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JEE Main & Advanced Physics Electrostatics & Capacitance Question Bank Self Evaluation Test - Electrostatic Potential and Capacitance

  • question_answer
                An uncharged parallel plate capacitor having a dielectric of dielectric constant K is connected to a similar air cored parallel plate capacitor charged to a potential \[{{V}_{0}}.\] The two share the charge, and the common potential becomes V. The dielectric constant K is

    A) \[\frac{{{V}_{0}}}{V}-1\]

    B) \[\frac{{{V}_{0}}}{V}+1\]

    C) \[\frac{V}{{{V}_{0}}}-1\]

    D) \[\frac{V}{{{V}_{0}}}+1\]

    Correct Answer: A

    Solution :

    [a] \[{{C}_{1}}=C,{{V}_{1}}={{V}_{0}},{{C}_{2}}=KC,{{V}_{2}}=0\] And \[{{V}_{common}}=V\] We know that \[{{V}_{common}}=\frac{{{C}_{1}}{{V}_{1}}+{{C}_{2}}{{V}_{2}}}{{{C}_{1}}+{{C}_{2}}}\] \[\therefore \,\,\,{{V}_{common}}=\frac{C{{V}_{0}}+KC\times O}{C+KC}\] or \[K=\frac{{{V}_{0}}}{V}-1\]


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