A parallel plate capacitor of area $\mathrm{A}$, plate separation $d$ and capacitance $C$ is filled with three dielectric materials having dielectric constants $k_1,k_2 \mathrm{a}\mathrm{n}\mathrm{d} k_3$ as shown. If a single dielectric material is to be used to have the same capacitance $C$ in the capacitor, then its dielectric constant $k$ is given by

• A

  $k=k_1+k_2+2k_3$
• B

  $k=\frac{k_1{k}_2}{k_1+k_2}+2k_3$
• C

  $\frac{1}{k}=\frac{1}{k_1}+\frac{1}{k_2}+\frac{1}{2k_3}$
• Correct answer
  D

  $\frac{1}{k}=\frac{1}{k_1+k_2}+\frac{1}{2k_3}$

Hence, the correct answer is option: 'D'.