Problem 3 [10 points] Liquid levels are often measured by detecting the change in capacitance as a liquid with dielectric constant k fills the space between the plates of a capacitor. Consider such a device comprised of a long parallel plate capacitor with rectangular plates of width 1 cm, length 1 meter, and spacing between the plates of 1 mm. The dielectric constant of the liquid is K=1.5. Find a formula relating the capacitance measured on an external capacitance meter to the level of the liquid, h, above the bottom edge of the capacitor. Express your result in the form C = C₁ + C₁*h and find Co and C₁. What is the capacitance when the liquid level is empty and when it is full? Assume we can calibrate the zero level of the capacitor perfectly (i.e. determine Co by measuring the capacitance with an empty vessel. Then, what is the precision of a capacitance measurement required for a 1% measurement of the liquid level?

Problem 3 [10 points] Liquid levels are often measured by detecting the change in capacitance as a liquid with dielectric constant k fills the space between the plates of a capacitor. Consider such a device comprised of a long parallel plate capacitor with rectangular plates of width 1 cm, length 1 meter, and spacing between the plates of 1 mm. The dielectric constant of the liquid is K=1.5. Find a formula relating the capacitance measured on an external capacitance meter to the level of the liquid, h, above the bottom edge of the capacitor. Express your result in the form C = C₁ + C₁*h and find Co and C₁. What is the capacitance when the liquid level is empty and when it is full? Assume we can calibrate the zero level of the capacitor perfectly (i.e. determine Co by measuring the capacitance with an empty vessel. Then, what is the precision of a capacitance measurement required for a 1% measurement of the liquid level?

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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