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:

• A. ${ϵ}_0({ϵ}_1+{ϵ}_2)A/d$
• B. $({ϵ}_1+{ϵ}_2)A/2d$
• C. ${ϵ}_A/d\left[d\ln \left({ϵ}_2/{ϵ}_1\right)\right]$
• D. ${ϵ}_0({ϵ}_1-{ϵ}_2)A/\left[d\ln \left({ϵ}_2/{ϵ}_1\right)\right]$

Answer 1

Answer: (B)

$({ϵ}_1+{ϵ}_2)A/2d$

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.

$C=\frac{Aϵ}{d}=\frac{({ϵ}_{{}_1}+{ϵ}_{{}_2})A}{2d}$