Analyzing Voltage Change of Capacitor Over Time

[MattRSK]

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.

 

[overt26]

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.

 

[Doc Al]

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