The expression for the capacity of the capacitor formed by compound dielectric placed between the plates of a parallel plate capacitor as shown in figure, will be (area of plate $ = A$)
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(a) As the given combination is in series
$\frac{1}{C_{e q}}=\frac{1}{C_{1}}+\frac{1}{C_{2}}+\frac{1}{C_{3}}$
$=\frac{d_{1}}{K_{1} \epsilon_{o} A}+\frac{d_{2}}{K_{2} \epsilon_{o} A}+\frac{d_{3}}{K_{3} \epsilon_{o} A}$
$\frac{1}{C_{e q}}=\frac{1}{\epsilon_{o} A}\left[\frac{d_{1}}{K_{1}}+\frac{d_{2}}{K_{2}}+\frac{d_{3}}{K_{3}}\right]$
$C_{e q}=\frac{\epsilon_{o} A}{\frac{d_{1}}{K_{1}}+\frac{d_{2}}{K_{2}}+\frac{d_{3}}{K_{3}}}$
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