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
    $\frac{1}{k}=\frac{1}{k_1}+\frac{1}{k_2}+\frac{1}{2k_3}$
     
  • $\frac{1}{k}=\frac{1}{k_1+k_2}+\frac{1}{2k_3}$
     
  • C
    $k=\frac{k_1k_2}{k_1+k_2}+2k_3$
     
  • D
    $k=k_1+k_2+2k_3$
     

Answer

Correct option: B.
$\frac{1}{k}=\frac{1}{k_1+k_2}+\frac{1}{2k_3}$
 
(b) $\frac{1}{k}=\frac{1}{k_1+k_2}+\frac{1}{2k_3}$

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