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KVPY Sample Paper KVPY Stream-SX Model Paper-12

  • question_answer
    Voltage rating of a parallel plate capacitor is 500 V. Its dielectric can withstand a maximum electric field of \[{{10}^{6}}\,\text{V/m}.\]The plate area is \[{{10}^{-4}}{{m}^{2}}.\] What is the dielectric constant if the capacitance is 15 pF? \[\text{given}\,{{\in }_{0}}=8.86\times {{10}^{-12}}{{\text{C}}^{\text{2}}}\text{/N}{{\text{m}}^{\text{2}}}\]

    A) 6.2

    B) 3.8

    C) 4.5

    D) 8.5

    Correct Answer: D

    Solution :

    \[C=\frac{A{{\in }_{0}}K}{d}\And V=Ed\] \[\Rightarrow \]   \[C=\frac{A{{\in }_{0}}KE}{V}\] \[K=\frac{CV}{A{{\in }_{0}}E}=\frac{(15\times {{10}^{-12}})(500)}{{{10}^{-4}}(8.86\times {{10}^{-12}})({{10}^{16}})}\]


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