Physics-
General
Easy

Question

Two identical square rods of metal are welded end to end as shown in figure (i), 20 calories of heat flows through it in 4 minutes. If the rods are welded as shown in figure (ii), the same amount of heat will flow through the rods in

  1. 1 minute    
  2. 2 minutes    
  3. 4 minutes    
  4. 16 minutes    

The correct answer is: 1 minute


    fraction numerator Q over denominator t end fraction equals fraction numerator K A capital delta theta over denominator l end fraction equals fraction numerator capital delta theta over denominator left parenthesis l divided by K A right parenthesis end fraction equals fraction numerator capital delta theta over denominator R end fraction (R = Thermal resistance)
    Þ t proportional to R (becauseQ and capital delta theta are same)
    Þ fraction numerator t subscript P end subscript over denominator t subscript S end subscript end fraction equals fraction numerator R subscript P end subscript over denominator R subscript S end subscript end fraction equals fraction numerator R divided by 2 over denominator 2 R end fraction equals fraction numerator 1 over denominator 4 end fractionÞt subscript P end subscript equals fraction numerator t subscript S end subscript over denominator 4 end fraction equals fraction numerator 4 over denominator 4 end fraction equals 1 m i n.
    (Series resistance R subscript S end subscript equals R subscript 1 end subscript plus R subscript 2 end subscript and parallel resistance 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)

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