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Capacitance and Resistance of a fluid

  1. Dec 11, 2008 #1

    TFM

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    1. The problem statement, all variables and given/known data

    A parallel plate air-spaced capacitor has a capacitance of 100pF. It is immersed in a fluid of resistivity 10 m. Calculate the resistance between the plates.

    2. Relevant equations

    [tex] C = \frac{\epsilon_0A}{d} [/tex]

    [tex] R = \frac{\rho l}{A} [/tex]

    3. The attempt at a solution

    I seemed to get this question too easily...

    First of all, I said that for the fluid, the area is the area of the pates, and l is the distance d between them, then I rearranged the resistivity equation into terms of a/d:

    [tex] \frac{A}{d} = \frac{\rho}{R} [/tex]

    then I substituted this equation into the capacitance equation:

    [tex] C = \epsilon_0\frac{\rho}{R} [/tex]

    rearrange for R:

    [tex] R = \epsilon_0 \frac{\rho}{C} [/tex]

    Insert values:

    [tex] R = \epsilon_0 \frac{10}{100*10^{-6}} [/tex]

    this gives a value of [tex] 8.85 * 10^{-7} [/tex] Ohms

    Does this look correct?

    TFM
     
  2. jcsd
  3. Dec 11, 2008 #2

    Redbelly98

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    You're almost there. What does the "p" in pF mean? Hint: it's not 10-6.
     
  4. Dec 12, 2008 #3

    TFM

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    pF is a pico Farad, I believe

    Iyt is 10^-12, not -6, that was illy of me - I should have remebered that 10^-6 is micro:redface:

    TFM
     
  5. Dec 12, 2008 #4

    TFM

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    Putting in my new value for C, I get the resistance to be:

    0.885 Ohms

    Does this look right now?

    TFM
     
  6. Dec 12, 2008 #5

    Redbelly98

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    Yes, that looks good.
     
  7. Dec 13, 2008 #6

    TFM

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    Excellent

    Thanks for your Assistance, Redbelly98, Most Appreciated :smile:

    TFM
     
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