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Question on linearizing equation

  1. Sep 16, 2016 #1
    1. The problem statement, all variables and given/known data
    toconvert.jpg

    I posted the entire question, but I am only conserned with part B.

    There was a circuit drawing on there but it is irrelevant for this part of the problem. One can solve it without knowing the circuit drawing.
    2. Relevant equations

    The application for Kirchoff's Voltage Law results in the equation

    Voltage(time in secs) = VoltageMax * (1 - e^(-t / RC) )

    The circuit in question is an RC circuit where I have a single capacitor and resistor in a loop.

    3. The attempt at a solution

    I have been struggling over how to figure out how to linearize the data. I have simplified the equation to the following form:

    [voltageAtTimeT / maxvoltage = (1 - e^(-t /RC) )

    And then I wanted to take the natural log to take the -t/RC out of the exponent and linearize it.

    However, I run into two problems: I do not know how to find the MaxVoltage as of now and the right hand side would become ln[ 1 - e^(-t / RC) ]. I can not simplify this right-hand side further as there is no law of logarithms that says that ln( a + b) can be simplified into a simpler form.

    Thus, I am stuck, and I would appreciated any guidance in how to solve this problem.
    Thanks in advance.
     
  2. jcsd
  3. Sep 16, 2016 #2

    kuruman

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    Gold Member

    If you wait forever, what do you think the maximum voltage across the charging capacitor will be?
    What if you did some algebra to isolate the exponential on one side of the equation and then take the natural log?

    Actually, your measurements were on the discharging capacitor, so you need to linearize that equation. The equation you quoted is for the charging capacitor.
     
  4. Sep 16, 2016 #3
    Thank you very much for the help!

    It is sad that I made such a careless error in choosing the wrong equation.
     
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