Analyzing Voltage Change of Capacitor Over Time

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SUMMARY

The discussion focuses on analyzing the voltage change of a capacitor over time, utilizing the equation DV/DT = -k fcn(v) to derive expressions for voltage as a function of time. The proposed functions for fcn(v) include constant, linear, and quadratic forms. Participants suggest using spreadsheet tools like Excel to plot voltage versus time and identify linear relationships through trend lines. The data collected shows a clear exponential decay in voltage from an initial 10V to 0.03V over 12 seconds.

PREREQUISITES
  • Understanding of capacitor behavior and transient analysis
  • Familiarity with differential equations and their applications
  • Proficiency in using spreadsheet software, particularly Excel
  • Knowledge of data visualization techniques, including trend lines
NEXT STEPS
  • Learn how to derive solutions for first-order differential equations
  • Explore capacitor discharge equations in electrical engineering
  • Investigate the use of Excel for data analysis and visualization
  • Study the principles of exponential decay in physical systems
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Students studying electrical engineering, physics enthusiasts analyzing capacitor behavior, and anyone interested in applying mathematical modeling to real-world scenarios.

MattRSK
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Homework Statement


The transient behaviour of a capacitor has been studied by measuring the voltage from across the device as a function of time. The following data has been obtained.

Time (s)/Voltage (v)
0 / 10
1 / 6.1
2 / 3.7
3 / 2.2
4 / 1.4
5 / 0.8
6 / 0.5
7 / 0.3
8 / 0.2
9 / 0.1
10 /0.07
12 /0.03

Homework Equations



The following relationship for the change in voltage, V, with time, t, has been proposed:

DV/DT = -k fcn(v)

Where k is a constant and fcn(v) could have one of the following forms:

1. fcn(v) = c (where c is a constant)
2. fcn(v) = V
3. fcn(v) = V2

(fcn is an abbreviation of the term "a function of")

I am to derive three corresponding expressions for V as a function of time.

The Attempt at a Solution



I am having trouble with where to start. I believe the aim is to find which equation, using the data, creates a linear relationship. Any help on how to derive the equations would be much appreciated.
 
Physics news on Phys.org
Have you drawn a plot of voltage vs time? Try using a spreadsheet application such as Excel - where you can use the trend line feature.
 

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