A current of 5A is passed through an aluminum conductor 50 cm long. The voltage at the ends

A current of 5A is passed through an aluminum conductor 50 cm long. The voltage at the ends of the conductor is 1.2V. Determine the diameter of the conductor.

Initial data: l (length of the aluminum conductor) = 50 cm (0.5 m); I (current passed through the aluminum conductor) = 5 A; U (voltage at the ends of the conductor) = 1.2 V.

Reference data: ρ (electrical resistivity of aluminum) = 0.028 Ohm * mm2 / m.

The diameter of the aluminum conductor is expressed from the equality: R = U / I = ρ * l / S = 4 * ρ * l / (Π * d ^ 2), whence d ^ 2 = 4 * ρ * l * I / (U * Π ) and d = √ (4 * ρ * l * I / (U * Π)).

Calculation: d = √ (4 * 0.028 * 0.5 * 5 / (1.2 * 3.14)) ≈ 0.27 mm.