Can the fit equation accurately predict the discharging of a capacitor?

  • Thread starter Thread starter mlostrac
  • Start date Start date
  • Tags Tags
    Capacitor
Click For Summary
SUMMARY

The discussion centers on the relationship between the fit equation A*exp(−Cx)+B and the discharging capacitor equation V = Vo e^-t/RC. The constants A, B, and C are defined as A=Vo, B=0, and C=1/RC, where V is viewed as a function of time. The fit equation serves as an approximation for the theoretical discharging behavior of a capacitor, with the need to adjust A, B, and C to achieve the best fit for experimental data. The discussion highlights the challenges in achieving a perfect fit due to practical limitations in data collection.

PREREQUISITES
  • Understanding of capacitor discharge principles
  • Familiarity with exponential functions and their applications
  • Knowledge of curve fitting techniques
  • Basic proficiency in data analysis and plotting
NEXT STEPS
  • Study the mathematical derivation of the capacitor discharge equation V = Vo e^-t/RC
  • Explore curve fitting methods using tools like Python's SciPy library
  • Investigate the concept of time constant (tau) in RC circuits
  • Learn about experimental error analysis in capacitor discharge experiments
USEFUL FOR

Students in physics or electrical engineering, researchers conducting experiments on capacitors, and anyone interested in the mathematical modeling of electrical circuits.

mlostrac
Messages
83
Reaction score
0
Hello, I'm just doing a lab on the discharging of a capacitor.

The data collected shows that at first the current is large because the voltage is large, so charge is lost quickly and the voltage decreases rapidly. As charge is lost the voltage is reduced making the current smaller so the rate of discharging becomes progressively slower.

I'm just wondering how the fit equation A*exp(−Cx)+B relates to the equation for a discharging capacitor V = Vo e^-t/RC ?
 
Physics news on Phys.org
Substitute in the values for A, C, and B; while the variable x in your case is t, since you're viewing V as a function of time. so A=Vo, B = 0, and C = 1/RC.
 
y = A*exp(−Cx)+B is an approximation to V = Vo e^-t/RC, in the xy plane, in cartesian coordinates.
When you plot your results (V against t) you need to fiddle with the A,B and C constants till you get the best fit.
Theoretically there would be a perfect combination of these three numbers, that fits your data perfectly, but this is rarely seen in practise - say why.

A would be Vo. B moves the fit up/down the y-axis (its probably 0).
Then C is then 1/RC, sometimes called the time constant, tau.
 

Similar threads

Replies
20
Views
2K
  • · Replies 4 ·
Replies
4
Views
4K
  • · Replies 9 ·
Replies
9
Views
3K
  • · Replies 1 ·
Replies
1
Views
3K
  • · Replies 5 ·
Replies
5
Views
2K
Replies
6
Views
1K
  • · Replies 2 ·
Replies
2
Views
1K
  • · Replies 3 ·
Replies
3
Views
4K
  • · Replies 3 ·
Replies
3
Views
3K
  • · Replies 7 ·
Replies
7
Views
2K