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A parallel plate capacitor of area A, plate separation d and capacitance C is filled with three different dielectric materials having dielectric constants $K_{1}, K_{2}$ and $K_{3}$ as shown. If a single dieletric material is to be used to have the same capacitance C is this capacitors, then its dielectric constant K is given by

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$\frac{1}{K} = \frac{1}{K_{1} + K_{2}} + \frac{1}{2 K_{3}}$

$\frac{1}{K} = \frac{1}{K_{1}} + \frac{1}{K_{2}} + \frac{1}{2 K_{3}}$

$K = \frac{K_{1} K_{2}}{K_{1} + K_{2}} + 2 K_{3}$

$K = K_{1} + K_{2} + 2 K_{3}$

answer is B.

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