Determine the cross-sectional area and length of the copper conductor if its resistance R

Determine the cross-sectional area and length of the copper conductor if its resistance R is 1 Ohm and the mass is 20 g.

Given: R = 1 Ohm; m = 20 g (0.02 kg).

Constants: ρm (copper density) = 8900 kg / m3; ρ (specific resistance) = 0.017 Ohm * mm2 / m (0.017 * 10-6 Ohm * m2 / m).

1) Conductor volume: V = m / ρm = 0.02 / 8900 = 2.25 * 10-6 m3.

2) Conductor length: R = ρ * l / S = ρ * l / (V / l) = ρ * l ^ 2 / V and l = √ (R * V / ρ) = √ (1 * 2.25 * 10 ^ -6 / 0.017 * 10 ^ -6) = 11.5 m.

3) Cross-sectional area: R = ρ * l / S = ρ * (V / S) / S = ρ * V / S2 and S = √ (ρ * V / R) = √ (0.017 * 10 ^ -6 * 2.25 * 10 ^ -6 / 1) = 1.96 * 10 ^ -7 m2 = 0.196 mm2.