What is the mass of a copper wire 1 km long with a resistance of 10 ohms?

L = 1 km = 1000 m.

R = 10 ohms.

ρ = 8.9 * 10 ^ 3 kg / m3.

ρ “copper = 1.7 * 10 ^ –8 Ohm * m.

m -?

We express the mass of the copper wire m by the formula: m = V * ρ, where V is the volume of the copper wire, ρ is the density of copper.

The volume of the copper wire V is expressed by the formula: V = S * L, where S is the cross-sectional area, L is the length of the copper wire.

m = S * L * ρ.

The resistance R of a uniform copper conductor is determined by the formula: R = ρ “copper * L / S, where ρ” copper is the resistivity of the material from which the conductor is made, L is the length of the conductor, S is the cross-sectional area of ​​the conductor.

S = ρ “copper * L / R.

m = ρ “copper * L * L * ρ / R = ρ” copper * L2 * ρ / R.

m = 1.7 * 10 ^ –8 Ohm * m * (1000 m) 2 * 8.9 * 10 ^ 3 kg / m3 / 10 Ohm = 15.13 kg.

Answer: a copper wire has a mass of m = 15.13 kg.