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JIPMER Jipmer Medical Solved Paper-2001

  • question_answer
    A parallel plane condenser is filled with two dielectrics as shown in figure. Area of each plate is A in m2 and the separation is d metre. The dielectric constants are \[{{K}_{1}}\] and \[{{K}_{2}}\] respectively. Its capacitance in farad will be:

    A) \[\frac{2{{\varepsilon }_{0}}A}{d}\left( \frac{{{K}_{1}}+{{K}_{2}}}{{{K}_{1}}{{K}_{2}}} \right)\]     

    B) \[\frac{{{\varepsilon }_{0}}A}{d}\left( \frac{{{K}_{1}}+{{K}_{2}}}{{{K}_{1}}{{K}_{2}}} \right)\]

    C)        \[\frac{{{\varepsilon }_{0}}A}{d}\left( \frac{{{K}_{1}}+{{K}_{2}}}{2{{K}_{1}}{{K}_{2}}} \right)\]

    D)        \[\frac{{{\varepsilon }_{0}}A{{K}_{1}}+{{K}_{2}}}{2({{d}_{2}}{{K}_{1}}+{{d}_{1}}{{K}_{2}})}\]        

    Correct Answer: B

    Solution :

    From the formula \[C=\frac{{{\varepsilon }_{0}}A}{\frac{1}{{{K}_{1}}}+\frac{1}{{{K}_{2}}}}=\frac{{{\varepsilon }_{0}}A}{t}\left( \frac{{{K}_{1}}{{K}_{2}}}{{{K}_{1}}+{{K}_{2}}} \right)\] \[=\frac{2{{\varepsilon }_{0}}A}{d}\left( \frac{{{K}_{1}}{{K}_{2}}}{{{K}_{1}}+{{K}_{2}}} \right)\]


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