KCET2017PhysicsElectrostatics
A piece of copper is to be shaped into a conducting wire of maximum resistance. The suitable length and diameter are and respectively.
Options
- A( L ) and ( d )
- B( 2 ~L ) and ( d )
- C( L / 2 ) and ( 2 ~d )
- D( 2 ~L ) and ( d / 2 )
Correct answer
D. ( 2 ~L ) and ( d / 2 )
Step-by-step solution
Resistance, ( R= L A ) where ( ) is resistivity; ( L ) is length; ( A ) is area Now, ( A= r²= ( d 2 )² ) Therefore, ( R= L (d / 2)² ) ( R L ) and ( R 1 d² ) Thus, the length and diameter of copper wire should be ( 2 ~L ) and ( d / 2 ), respectively.