A physics problem in a book?

Question

suppose that you wish to fabricate a uniform wire out of 1.00g of copper. if the wire is to have a resistance of R = 0.500(omega), and if all of the copper is to be used, what will be (a) the length and (b) the diameter of this wire?

the answers are (a) 1.82m (b)280um

how do i get there?

Answer 1

Solve the system of equations

R = (4 r L) / (π d²)

m = (D L π d²) / 4

where

R = 0.5 Ω (resistance of the wire)

r = 16.78 nΩm (specific resistivity of copper)

m = 1 g (mass of the copper)

D = 8960 kg/m³ (density of copper)

L – length of the wire

d – diameter of the wire

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