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12th Class Physics Electrostatics & Capacitance Question Bank MCQ - Electrostatic Potential and Capacitance

  • question_answer
    The capacitance of a parallel plate capacitor with air as medium is\[3\mu F\]. With the introduction of a dielectric medium between the plates, the capacitance becomes\[15\mu F\]. The permittivity of the medium is:

    A) \[5\,{{C}^{2}}{{N}^{-1}}{{m}^{-2}}\]                    

    B) \[15\,{{c}^{2}}{{N}^{-1}}{{m}^{-2}}\]

    C) \[0.44\times {{10}^{-10}}{{C}^{2}}{{N}^{-1}}{{m}^{-2}}\]          

    D) \[8.854\times {{10}^{-11}}{{C}^{2}}{{N}^{-1}}{{m}^{-2}}\]

    Correct Answer: C

    Solution :

    (c) \[0.44\times {{10}^{-10}}{{C}^{2}}{{N}^{-1}}{{m}^{-2}}\]       Capacitance of a parallel plate capacitor with air is \[C=\frac{{{\varepsilon }_{0}}A}{d}\] Capacitance of a same parallel plate capacitor with the introduction of a dielectric medium is \[C'=\frac{K{{\varepsilon }_{0}}A}{d}\] where, K is the dielectric constant of a medium. Or \[\frac{C'}{C}=K\] or \[K=\frac{15}{3}=5\]or \[K=\frac{\varepsilon }{{{\varepsilon }_{0}}}\] Or \[\varepsilon =K{{\varepsilon }_{0}}=5\times 8.854\times {{10}^{-12}}\] \[=0.44\times {{10}^{-10}}{{C}^{2}}{{N}^{-1}}{{m}^{-2}}\]


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