Physics-
General
Easy

Question

We have two wires A and B of same mass and same material. The diameter of the wire A is half of that B. If the resistance of wire A is 24 ohm then the resistance of wire B will be

  1. 12 Ohm    
  2. 3.0 Ohm    
  3. 1.5 Ohm    
  4. None of the above    

The correct answer is: 1.5 Ohm


    Same mass, same material i.e. volume is same or Al = constant
    Also, R equals rho fraction numerator l over denominator A end fraction Þ fraction numerator R subscript 1 end subscript over denominator R subscript 2 end subscript end fraction equals fraction numerator l subscript 1 end subscript over denominator l subscript 2 end subscript end fraction cross times fraction numerator A subscript 2 end subscript over denominator A subscript 1 end subscript end fraction equals open parentheses fraction numerator A subscript 2 end subscript over denominator A subscript 1 end subscript end fraction close parentheses to the power of 2 end exponent open parentheses fraction numerator d subscript 2 end subscript over denominator d subscript 1 end subscript end fraction close parentheses to the power of 4 end exponent
    Þ fraction numerator 24 over denominator R subscript 2 end subscript end fraction equals open parentheses fraction numerator d over denominator d rightwards arrow over short leftwards arrow divided by rightwards arrow over short leftwards arrow 2 end fraction close parentheses to the power of 4 end exponent equals 16 Þ R subscript 2 end subscript equals 1.5 capital omega.

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