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Exercise:
A simple Leyden jar consists of an acrylic glass tube with length lO and outer radius roO. The inside and outside of the tube are coated with aluminium foils. The Leyden jar has a capacitance of CO. Calculate the thickness of the tube.

Solution:
Using the capacitance of a cylindrical capacitor we have C fracpikappavarepsilon_ Llnfracr_or_i We have to solve this for the inner radius: lnfracr_or_i fracpikappavarepsilon_ LC fracr_or_i expleftfracpikappavarepsilon_ LCright r_i r_oexpleft-fracpikappavarepsilon_ LCright The thickness is therefore given by d r_o-r_i dF rotimesleft-expleft-fracpitimes ktimes ncepstimes lCrightright d approx resultdP- Since the thickness of the tube is quite small compared to the diameter of the tube we can think of the capacitor as a parallel plate capacitor with an area corresponding to the mantle surface of the tube: C kappavarepsilon_fracAd kappavarepsilon_fracpi r_o Ld This can easily be solved for the thickness: d dapprF ktimesncepstimesfracpitimes rotimes lC dappr approx resultdapprP- The result does not perfectly agree with the more complicated calculation for the cylindrical capacitor but it is a good approximation.
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Exercise:
A simple Leyden jar consists of an acrylic glass tube with length lO and outer radius roO. The inside and outside of the tube are coated with aluminium foils. The Leyden jar has a capacitance of CO. Calculate the thickness of the tube.

Solution:
Using the capacitance of a cylindrical capacitor we have C fracpikappavarepsilon_ Llnfracr_or_i We have to solve this for the inner radius: lnfracr_or_i fracpikappavarepsilon_ LC fracr_or_i expleftfracpikappavarepsilon_ LCright r_i r_oexpleft-fracpikappavarepsilon_ LCright The thickness is therefore given by d r_o-r_i dF rotimesleft-expleft-fracpitimes ktimes ncepstimes lCrightright d approx resultdP- Since the thickness of the tube is quite small compared to the diameter of the tube we can think of the capacitor as a parallel plate capacitor with an area corresponding to the mantle surface of the tube: C kappavarepsilon_fracAd kappavarepsilon_fracpi r_o Ld This can easily be solved for the thickness: d dapprF ktimesncepstimesfracpitimes rotimes lC dappr approx resultdapprP- The result does not perfectly agree with the more complicated calculation for the cylindrical capacitor but it is a good approximation.
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Attributes & Decorations
Branches
Electrostatics
Tags
capacitance, capacitor, cylindrical capacitor, parallel plate capacitor
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Difficulty
(2, default)
Points
0 (default)
Language
ENG (English)
Type
Calculative / Quantity
Creator by
Decoration