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VMMC VMMC Medical Solved Paper-2010

  • question_answer
    An uncharged capacitor with a solid dielectric is connected to a similar air capacitor charged to a potential of \[{{V}_{0}}\]. If the common potential after sharing of charges becomes V, then the dielectric constant of the dielectric must be

    A)  \[{{V}_{0}}/V\]

    B)  \[\frac{V}{{{V}_{0}}}\]

    C) \[\frac{({{V}_{o}}-V)}{V}\]          

    D)        \[\frac{({{V}_{o}}-V)}{{{V}_{0}}}\]

    Correct Answer: C

    Solution :

    Common potential, \[\text{V = }\frac{\text{Total}\,\text{charge}}{\text{Total}\,\text{capacitance}}\] \[V=\frac{{{C}_{1}}{{V}_{1}}+{{C}_{2}}{{V}_{2}}}{{{C}_{1}}+{{C}_{2}}}\] \[=\frac{0+C{{V}_{0}}}{KC+C}\] \[=\frac{C{{V}_{0}}}{C(1+K)}\] \[V=\frac{{{V}_{0}}}{(1+K)}\] \[K=\frac{{{V}_{0}}}{V}-1\] \[K=\frac{{{V}_{0}}-V}{V}\]


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