A copper wire with a cross section of 1mm2 must be replaced with a steel wire of the same length, without changing

A copper wire with a cross section of 1mm2 must be replaced with a steel wire of the same length, without changing the resistance of the conductor. What section do you need to take the steel wire.

Given:

r1 = 0.017 Ohm * mm2 / m – copper resistivity;

r2 = 0.1 Ohm * mm2 / m – steel resistivity;

R1 = R2 = R – the resistance of the conductors is the same;

l1 = l2 = l – the length of the conductors is the same;

s1 = 1 mm2 (millimeter squared) – cross-section of the copper conductor.

It is required to determine s2 (mm2) – the cross-section of the steel conductor.

We have two equalities:

s1 = r1 * l1 / R1 = r1 * l / R;

s2 = r2 * l2 / R2 = r2 * l / R.

Dividing the first equality by the second, we get:

s1 / s2 = (r1 * l / R) / (r2 * l / R) = r1 / r2, from here we find that:

s2 = s1 * r2 / r1 = 1 * 0.1 / 0.017 = 0.1 / 0.017 = 5.9 mm2 (the result has been rounded to one decimal place).

Answer: to replace a copper wire with a steel wire of the same length and resistance, its cross section must be 5.9 mm2.