Joint Entrance Examination/2000 Screening/Q023 capcitors and dielectric, equivalent capcitance

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Original Question by Dharav ^talk

Here's the question...

A parallel plate capaciter of area A, plate separation d and capacitance C is filled with three different dielectric materials having dielectric constants k1, k2 and k3 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... $\frac{1}{k}=\frac{1}{k_1}+\frac{1}{k_2}+\frac{1}{2k_3}$ $\frac{1}{k}=\frac{1}{k_1+k_2}+\frac{1}{2k_3}$ $\frac{1}{k}=\frac{k_1{k}_2}{k_1+k_2}+\frac{1}{k_2}+2k_3$ $\frac{1}{k}=\frac{k_3{k}_1}{k_1+k_2}+\frac{k_2{k}_3}{k_2+k_3}$ Posted by Dharav talk 05:08, 18 August 2009 (UTC)

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