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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 dielectric material is to be used to have the same capacitance $C$ in this capacitor, then its dielectric constant $k$ is given by
  • A$\frac{1}{k} = \frac{1}{{{k_1}}} + \frac{1}{{{k_2}}} + \frac{1}{{2{k_3}}}$
  • B$\frac{1}{k} = \frac{1}{{{k_1} + {k_2}}} + \frac{1}{{2{k_3}}}$
  • C$k = \frac{{{k_1}{k_2}}}{{{k_1} + {k_2}}} + 2{k_3}$
  • D$k = {k_1} + {k_2} + 2{k_3}$
IIT 2000, Diffcult
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