Capacitance of two plates written in terms of height of liquid dielectric

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

    A liquid-level transducer consists of two parallel plates of conductor immersed in an insulating liquid. When the tank is empty the capacitance of the plates is 200pF. The relative dielectric constant of the liquid is 25. Determine an expression for the capacitance C as a function of the height x of the liquid.


    3. The attempt at a solution

    I understand the equation and how to use the dielectric constant. However, I'm not sure how to incorporate the combination of the part immersed in the liquid, and the part which isn't. Furthermore, when I try to plug known variables into the equation for the starting condition (no liquid), I have two unknowns--the width and the distance between the plates. How do I approach this problem?
  2. jcsd
  3. vk6kro

    vk6kro 4,059
    Science Advisor

    You can make reasonable assumptions here.
    If you pick a width for the plate and make it 2 cm....
    You know the height of the plates and the capacitance in air, so you can work out the spacing.

    Also, you know the capacitance in air per cm of height of the sensor, so you can add the capacitance of the uncovered height of the sensor after you have worked out the capacitance of the covered section.
  4. Treat it as two capacitors in parallel, each with area as a function of x and different dielectrics.
  5. may i know about the equation?
    and can anyone explain the equation? thank you...
  6. NascentOxygen

    Staff: Mentor

    The equation for capacitance of a parallel plate capacitor. It involves plate area, plate spacing, the permittivity of the dielectric, and a few constants.
  7. rude man

    rude man 5,512
    Homework Helper
    Gold Member

    You don't need to worry about plate spacing or width, or the formula for an ideal capacitor's capacitance with fringe effects ignored, etc. etc. They don't matter and you should not be using eirther W or d in your computation. You need L, and C(x=0) = 200 pF, and the relative dielectric coeff. of 25, is all.
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