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NEET NEET SOLVED PAPER 2016 Phase-II

  • question_answer
    A parallel-plate capacitor of area A, plate separation d and capacitance C is filled with four dielectric materials having dielectric constants \[{{K}_{1}},{{K}_{2}},{{K}_{3}}\,and\,{{K}_{4}}\] as shown in the figure below. 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)  \[K={{K}_{1}}+{{K}_{2}}+{{K}_{3}}+3{{K}_{4}}\]

    B)  \[K=\frac{2}{3}({{K}_{1}}+{{K}_{2}}+{{K}_{3}})+2{{K}_{4}}\]

    C)  \[\frac{2}{K}=\frac{3}{{{K}_{1}}+{{K}_{2}}+{{K}_{3}}}+\frac{1}{{{K}_{4}}}\]

    D)  \[\frac{1}{K}=\frac{1}{{{K}_{1}}}+\frac{1}{{{K}_{2}}}+\frac{1}{{{K}_{3}}}+\frac{3}{2{{K}_{4}}}\]

    Correct Answer: C

    Solution :

    \[{{K}_{1}},{{K}_{2}}\,and\,{{K}_{3}}\]are in parallel so Arithmetic mean. \[{{K}_{eq}}=\frac{{{K}_{1}}+{{K}_{2}}+{{K}_{3}}}{3}\] \[{{K}_{eq}}\] is an series with\[K{{ & }_{4}}\]. So harmonic mean. \[\Rightarrow \frac{2}{k}=\frac{1}{{{K}_{eq}}}+\frac{1}{{{K}_{4}}}\] \[\Rightarrow \frac{2}{k}=\frac{3}{{{K}_{1}}+{{K}_{2}}+{{K}_{3}}}+\frac{1}{{{K}_{4}}}\]


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