When a conductor with a diameter of 0.5 mm and a length of 4.5 m was included in the electrical circuit

When a conductor with a diameter of 0.5 mm and a length of 4.5 m was included in the electrical circuit, the potential difference at its ends turned out to be 1.2 V at a current of 1A. What is the resistivity of the conductor material?

d = 0.5 mm.

L = 4.5 m.

U = 1.2 V.

I = 1 A.

ρ -?

According to Ohm’s law, the resistance of the conductor R is equal to the ratio of the potential difference at the ends of the conductor U to the current in the conductor I: R = U / I.

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.

The cross-sectional area of ​​the conductor S is expressed by the formula: S = P * d ^ 2/4.

R = 4 * ρ * L / P * d ^ 2.

U / I = 4 * ρ * L / P * d ^ 2.

ρ = U * P * d ^ 2 / I * 4 * L.

ρ = 1.2 V * 3.14 * (0.5 mm) ^ 2/1 A * 4 * 4.5 m = 0.052 Ohm * mm2 / m.

Answer: the specific resistance of the substance of which the conductor is composed is ρ = 0.052 Ohm * mm2 / m.