The resistance of the copper wire is 1 (Ohm), and its mass is 1 kg. Determine the length and cross-sectional area.

Given: R = 1 Ohm; m = 1 kg; r = 0.018 * 10 ^ -6 Ohm * m ^ 2 / m; ρ = 8920 kg / m ^ 3;
Decision:
According to the formula R = r * l / S; also m = V * ρ = ρ * l * S. Let us express the length of the copper wire from both formulas: l = R * S / r; l = m / (ρ * S); now we equate the right-hand sides of both expressions: R * S / r = m / (ρ * S); now we express the area from the obtained equality:
R * S / r = m / (ρ * S)
R * ρ * S = m * r
S ^ 2 = m * r / (R * ρ)
S = √ (m * r / (R * ρ))
Now we substitute the numerical values and calculate the area: S = √ (1 kg * 0.018 * 10 ^ -6 Ohm * m ^ 2 / m / (1 Ohm * 8920 kg / m ^ 3)) = 0.2 * 10 ^ -6 m ^ 2.
Now let’s calculate the length of the wire by the formula: l = R * S / r; l = 0.2 * 10 ^ -6 m ^ 2 * 1 Ohm / 0.018 * 10 ^ -6 Ohm * m ^ 2 / m = 11.111 m
Answer: l = 11.111 m; S = 0.2 * 10 ^ -6 m ^ 2.