RAJASTHAN PMT Rajasthan - PMT Solved Paper-1998

  • question_answer
    As shown in the figure half the space between plates of a capacitor is filled with an insulator material of dielectric constant\[K,\]if initial capacity was \[C\] then the new capacity is:

    A) \[\frac{C}{2}(K+1)\]                                       

    B) \[\frac{C}{2(K+1)}\]

    C) \[\frac{(K+1)}{2C}\]       

    D)        \[C\,(K+1)\]

    Correct Answer: A

    Solution :

    We can assume that both capacitors are joined in parallel. In parallel \[C={{C}_{1}}+{{C}_{2}}\]                                 \[=\frac{{{\varepsilon }_{0}}A}{2d}+\frac{{{\varepsilon }_{0}}AK}{2d}\]                                 \[C=\frac{{{\varepsilon }_{0}}A}{2d}(1+K)\]                                 \[C=\frac{1}{2}\left[ \frac{{{\varepsilon }_{0}}A}{d}(K+1) \right]\]                                 \[=\frac{C}{2}(K+1)\]


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