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CET Karnataka Medical CET - Karnataka Medical Solved Paper-2001

  • question_answer
    Three rods of same dimensions are arranged as shown in figure they have thermal conductivities \[{{K}_{1}},\text{ }{{K}_{2}}\]and \[{{K}_{3}}.\]The points P and Q are maintained a at different temperatures for the heat to flow at the same rate along PRQ and PQ:

    A)  \[{{K}_{3}}=\frac{1}{2}\left( {{K}_{1}}+{{K}_{2}} \right)\]

    B)  \[{{K}_{3}}={{K}_{1}}+{{K}_{2}}\]

    C)  \[{{K}_{3}}=\frac{{{K}_{1}}{{K}_{2}}}{{{K}_{1}}+{{K}_{2}}}\]

    D)  \[{{K}_{3}}=2\left( {{K}_{1}}+{{K}_{2}} \right)\]

    Correct Answer: C

    Solution :

     The relation for the heat flow is given by      \[\frac{Q}{t}=\frac{KA({{Q}_{2}}-{{Q}_{1}})}{l}\] Now equivalent conductivity of PRQ is given by \[l=\frac{l+l}{\frac{l}{{{K}_{1}}}+\frac{l}{{{K}_{2}}}}=\frac{2{{K}_{1}}{{K}_{2}}}{{{K}_{1}}+{{K}_{2}}}\] \[{{K}_{3}}=\frac{{{K}_{1}}{{K}_{2}}}{{{K}_{1}}+{{K}_{2}}}\]


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