Can the Capacitor QT Equation Help Reduce Noise in Amplifiers?

[JackDixon]

Homework Statement

Good evening. I have just done a course in physics about exponential decay, and had a (very) pedantic question about the equation for the discharge of a capacitor. My logic goes like this: the exponential equation for working out how much charge remains in a capacitor is asymptotic of Q=0 by the model I have been shown no matter what value of t has elapsed since the beginning of discharge. I understand that this is a very good model for predicting out comes, but I cannot think of a mechanism by which there will always be a small charge left in the capacitor- especially when t is sufficiently large enough so that Q<1.6E-19C, which is the charge of an electron. Can anyone provide an updated mathematical model, or possibly explain why my logic is wrong?
Thanks!

Relevant Equations

Equation in solution attempt.

Q_T=Q₀e^t/τ

 

[BvU]

Hello Jack, $\quad$ $\quad$ !

First thing that comes to mind is to note a minus sign is missing .

And then I'd say nothing's wrong with the model down to nine or so orders of magnitude. By then the discharging voltage disappears in the noise due to other effects (electromagnetic noise). That's generally considered pretty good for a model...

 

[JackDixon]

Hello Jack, $\quad$ $\quad$ !

First thing that comes to mind is to note a minus sign is missing .

And then I'd say nothing's wrong with the model down to nine or so orders of magnitude. By then the discharging voltage disappears in the noise due to other effects (electromagnetic noise). That's generally considered pretty good for a model...

Ok, so it is fact a model. I didn't know EM noise was a thing. Thank you :)

 

[CWatters]

Noise can be quite a problem in many circuits, for example when you are trying to amplify very weak radio signals. Amplifiers not only magnify the wanted signal but they also magnify any noise that comes with the signal and they add some noise themselves. "Instrumentation and noise" is a common university module for undergraduate electronics engineers.