Question

Two copper wires with different cross-section areas and same length of 10.5 m long are connected in parallel. When a current of 1.5 A is passed through the combination, it is found that the current in one of the wires is 0.9 A. The diameter of the same wire is 1.25 mm. Determine the diameter of the other wire. Resistivity of copper is 0.017 µΩm.

Answer 1

1.02 mm

Step-by-step explanation:

You want the diameter of a wire in parallel with a 1.25 mm diameter wire carrying 0.9 A if the total current in the two same-length wires is 1.5 A.

Current

The current in the second wire is 1.5 A -0.9 A = 0.6 A.

The current is proportional to the square of the diameter, so ...

(0.6 A)/(0.9 A) = (d/(1.25 mm))²

d² = (2/3)(1.25 mm)²

d = (1.25 mm)√(2/3) ≈ 1.02 mm

The diameter of the other wire is about 1.02 mm.