Physics-
General
Easy

Question

Two conducting rods A and B of same length and cross-sectional area are connected (i) In series (ii) In parallel as shown. In both combination a temperature difference of 100 ℃ is maintained. If thermal conductivity of A is 3 K and that of B is K then the ratio of heat current flowing in parallel combination to that flowing in series combination is

  1. fraction numerator 16 over denominator 3 end fraction    
  2. fraction numerator 3 over denominator 16 end fraction    
  3. fraction numerator 1 over denominator 1 end fraction    
  4. fraction numerator 1 over denominator 3 end fraction    

The correct answer is: fraction numerator 16 over denominator 3 end fraction


    Heat current H equals fraction numerator increment theta over denominator R end fraction rightwards double arrow fraction numerator H subscript P end subscript over denominator H subscript S end subscript end fraction equals fraction numerator R subscript S end subscript over denominator R subscript P end subscript end fraction
    In first case : R subscript S end subscript equals R subscript 1 end subscript plus R subscript 2 end subscript equals fraction numerator l over denominator open parentheses 3 K close parentheses A end fraction plus fraction numerator l over denominator K A end fraction equals fraction numerator 4 over denominator 3 end fraction fraction numerator l over denominator K A end fraction
    In second case : R subscript P end subscript equals fraction numerator R subscript 1 end subscript R subscript 2 end subscript over denominator R subscript 1 end subscript plus R subscript 2 end subscript end fraction equals fraction numerator fraction numerator 1 over denominator left parenthesis 3 K right parenthesis A end fraction cross times fraction numerator l over denominator K A end fraction over denominator open parentheses fraction numerator l over denominator open parentheses 3 K close parentheses A end fraction plus fraction numerator l over denominator K A end fraction close parentheses end fraction equals fraction numerator l over denominator 4 K A end fraction
    therefore fraction numerator H subscript P end subscript over denominator H subscript S end subscript end fraction equals fraction numerator fraction numerator 4 l over denominator 3 K A end fraction over denominator fraction numerator l over denominator 4 K A end fraction end fraction equals fraction numerator 16 over denominator 3 end fraction

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