Difference Between Capacitor Equations: q=Q(1-e^-t/RC) & q=Qe^-t/RC

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Homework Help Overview

The discussion revolves around understanding the differences between two capacitor equations: q=Q(1-e^-t/RC) and q=Qe^-t/RC. Participants are exploring the context of capacitor charging and discharging behaviors in electrical circuits.

Discussion Character

  • Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • Participants are attempting to clarify the significance of the "1-" in the first equation and how it relates to the charging process of a capacitor. There is also an exploration of the conditions under which each equation applies, particularly regarding whether the capacitor is charging or discharging.

Discussion Status

Some participants have provided insights into the scenarios represented by each equation, indicating that one describes the charging of an uncharged capacitor while the other describes the discharging of a charged capacitor. However, there is still some uncertainty regarding the implications of the equations and their derivations.

Contextual Notes

Participants are working within the constraints of understanding capacitor behavior in circuit analysis, specifically focusing on the initial and final states of charge over time.

arthur01
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hey guys, have a quick question

just wanted to know what is the difference between these two equations, i couldn't find anything on google

q=Q(1-e^-t/RC)

and

q=Qe^-t/RC


why does one have 1 subtracting the rest of the equation, and the other doesn't

thanks!
 
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I understand that in the first equation the capacitor is uncharged before the switch is closed, and when the switch is closed at t=0, charge (q) will increase.

I just don't understand what the "1-" has to do with the problem
 
wait i think i got it, in the second equation, the capacitor is charged, and it is discharging.

in the first equation, it is uncharged. is this correct?
 
The second equation is for a series connection of a voltage source, resistor, and a capacitor. Applying KVL around the loop and integrating, that is the result. The case is indeed for a capacitor discharging; hence the exponential decay.
 
Try calculating Q for t=0 and t=∞...

1) q=Q(1-e^-t/RC)

t=0, q=0
t=∞, q=Q
= charging

2) q=Qe^-t/RC

t=0, q=Q
t=∞, q=0
= discharging
 

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