A parallel-plate capacitor of area A,  plate separation d and capacitance C is filled wih four dielectric materials having dielectric constants k1, k2, k3 and k4 as shown in the figure below. If a single dielectric material is to be used to have the same capacitance C in this capacitor, then its dielectric constant k is given by

  • Option 1)

    k = k_1 + k_2 + k_3 + 3k_4

  • Option 2)

    k = \frac{2} {3}\left( {k_1 + k_2 + k_3 } \right) + 2k_4

  • Option 3)

    \frac{2} {k} = \frac{3} {{k_1 + k_2 + k_3 }} + \frac{1} {{k_4 }}

  • Option 4)

    \frac{1} {k} = \frac{1} {{k_1 }} + \frac{1} {{k_2 }} + \frac{1} {{k_3 }} + \frac{3} {{2k_4 }}

 

Answers (1)

As we discussed

If K filled between the plates -

{C}'=K\frac{\epsilon _{0}A}{d}={C}'=Ck

 

 

- wherein

C\propto A

C\propto\frac{1}{d}

 

 and

Parallel Grouping -

C_{eq}=C_{1}+C_{2}+cdots

- wherein

 

 C_{1}=\frac{2\varepsilon _{oK_{1A}}}{3d},C_{2}=\frac{2K_{2}\varepsilon oA}{3d}

C_{3}=\frac{2\varepsilon _{oK_{3}A}}{3d},C_{4}=\frac{_{2}\varepsilon oK_{4}A}{d}

\frac{1}{C_{AB}}=\frac{1}{C_{1}+C_{2}+C_{3}}+\frac{1}{C_{4}}=\frac{1}{K(\frac{\epsilon oA}{d})}=\frac{1}{\frac{2\epsilon oA}{3d}}(K_{1}+K_{2}+K_{3})+\frac{1}{\frac{2\epsilon oA}{d}}K_{4}

\frac{1}{K}=\frac{3}{2(K_{1+K_{2}+K_{3}})}+\frac{1}{2K_{4}}\\ \frac{2}{K}=\frac{3}{(K_{1+K_{2}+K_{3}})}+\frac{1}{2K_{4}}=\frac{2}{K}=\frac{3}{(K_{1+K_{2}+K_{3}})}+\frac{1}{K_{4}}


Option 1)

k = k_1 + k_2 + k_3 + 3k_4

This option is incorrect 

Option 2)

k = \frac{2} {3}\left( {k_1 + k_2 + k_3 } \right) + 2k_4

This option is incorrect 

Option 3)

\frac{2} {k} = \frac{3} {{k_1 + k_2 + k_3 }} + \frac{1} {{k_4 }}

This option is correct 

Option 4)

\frac{1} {k} = \frac{1} {{k_1 }} + \frac{1} {{k_2 }} + \frac{1} {{k_3 }} + \frac{3} {{2k_4 }}

This option is incorrect 

Most Viewed Questions

Preparation Products

Knockout NEET May 2024

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 40000/-
Buy Now
Knockout NEET May 2025

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 45000/-
Buy Now
Knockout NEET Aug 2021 (One Month)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 14000/- ₹ 4999/-
Buy Now
Knockout NEET Aug 2021

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 22999/- ₹ 9999/-
Buy Now
Test Series NEET Aug 2021

Unlimited Chapter Wise Tests, Unlimited Subject Wise Tests, Unlimited Full Mock Tests, Get Personalized Performance Analysis Report,.

₹ 6999/- ₹ 2999/-
Buy Now
Boost your Preparation for NEET 2021 with Personlized Coaching
 
Exams
Articles
Questions