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A parallel plate capacitor is made of two dielectric blocks in series. One of the blocks has thickness $d_1$ and dielectric constant $k_1$ and the other has thickness $d_2$ and dielectric constant $k_2$ as shown in Fig. This arrangement can be thought as a dielectric slab of thickness $d (= d_1+d_2)$ and effective dielectric constant k. The k is

$\begin{array}{1 1} \large\frac{k_1d_1+k_2d_2}{d_1+d_2} \\\large\frac{k_1d_1+k_2d_2}{k_1+k_2} \\ \large\frac{k_1k_2(d_1+d_2)}{k_1d_1+k_2d_2} \\ \large\frac{2k_1k_2}{k_1+k_2} \end{array} $

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Solution :
$k=\large\frac{k_1k_2(d_1+d_2)}{k_1d_1+k_2d_2}$
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