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

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SUMMARY

The discussion clarifies the difference between two capacitor equations: q=Q(1-e^-t/RC) and q=Qe^-t/RC. The first equation describes the charging process of a capacitor, where q represents the charge at time t, Q is the maximum charge, and RC is the time constant. In contrast, the second equation represents the discharging process of a capacitor, indicating that the charge decreases exponentially over time. The key distinction lies in the initial and final conditions of the capacitor, with the first equation applicable when the capacitor is initially uncharged and the second when it is fully charged.

PREREQUISITES
  • Understanding of capacitor charging and discharging principles
  • Familiarity with the time constant (RC) in electrical circuits
  • Knowledge of Kirchhoff's Voltage Law (KVL)
  • Basic calculus for integrating exponential functions
NEXT STEPS
  • Study the derivation of capacitor charging equations in RC circuits
  • Learn about the implications of time constants in circuit design
  • Explore the applications of exponential decay in electronics
  • Investigate the behavior of capacitors in series and parallel configurations
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Electrical engineers, physics students, and anyone interested in understanding capacitor behavior in circuits will benefit from this discussion.

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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