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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![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?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F23fa2d5b-f89e-49eb-bc59-8ce7530b4e92%2F7ef8dea6-bb19-4e18-aa82-86d0c7f54eea%2Fsv4tus6_processed.jpeg&w=3840&q=75)
Transcribed Image Text: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?
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