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Two parallel plate capacitors X and Y have a same area of plates and same separations between them. X has air between the plates while Y contains a dielectric medium of K=4.
1.Calculate capacitance of each capacitor if equivalent capacitance of the combination is 4 micro farad 
2. Calculate  the potential difference between plate X and Y. 
3.Estimate the ratio of electrostatic energy stored in x and Y. 

Asked by Priyanka 15th November 2017, 3:43 PM
Answered by Expert
Answer:
Two parallel plate capacitors X and Y have a same area of plates and same separations between them. X has air between the plates while Y contains a dielectric medium of K=4.
1.Calculate capacitance of each capacitor if equivalent capacitance of the combination is 4 micro farad 
2. Calculate  the potential difference between plate X and Y. 
3.Estimate the ratio of electrostatic energy stored in x and Y. 
 
begin mathsize 16px style factorial right parenthesis space C equals fraction numerator element of subscript 0 K A over denominator d end fraction space semicolon C x equals fraction numerator begin display style element of subscript 0 K A end style over denominator begin display style d end style end fraction equals fraction numerator begin display style element of subscript 0 A end style over denominator begin display style d end style end fraction space space space left parenthesis K equals 1 space f o r space a i r right parenthesis semicolon space C y equals fraction numerator begin display style element of subscript 0 4 A end style over denominator begin display style d end style end fraction space space left parenthesis K equals 4 space g i v e n right parenthesis

C y equals 4 X C x

1 over C subscript e q end subscript equals fraction numerator 1 over denominator C x end fraction plus fraction numerator 1 over denominator C y end fraction

fraction numerator begin display style 1 end style over denominator begin display style 4 end style end fraction equals fraction numerator begin display style 1 end style over denominator begin display style C x end style end fraction plus fraction numerator begin display style 1 end style over denominator begin display style 4 C x end style end fraction

C x equals space 5 u F
C y equals 20 u F

2 right parenthesis space space Q equals C subscript e q end subscript x space V space equals space 4 space x space V space space space space space space space space space left parenthesis " V " space v o l t a g e space i s space r e q u i r e d space t o space f i n d space Q right parenthesis

V x equals fraction numerator Q over denominator C x end fraction space semicolon space V y equals fraction numerator begin display style Q end style over denominator begin display style C y end style end fraction

3 right parenthesis space E n e r g y space i s space g i v e n space a s space

E equals fraction numerator Q squared over denominator 2 C end fraction space semicolon E x equals fraction numerator begin display style Q squared end style over denominator begin display style 2 C x end style end fraction semicolon space E y equals fraction numerator begin display style Q squared end style over denominator begin display style 2 C y end style end fraction

fraction numerator E x over denominator E y end fraction equals fraction numerator C y over denominator C x end fraction equals 4 over 1
space








end style
Answered by Expert 6th December 2017, 5:12 PM
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