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NEET Sample Paper NEET Sample Test Paper-74

  • question_answer
    If a parallel plate capacitor has capacity C, on inserting a dielectric slab of relative permittivity K and thickness equal to one-fourth of the plate separation is placed between the plates, then its capacity becomes C'. The value of C'/C will be

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

    B)  \[\frac{2\,K}{K+1}\]

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

    D) \[\frac{4\,K}{3\,K+1}\]

    Correct Answer: D

    Solution :

    \[C\,=\,\frac{{{\varepsilon }_{0}}A}{d}\,\,and\,\,C'=\frac{{{\varepsilon }_{0}}A}{d-\frac{d}{4}\left( 1-\frac{1}{K} \right)}=\frac{4\,{{\varepsilon }_{0}}A}{3d+\frac{d}{K}}\] \[\Rightarrow \,\,\,C'=\frac{4K}{(3K+1)}\left( \frac{{{\varepsilon }_{0}}A}{d} \right)=\frac{4\,KC}{(3K+1)}\] \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\frac{C'}{C}=\frac{4K}{(3K+1)}\]


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