Capacitance and Resistance of a fluid

  1. 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. Redbelly98

    Redbelly98 12,053
    Staff Emeritus
    Science Advisor
    Homework Helper

    You're almost there. What does the "p" in pF mean? Hint: it's not 10-6.
     
  4. 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. Putting in my new value for C, I get the resistance to be:

    0.885 Ohms

    Does this look right now?

    TFM
     
  6. Redbelly98

    Redbelly98 12,053
    Staff Emeritus
    Science Advisor
    Homework Helper

    Yes, that looks good.
     
  7. Excellent

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

    TFM
     
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