The resistance of the copper wire is 1 Ohm, its weight is 1 kg. What is the length of the wire and its cross-sectional area.

R = 1 ohm.

m = 1 kg.

ρ = 8900 kg / m3.

ρ “= 1.7 * 10-8 Ohm * m.

L -?

S -?

The density of copper ρ is expressed by the formula: ρ = m / V, where m is the mass of the wire, V is the volume of the wire.

V = m / ρ.

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

L * S = m / ρ.

L = m / ρ * S.

The wire resistance R is expressed by the formula: R = ρ “* L / S, where ρ” is the resistivity of copper.

L = R * S / ρ “.

m / ρ * S = R * S / ρ “.

S = √ (m * ρ “/ ρ * R).

S = √ (1 kg * 1.7 * 10-8 Ohm * m / 8900 kg / m3 * 1 Ohm) = 1.4 * 10-6 m2.

L = 1 Ohm * 1.4 * 10-6 m2 / 1.7 * 10-8 Ohm * m = 82 m.

Answer: S = 1.4 * 10-6 m2, L = 82 m.