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JEE Main & Advanced Physics Transmission of Heat Question Bank Conduction

  • question_answer
    If two metallic plates of equal thicknesses and thermal conductivities \[{{K}_{1}}\]and \[{{K}_{2}}\] are put together face to face and a common plate is constructed, then the equivalent thermal conductivity of this plate will be    [MP PMT 1991]

    A)            \[\frac{{{K}_{1}}{{K}_{2}}}{{{K}_{1}}+{{K}_{2}}}\]     

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

    C)            \[\frac{{{(K_{1}^{2}+K_{2}^{2})}^{3/2}}}{{{K}_{1}}{{K}_{2}}}\]         

    D)            \[\frac{{{(K_{1}^{2}+K_{2}^{2})}^{3/2}}}{2{{K}_{1}}{{K}_{2}}}\]

    Correct Answer: B

    Solution :

                       In series \[{{R}_{eq}}={{R}_{1}}+{{R}_{2}}\] Þ \[\frac{2l}{{{K}_{eq}}A}=\frac{l}{{{K}_{1}}A}+\frac{l}{{{K}_{2}}A}\]            Þ \[\frac{2}{{{K}_{eq}}}=\frac{1}{{{K}_{1}}}+\frac{1}{{{K}_{2}}}\] Þ \[{{K}_{eq}}=\frac{2{{K}_{1}}{{K}_{2}}}{{{K}_{1}}+{{K}_{2}}}\]


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