The gap between the plates of parallel plate capacitor of area $A$ and distance between plates $d$ is filled with dielectric whose permitivity varies linearly from $ϵ_{1}$ at one plate to $ϵ_{2}$ at the other. The capacitance of capacitor is:
$ϵ_{A} / d [d ln (ϵ_{2} / ϵ_{1})]$
$ϵ_{0} (ϵ_{1} + ϵ_{2}) A / d$
$(ϵ_{1} + ϵ_{2}) A / 2 d$
$ϵ_{0} (ϵ_{1} - ϵ_{2}) A / [d ln (ϵ_{2} / ϵ_{1})]$

Question

The gap between the plates of parallel plate capacitor of area $A$ and distance between plates $d$ is filled with dielectric whose permitivity varies linearly from $ϵ_{1}$ at one plate to $ϵ_{2}$ at the other. The capacitance of capacitor is:
$ϵ_{A} / d [d ln (ϵ_{2} / ϵ_{1})]$
$ϵ_{0} (ϵ_{1} + ϵ_{2}) A / d$
$(ϵ_{1} + ϵ_{2}) A / 2 d$
$ϵ_{0} (ϵ_{1} - ϵ_{2}) A / [d ln (ϵ_{2} / ϵ_{1})]$

Toppr Admin · Accepted Answer

If the permitivity varies linearly means that the change is uniform-xA0-In that case the average permitivity -x3F5-1-x3F5-22will be considered-C-A-x3F5-d-x3F5-1-x3F5-2-A2d

If the permitivity varies linearly means that the change is uniform. In that case the average permitivity ϵ1+ϵ22will be considered.C=Aϵd=(ϵ1+ϵ2)A2d

If the permitivity varies linearly means that the change is uniform.
In that case the average permitivity $\frac{ϵ_{_{1}} + ϵ_{_{2}}}{2}$ will be considered.
$C = \frac{A ϵ}{d} = \frac{(ϵ_{_{1}} + ϵ_{_{2}}) A}{2 d}$