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NEET Sample Paper NEET Sample Test Paper-80

  • question_answer
    A parallel plate capacitor of area A, plate separation d and capacitance C is filled with two B different dielectric materials having dielectric constant \[{{k}_{1}},\,\,{{k}_{2}}\] as shown in figure. If a single dielectric material is used to have the same capacitance C in this capacitor, then its equivalent dielectric constant k is given by  

    A)  \[\left( {{k}_{1}}+\,{{k}_{2}} \right)/2\]                       

    B)  \[2{{k}_{1}}{{k}_{2}}/\left( {{k}_{1}}+\,{{k}_{2}} \right)\]

    C)  \[{{k}_{1}}{{k}_{2}}/\left( {{k}_{1}}+\,{{k}_{2}} \right)\]      

    D)  None of these

    Correct Answer: B

    Solution :

    Capacitance of a capacitor is given by \[C=\frac{{{\varepsilon }_{0}}kA}{d}\] According to question, \[{{C}_{1}}\,\,=\,\,\frac{{{k}_{1}}{{\varepsilon }_{0}}A}{d/2}\] \[=\frac{2{{k}_{1}}{{\varepsilon }_{0}}A}{d}\] Similarly,     \[{{C}_{2}}\,\,=\,\,\frac{2{{k}_{2}}{{\varepsilon }_{0}}A}{d}\] Now, these capacitor are in series \[C=\frac{{{C}_{1}}{{C}_{2}}}{({{C}_{1}}+{{C}_{2}})}\] Also,           \[C=\frac{{{C}_{1}}{{C}_{2}}}{({{C}_{1}}+{{C}_{2}})}\] \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{{k}_{eq}}=\frac{2{{k}_{1}}{{k}_{2}}}{{{k}_{1}}+{{k}_{2}}}\]


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