Browse by Stream
Discuss Doubts
Home
Search for Exam, Articles, Questions
get app
Go To Your Study Dashboard
  1. Home
  2. I have a doubt, kindly clarify. - Electrostatics - JEE Main-9

Filters

Select Stream
Select Type
Select Exam
Select Subject
Select Chapter
Q&A - Ask Doubts and Get Answers
Q
Engineering

I have a doubt, kindly clarify. - Electrostatics - JEE Main-9

Two identical parallel plate capacitors, of capacitance C each, have plates of area A, separated by a distance d. The space between the plates of the two capacitors, is filled with three dieletrics, of equal thickness and dielectric constants K_{1},K_{2}andK_{3}. The first capacitors is filled as shown in fig. I, and the second one is filled as shown in fig II. 

If these two modified capacitors are charged by the same potential V, the ratio of the energy stored in the two, would be (E_{1} refers to capacitors (I) and E_{2} to capacitor (II) ): 

  • Option 1)

    \frac{E_{1}}{E_{2}}=\frac{9K_{1}K_{2}K_{3}}{(K_{1}+K_{2}+K_{3})(K_{2}K_{3}+K_{3}K_{1}+K_{1}K_{2})}

  • Option 2)

    \frac{E_{1}}{E_{2}}=\frac{(K_{1}+K_{2}+K_{3})(K_{2}K_{3}+K_{3}K_{1}+K_{1}K_{2})}{9K_{1}K_{2}K_{3}}

  • Option 3)

    \frac{E_{1}}{E_{2}}=\frac{K_{1}K_{2}K_{3}}{(K_{1}+K_{2}+K_{3})(K_{2}K_{3}+K_{3}K_{1}+K_{1}K_{2})}

  • Option 4)

    \frac{E_{1}}{E_{2}}=\frac{(K_{1}+K_{2}+K_{3})(K_{2}K_{3}+K_{3}K_{1}+K_{1}K_{2})}{K_{1}K_{2}K_{3}}

 
Answers (1)
Views
S solutionqc

Arrangement I \rightarrow capacities in series

\frac{1}{C_1}=\frac{d/3}{K_{1}\varepsilon _{0}A}+\frac{d/3}{K_{2}\varepsilon _{0}A}+\frac{d/3}{K_{3}\varepsilon _{0}A}

\Rightarrow C_{1}=\frac{3K_{1}K_{2}K_{3}\varepsilon _{0}A}{d(K_{1}K_{2}+K_{2}K_{3}+K_{3}K_{1})}

Arrangement II \rightarrow capacitors in parallel

C_{2}=\frac{K_{1}\varepsilon _{0}(A/3)}{d}+\frac{K_{2}\varepsilon _{0}(A/3)}{d}+\frac{K_{3}\varepsilon _{0}(A/3)}{d}

       =\frac{(K_{1}+K_{2}+K_{3})\varepsilon _{0}A}{3d}

\frac{E_{1}}{E_{2}}=\frac{ \frac{1}{2}c_{1}V^{2} }{ \frac{1}{2}c_{2}V^{2}}=\frac{c_{1}}{c_{2}}=\frac{9K_{1}K_{2}K_{3}}{(K_{1}K_{2}+K_{2}K_{3}+K_{3}K_{1})(K_{1}+K_{2}+K_{3})}


Option 1)

\frac{E_{1}}{E_{2}}=\frac{9K_{1}K_{2}K_{3}}{(K_{1}+K_{2}+K_{3})(K_{2}K_{3}+K_{3}K_{1}+K_{1}K_{2})}

Option 2)

\frac{E_{1}}{E_{2}}=\frac{(K_{1}+K_{2}+K_{3})(K_{2}K_{3}+K_{3}K_{1}+K_{1}K_{2})}{9K_{1}K_{2}K_{3}}

Option 3)

\frac{E_{1}}{E_{2}}=\frac{K_{1}K_{2}K_{3}}{(K_{1}+K_{2}+K_{3})(K_{2}K_{3}+K_{3}K_{1}+K_{1}K_{2})}

Option 4)

\frac{E_{1}}{E_{2}}=\frac{(K_{1}+K_{2}+K_{3})(K_{2}K_{3}+K_{3}K_{1}+K_{1}K_{2})}{K_{1}K_{2}K_{3}}

Similar Questions

Related Chapters

Exams
Articles
Questions