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 ${ \varepsilon _1}$ at one plate to ${ \varepsilon _2}$ at the other. The capacitance of capacitor is
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 ${ \varepsilon _1}$ at one plate to ${ \varepsilon _2}$ at the other. The capacitance of capacitor is
- [JEE MAIN 2014]
- A
${ \varepsilon _0}\left( {{ \varepsilon _1} + { \varepsilon _2}} \right)A/d$
- B
${ \varepsilon _0}\left( {{ \varepsilon _2} + { \varepsilon _1}} \right)A/2d$
- C
${ \varepsilon _0}\,A/\left[ {d\,\ln \left( {{ \varepsilon _2}/{ \varepsilon _1}} \right)} \right]$
- D
${ \varepsilon _0}\left( {{ \varepsilon _2} - { \varepsilon _1}} \right)A/\left[ {d\,\ln \left( {{ \varepsilon _2}/{ \varepsilon _1}} \right)} \right]$
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