MCQ
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 dielectric material is to be used to have the same capacitance $C$ in this capacitor, then its dielectric constant k is given by
  • A
    $\frac{1}{ k }=\frac{1}{ k _1}+\frac{1}{ k _2}+\frac{1}{2 k _8}$
  • $\frac{1}{ k }=\frac{1}{ k _1+ k _2}+\frac{1}{2 k _1}$
  • C
    $k =\frac{ k _1 k _2}{ k _1+ k _2}+2 k _3$
  • D
    $k = k _1+ k _2+2 k _3$

Answer

Correct option: B.
$\frac{1}{ k }=\frac{1}{ k _1+ k _2}+\frac{1}{2 k _1}$
$\frac{1}{ k }=\frac{1}{ k _1+ k _2}+\frac{1}{2 k _1}$

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