A parallel-plate capacitor of area A, plate separation d and capacitance C is filled with four dielectric materials having dielectric constants ${\mathrm{k}}_1 ,{\mathrm{k}}_2 ,{\mathrm{k}}_3 \mathrm{and} {\mathrm{k}}_4$ as shown in the figure. lf 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

  $\frac{2}{\mathrm{k}}=\frac{3}{{\mathrm{k}}_1+{\mathrm{k}}_2+{\mathrm{k}}_3}+\frac{1}{{\mathrm{k}}_4}$

• B

  $\frac{1}{\mathrm{k}}=\frac{1}{{\mathrm{k}}_1}+\frac{1}{{\mathrm{k}}_2}+\frac{1}{{\mathrm{k}}_3}+\frac{3}{2{\mathrm{k}}_4}$

• C

  $\mathrm{k}={\mathrm{k}}_1+{\mathrm{k}}_2+{\mathrm{k}}_3+3{\mathrm{k}}_4$

• D

  $\mathrm{k}=\frac{2}{3}\left({\mathrm{k}}_1+{\mathrm{k}}_2+{\mathrm{k}}_3\right)=2{\mathrm{k}}_4$