Question
Wed March 04, 2015 By: Gunjan Bujade

Derive an expression for the capacity of a parallel plate capacitor with
  • conductor between the plates
  • dielectriic slab of thickness t

Expert Reply
Priyanka Kumbhar
Thu March 05, 2015
Expression for the capacity of a parallel pate with conductor between the paltes.
 
 
begin mathsize 12px style The space capacitance space of space straight a space parallel space plate space capacitor space is space given space as comma straight C space equals space fraction numerator element of subscript 0 space straight A over denominator straight d end fraction where comma space element of subscript 0 space space equals space permitivity space in space free space space space space space space space space space space space space space space space space space space space straight A space equals space area space plate space space space space space space space space space space space space space space space space space straight d space equals space plate space separation space distance Let comma space plus-or-minus straight Q space charge space placed space on space the space capacitor space plates space as space shown space in space figure The space free space current space in space the space conductor space flow space when space the space conducting space slab space and space thickness space straight t space less than space straight D space in space introduced space between space the space plate. The space charges space plus-or-minus straight Q space arises space on space two space facesof space slab space in space such space way space that space the space electric space field space inside space the space slab space reduced space to space zero. Hence comma space intial space electric space field space straight E subscript 0 space will space exists space over space straight a space distacne space left parenthesis straight d minus straight t right parenthesis. space The space potential space difference comma space straight V space equals space straight E subscript 0 left parenthesis straight d minus straight t right parenthesis space equals space straight sigma over element of subscript 0 space left parenthesis straight d minus straight t right parenthesis space space where space straight sigma space equals space charge space density straight V space equals space fraction numerator straight Q over denominator element of subscript 0 space straight A end fraction space left parenthesis straight d minus straight t right parenthesis because space straight C space equals space straight Q over straight A therefore space straight C space equals space fraction numerator element of subscript 0 space AQ over denominator straight Q left parenthesis straight d minus straight t right parenthesis end fraction space equals space fraction numerator element of subscript 0 space straight A over denominator left parenthesis straight d minus straight t right parenthesis end fraction space equals space fraction numerator element of subscript 0 space straight A over denominator straight d open parentheses 1 minus begin display style straight t over straight d end style close parentheses end fraction space equals space fraction numerator element of subscript 0 space straight A divided by straight d over denominator open parentheses 1 minus straight t over straight d close parentheses end fraction space therefore space straight C space equals space fraction numerator straight C subscript 0 over denominator open parentheses 1 minus straight t over straight d close parentheses end fraction space space open parentheses straight C subscript 0 space equals element of subscript 0 space straight A divided by straight d space close parentheses Here comma space straight C space greater than space straight C subscript 0. space straight i. straight e. space Capacitance space increase space when space conductor space slab space is space introduced space between space parallel space plates space of space capacitor.  space space space space space space space space space space end style
Kindly ask other derivation as a separate query.
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