Question

A certain piece of copper is to be shaped into a wire of minimum resistance. Its
length and diameter should be

Answer 1

The piece of a copper should be shaped with minimum wire for the resistance  'R'

Length of a wire is greater than its resistance 'L'

The cross-sectional area with less than resistance is 'A'

Therefore

resistivity of a material r with greater resistivity for its resistance

resistance = resistivity × length / area

'R=L/A'

From the question, the length and diameter should be ( L/ 2, 2D ) where resistance is minimum.

Answer 2

complete question is

choose one of the option in given below

(a) should be, respectively, L and A

(b) should be, respectively, 2L and A/2

(c) should be, respectively, L/2 and 2A

(d) do not matter, since the volume of copper

remains the same.

R = ρ L /A

case a R = ρ L /A

case b = R = ρ 2L /(A/2) = 4  ρ L /A

case c = R = (ρ L/2) /2A = (1/4) ρ L /A

option C has minimum resistance

L = L/2

A = 2A

2A = πR²

=> R = √(2A/π)

=> Diameter = 2R = 2√(2A/π)