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The length of a given cylindrical wire is increased by 100 % . Due to the consequent decrease in diameter the change in the resistance of the wire will be

Options

  1. A200 %
  2. B100 %
  3. C50 %
  4. D300 %

Correct answer

D. 300 %

Step-by-step solution

L ₁=2 l or ( r ^2 l )= ( r ₂^2 )(2 l ) r ₂= r 2 ; R = 1 ^2 R _ new =( ) 21 ( )( r / 2 )^2 = ( ) 4 l ( ) r ^2 =4 R R =4 R - R =3 R R R %= 3 R R 100=300 %

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