equal to 1/3? and then somehow e^-t/Tau is positive.

Could someone explain these steps to me?

That step is just a little basic algebra. They left out a couple steps. Start with $\frac{2}{3} Q_f =Q_f(1-e^{-t/\tau})$ and solve for t.

 

[phystro]

Answering your first question, remove Qf from both sides, and then just rearrange terms. ( I assume that you are familiar with that).
As regards your second question: e^-t/Tau= 1/(e^t/Tau) so it will be always positive.
https://www.wolframalpha.com/input/?i=plot+e^-x