Question

Suppose you wish to fabricate a uniform wire out of 1.05 g of copper. If the wire is to have a resistance R = 0.370 Ω, and if all the copper is to be used, find the following. (a) What will be the length of the wire? m (b) What will be the diameter of the wire? mm

Answer 1

here,

mass , m = 1.05 g = 0.00105 kg

let the length of wire be l and diameter be d

density of wire , d = 8960 kg/m^3

resistivity of wire , p = 1.68 * 10^-9 ohm.m

volume , V = mass /density = pi * (d/2)^2 * l

0.00105 /8960 = pi * (d/2)^2 * l .....(1)

resistance , R = p * l/area

0.37 = 1.68 * 10^-8 * l /(pi * (d/2)^2) .....(2)

from (1) and (2)

d = 3.05 * 10^-4 m

l = 1.61 m

a)

the length of wire is 1.61 m

b)

the diameter of wire is 3.05 * 10^-4 m