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

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Discussion Overview

The discussion revolves around determining an expression for the capacitance of two parallel plates immersed in a liquid dielectric, specifically as a function of the height of the liquid. The context includes a homework problem involving a liquid-level transducer and the application of dielectric constants in capacitance calculations.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant expresses uncertainty about how to incorporate the portion of the plates that is immersed in the liquid versus the portion that is not, and mentions having two unknowns when attempting to use the capacitance equation.
  • Another participant suggests making reasonable assumptions, such as selecting a width for the plates, to simplify the calculations and determine the spacing based on known conditions.
  • A different participant proposes treating the system as two capacitors in parallel, each with varying areas and dielectrics based on the height of the liquid.
  • One participant requests clarification on the equation for capacitance, indicating a need for further explanation of the underlying concepts.
  • Another participant provides a brief overview of the capacitance equation for parallel plate capacitors, mentioning the factors involved such as plate area and dielectric permittivity.
  • Lastly, a participant argues that plate spacing and width should not be considered in the calculations, emphasizing the importance of using the liquid height and the known capacitance in air instead.

Areas of Agreement / Disagreement

The discussion contains multiple competing views on how to approach the problem, with no consensus reached on the best method for calculating the capacitance as a function of the liquid height.

Contextual Notes

Participants have not resolved the assumptions regarding plate dimensions and how they affect the capacitance calculations. There is also uncertainty about the relevance of fringe effects and the specific parameters needed for the calculations.

mikebai1990
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Homework Statement



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.

http://img32.imageshack.us/img32/6172/img1267s.jpg


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?
 
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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.
 
Treat it as two capacitors in parallel, each with area as a function of x and different dielectrics.
 
may i know about the equation?
and can anyone explain the equation? thank you...
 
The equation for capacitance of a parallel plate capacitor. It involves plate area, plate spacing, the permittivity of the dielectric, and a few constants.
 
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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