The resistance of the copper wire is R = 1 Ohm, its mass is m = 1 kg.

The resistance of the copper wire is R = 1 Ohm, its mass is m = 1 kg. Find the length of the wire l and its cross-sectional area S. The density of copper is 8900 kg / m3

R = 1 ohm.

m = 1 kg.

ρ = 8900 kg / m3.

ρ “= 1.7 * 10-8 Ohm * m.

l -?

S -?

The resistance R of a cylindrical homogeneous conductor is determined by the formula: R = ρ “* l / S, where ρ” 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 “* l / R.

We express the density of the conductor ρ as the ratio of the mass of the conductor m to its volume V: ρ = m / V.

Since the conductor has a cylindrical shape, its volume V is expressed by the formula: V = S * l.

ρ = m / S * l.

S = m / ρ * l.

ρ “* l / R = m / ρ * l.

l = √ (R * m / ρ “* ρ).

l = √ (1 m * 1 kg / 1.7 * 10-8 Ohm * m * 8900 kg / m3) = 81.3 m.

S = 1 kg / 8900 kg / m3 * 81.3 m = 1.4 * 10-6 m2.

Answer: copper wire has a length l = 81.3 m, cross-sectional area S = 1.4 * 10-6 m2.