Find the resistance R of a copper wire of mass m = 4kg and diameter d = 1.4mm.
Find the resistance R of a copper wire of mass m = 4kg and diameter d = 1.4mm. Copper density D = 8.9 * 10 ^ 3 kg / m ^ 3, copper resistivity = 17nOhm * m.
m = 4 kg.
d = 1.4 mm = 1.4 * 10 ^ -3 m.
ρ = 8.9 * 10 ^ 3 kg / m3.
ρ “= 17 nOhm * m = 17 * 10 ^ -9 Ohm * m.
We will assume that the copper conductor has a cylindrical shape, therefore, its resistance R is expressed by the formula: R = ρ “* l / S, where ρ” is the resistivity of copper, l is the length of the conductor, S is the cross-sectional area.
We express the mass of the conductor m by the formula: m = V * ρ, where V is the volume of the conductor, ρ is the density of copper.
V = S * l.
m = S * l * ρ.
l = m / S * ρ.
R = ρ “* m / S ^ 2 * ρ.
Since in cross section the conductor has the shape of a circle, then S = P * d ^ 2/4.
R = 16 * ρ “* m / П ^ 2 * d ^ 4 * ρ.
R = 16 * 17 * 10 ^ -9 Ohm * m * 4 kg / (3.14) ^ 2 * (1.4 * 10 ^ -3 m) ^ 4 * 8.9 * 10 ^ 3 kg / m3 = 3.3 ohm.
Answer: copper wire has a resistance of R = 3.3 ohms.