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A parallel plate capacitor with plate area ' \(A\) ' and distance of separation ' \(d\) ' is filled with a dielectric. W…

Q1
PYQ

A parallel plate capacitor with plate area ' \(A\) ' and distance of separation ' \(d\) ' is filled with a dielectric. What is the capacity of the capacitor when permittivity of the dielectric varies as:
\[\begin{aligned}& \varepsilon(x)=\varepsilon_0+k x, \text { for }\left(0

a

0

b

\(\frac{k A}{2} \ell n\left(\frac{2 \varepsilon_0}{2 \varepsilon_0-k d}\right)\)

c

\(\frac{k A}{2 \ell n\left(\frac{2 \varepsilon_0+k d}{2 \varepsilon_0}\right)}\)

d

\(\left(\varepsilon_0+\frac{k d}{2}\right)^{2 / k A}\)

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