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Question

If two metallic plates of equal thicknesses and thermal conductivities K subscript 1 end subscriptand K subscript 2 end subscript are put together face to face and a common plate is constructed, then the equivalent thermal conductivity of this plate will be

  1. fraction numerator K subscript 1 end subscript K subscript 2 end subscript over denominator K subscript 1 end subscript plus K subscript 2 end subscript end fraction    
  2. fraction numerator 2 K subscript 1 end subscript K subscript 2 end subscript over denominator K subscript 1 end subscript plus K subscript 2 end subscript end fraction    
  3. fraction numerator left parenthesis K subscript 1 end subscript superscript 2 end superscript plus K subscript 2 end subscript superscript 2 end superscript right parenthesis to the power of 3 divided by 2 end exponent over denominator K subscript 1 end subscript K subscript 2 end subscript end fraction    
  4. fraction numerator left parenthesis K subscript 1 end subscript superscript 2 end superscript plus K subscript 2 end subscript superscript 2 end superscript right parenthesis to the power of 3 divided by 2 end exponent over denominator 2 K subscript 1 end subscript K subscript 2 end subscript end fraction    

The correct answer is: fraction numerator 2 K subscript 1 end subscript K subscript 2 end subscript over denominator K subscript 1 end subscript plus K subscript 2 end subscript end fraction


    In series R subscript e q end subscript equals R subscript 1 end subscript plus R subscript 2 end subscript Þ fraction numerator 2 l over denominator K subscript e q end subscript A end fraction equals fraction numerator l over denominator K subscript 1 end subscript A end fraction plus fraction numerator l over denominator K subscript 2 end subscript A end fraction
    Þ fraction numerator 2 over denominator K subscript e q end subscript end fraction equals fraction numerator 1 over denominator K subscript 1 end subscript end fraction plus fraction numerator 1 over denominator K subscript 2 end subscript end fraction Þ K subscript e q end subscript equals fraction numerator 2 K subscript 1 end subscript K subscript 2 end subscript over denominator K subscript 1 end subscript plus K subscript 2 end subscript end fraction

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