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 dielectrics, of equal thickness

Correct answer: A. E _ 1 E _ 2 = 9K _ 1 K _ 2 K _ 3 ( K _ 1 K _ 2 K _ 3 ) ( K _ 2 K _ 3 + K _ 3 K _ 1 K _ 1 + K _ 1 K _ 2 ) Energy stored in a capacitor E = (1)/(2)C V ^ 2 ⇒ E _ 1 E _ 2 = C _ 1 C _ 2 C _ 1 = ( d 3 ε _ 0 k _ 1 A + d 3 ε _ 0 A k _ 2 + d 3 ε _ 0 A k _ 3 ) ^ - 1 = ( d 3A ε _ 0 ) ^ - 1 ( 1 k _ 1 + 1 k _ 2 + 1 k _ 3 ) ^ - 1 = ( d 3A ε _ 0 ) ^ - 1 ( k _ 1 k _ 2 + k _ 2 k _ 3 + k _ 3 k _ 1 k _ 1 k _ 2 k _ 3 ) ^ - 1 C _ 1 = 3A ε _ 0 d ( k _ 1 k _ 2 k _ 3 k _ 1 k _ 2 + k _ 2 k _ 3 + k _ 3 k _ 1 ) C _ 2 = ε _ 0 ((A)/(3)) k _ 1 d + ε _ 0 ((A)/(3)) k _ 2 d + ε _ 0 ((A)/(3)) k _ 3 d ∴ C _ 1 C _ 2 = E _ 1 E _ 2 = 9 k _ 1 k _ 2 k _ 3 ( k _ 1 + k _ 2 + k _ 3 )( k _ 1 k _ 2 + k _ 2 k _ 3 + k _ 3 k _ 1 )

JEE Main 201912 AprilMorning Shift

Exam: JEE Main
Year: 2019
Date: 12 April
Shift: Morning Shift
Subject: Physics
Chapter: Capacitance

JEE Main 2019 · 12 April · Morning Shift · Physics · Capacitance

Two identical parallel plate capacitors, of capacitance C each,...

Two identical parallel plate capacitors, of capacitance

C

each, have plates of area A,

separated by a distance

. The space between the plates of the two capacitors, is filled with three dielectrics, of equal thickness and dielectric constants

{K}_{1}, {K}_{2} and {K}_{3}

. The first capaciitor is filled as shown in figure

and the second one is filled as shown in figure

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 capacitor \left(I\right) and {E}_{2}

to capacitor

( II ) ):

Two identical parallel plate capacitors, of capacitance C each, have plates of area A, separated by a distance d . The

Options

A $\dfrac{{E}_{1}}{{E}_{2}} = \dfrac{9K{}_{1}K{}_{2}K{}_{3}}{( K{}_{1}K{}_{2}K{}_{3} ) ( K{}_{2}K{}_{3} + K{}_{3}K{}_{1}K{}_{1} + K{}_{1}K{}_{2} )}$
B $\dfrac{{E}_{1}}{{E}_{2}} = \dfrac{( K{}_{1}K{}_{2}K{}_{3} ) ( K{}_{2}K{}_{3} + K{}_{3}K{}_{1}K{}_{1} + K{}_{1}K{}_{2} )}{{K}_{1}{K}_{2}{K}_{3}}$
C $\dfrac{{E}_{1}}{{E}_{2}} = \dfrac{( K{}_{1}K{}_{2}K{}_{3} ) ( K{}_{2}K{}_{3} + K{}_{3}K{}_{1}K{}_{1} + K{}_{1}K{}_{2} )}{9{K}_{1}{K}_{2}{K}_{3}}$
D $\dfrac{{E}_{1}}{{E}_{2}} = \dfrac{{K}_{1}{K}_{2}{K}_{3}}{( K{}_{1}K{}_{2}K{}_{3} ) ( K{}_{2}K{}_{3} + K{}_{3}K{}_{1}K{}_{1} + K{}_{1}K{}_{2} )}$