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https://texercises.com/exercise/partially-filled-capacitor/
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Exercise:
A dielectric plate with dielectric constant kappa is inserted between the plates of a parallel plate capacitor. The thickness of the plate is two thirds of the distance between the plates. abcliste abc Derive a formal expression for the change in capacitance. abc Calculate the percentage change for a dielectric constant of kO. abcliste

Solution:
abcliste abc The partially filled capacitor can be erpreted as two capacitors in series: The first capacitor has two thirds of the total distance between the plates and is completely filled with the dielectric material the second capacitor has one third of the thickness and is empty. The two partial capacitances are C_ kappavarepsilon_fracA/ d frackappa C_ C_ varepsilon_fracA/ d C_ where C_ varepsilon_fracAd is the capacitance of the empty capacitor. The capacitance of the partially filled capacitor is C leftfracC_+fracC_right^- leftfrackappa+fracright^- C_ leftfrac+kappakapparight^- C_ resultCF C_ abc fracCC_ CF frackX+kX resultCP This corresponds to a decrease of CdiffabsP. abcliste
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Exercise:
A dielectric plate with dielectric constant kappa is inserted between the plates of a parallel plate capacitor. The thickness of the plate is two thirds of the distance between the plates. abcliste abc Derive a formal expression for the change in capacitance. abc Calculate the percentage change for a dielectric constant of kO. abcliste

Solution:
abcliste abc The partially filled capacitor can be erpreted as two capacitors in series: The first capacitor has two thirds of the total distance between the plates and is completely filled with the dielectric material the second capacitor has one third of the thickness and is empty. The two partial capacitances are C_ kappavarepsilon_fracA/ d frackappa C_ C_ varepsilon_fracA/ d C_ where C_ varepsilon_fracAd is the capacitance of the empty capacitor. The capacitance of the partially filled capacitor is C leftfracC_+fracC_right^- leftfrackappa+fracright^- C_ leftfrac+kappakapparight^- C_ resultCF C_ abc fracCC_ CF frackX+kX resultCP This corresponds to a decrease of CdiffabsP. abcliste
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Branches
Electrostatics
Tags
capacitance, capacitor, dielectric, electrostatics, series
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Difficulty
(2, default)
Points
0 (default)
Language
ENG (English)
Type
Calculative / Quantity
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