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Thread: changing in time problem

  1. #1
    Super Member
    Oct 2007

    changing in time problem

    Ok two resistors R1 and R2 are connected parallel.

    Total resistance is given by R^-1 = R1^-1 + R2^-1
    R1 is 80 ohms & increases at 0.3 ohms per sec
    R2 is 100 ohms & increases at 0.2 ohms per sec
    so the question is now, "how fast is R changing at that time?"
    not sure how to go about this question. any help much appreciated
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  2. #2
    MHF Contributor
    skeeter's Avatar
    Jun 2008
    North Texas
    looks familiar ...

    R^{-1} = R_1^{-1} + R_2^{-1}

    take the time derivative ...

    -R^{-2} \cdot \frac{dR}{dt} = -R_1^{-2} \cdot \frac{dR_1}{dt} - R_2^{-2} \cdot \frac{dR_2}{dt}

    get rid of the negative exponents and isolate \frac{dR}{dt} ...

    \frac{dR}{dt} = \frac{R^2}{R_1^2} \cdot \frac{dR_1}{dt} + \frac{R^2}{R_2^2} \cdot \frac{dR_2}{dt}

    you have all the info for R1 and R2 ... calculate R from the original equation and determine dR/dt.
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