Physics-
General
Easy

Question

A short-circuited coil is placed in a time-varying magnetic field. Electrical power is dissipated due to the current induced in the coil. If the number of turns were to be quadrupled and the wire radius halved, the electrical power dissipated would be

  1. Halved    
  2. The same    
  3. Doubled    
  4. Quadrupled    

The correct answer is: The same


    Sol. Power P equals fraction numerator e to the power of 2 end exponent over denominator R end fraction semicolon hence e equals negative open parentheses fraction numerator d phi over denominator d t end fraction close parentheses where phi equals N B A
    therefore e equals negative   N A open parentheses fraction numerator d B over denominator d t end fraction close parentheses Also R proportional to fraction numerator l over denominator r to the power of 2 end exponent end fraction
    Where R = resistance, r = radius, l = Length
    therefore P proportional to fraction numerator N to the power of 2 end exponent r to the power of 2 end exponent over denominator l end fraction rightwards double arrow fraction numerator P subscript 1 end subscript over denominator P subscript 2 end subscript end fraction equals 1

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