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Byju's Answer

Standard XII

Physics

Capacitance of Parallel Plate Capacitor

The gap betwe...

Question

The gap between the plates of a parallel plate capacitor of area $A$ and distance between plates $d$ , is filled with a dielectric whose permittivity varies linearly from $ϵ_{1}$ at one plate to $ϵ_{2}$ at the other. The capacitance of capacitor is :

ϵ_{0} (ϵ_{1} + ϵ_{2}) A / d

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ϵ_{0} (ϵ_{2} + ϵ_{1}) A / 2 d

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ϵ_{A} / d [d l n (ϵ_{2} / ϵ_{1})]

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ϵ_{0} (ϵ_{2} - ϵ_{1}) A / [d l n (ϵ_{2} / ϵ_{1})]

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Solution

The correct option is D $ϵ_{0} (ϵ_{2} - ϵ_{1}) A / [d l n (ϵ_{2} / ϵ_{1})]$
Answer is D.
All the capacitances are connected in series.
We know that, Capacitance is given by
$C = \frac{K ϵ A}{d}$
Equivalent capacitance is
$\frac{1}{C} = \int_{ϵ_{2} / ϵ_{o}}^{ϵ_{1} / ϵ_{0}} \frac{K ϵ A}{d} d x$
$C = \frac{ϵ_{o} (ϵ_{2} - ϵ_{1}) A}{d ln (\frac{ϵ_{2}}{ϵ_{1}})}$

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The gap between the plates of a parallel plate capacitor of area A and distance between plates d, is filled with a dielectric whose permittivity varies linearly from ϵ1 at one plate to ϵ2 at the other. The capacitance of capacitor is :

The correct option is D ϵ0(ϵ2−ϵ1)A/[dln(ϵ2/ϵ1)]Answer is D.All the capacitances are connected in series.We know that, Capacitance is given byC=KϵAdEquivalent capacitance is1C=∫ϵ1/ϵ0ϵ2/ϵoKϵAddxC=ϵo(ϵ2−ϵ1)Adln(ϵ2ϵ1)

The gap between the plates of a parallel plate capacitor of area $A$ and distance between plates $d$ , is filled with a dielectric whose permittivity varies linearly from $ϵ_{1}$ at one plate to $ϵ_{2}$ at the other. The capacitance of capacitor is :