Physics-
General
Easy

Question

Three rods of same dimensions are arranged as shown in figure. They have thermal conductivities K subscript 1 end subscript comma K subscript 2 end subscript and K subscript 3 end subscript. The points P and Q are maintained at different temperatures for the heat to flow at the same rate along P R Q and P Q then which of the following options is correct

  1. K subscript 3 end subscript equals fraction numerator 1 over denominator 2 end fraction left parenthesis K subscript 1 end subscript plus K subscript 2 end subscript right parenthesis    
  2. K subscript 3 end subscript equals K subscript 1 end subscript plus K subscript 2 end subscript    
  3. K subscript 3 end subscript equals 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    
  4. K subscript 3 end subscript equals 2 left parenthesis K subscript 1 end subscript plus K subscript 2 end subscript right parenthesis    

The correct answer is: K subscript 3 end subscript equals 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


    The given arrangement of rods can be redrawn as follows

    It is given that H subscript 1 end subscript equals H subscript 2 end subscript
    rightwards double arrow fraction numerator K A left parenthesis theta subscript 1 end subscript minus theta subscript 2 end subscript right parenthesis over denominator 2 l end fraction equals fraction numerator K subscript 3 end subscript A left parenthesis theta subscript 1 end subscript minus theta subscript 2 end subscript right parenthesis over denominator l end fraction rightwards double arrow K subscript 3 end subscript equals fraction numerator K over denominator 2 end fraction equals 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

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