What is the required cross-sectional area for the resistance of an aluminum wire to be the same as that

What is the required cross-sectional area for the resistance of an aluminum wire to be the same as that of a copper wire of the same length with a cross-sectional area of 6.8mm ^ 2?

1. Let’s write the expression for the resistivity
ρsp = R * Ssec / l, ude R is the resistance of the wire, l is the length of the wire, Ssec is the cross-sectional area.
2. Let us express the resistance from this expression:
R = ρsp * l / Ssec.
By condition, we have R and l – equal, then:
Ra = ρsp * l / Ssection.
Rm = ρsm * l / Ssec.
ρsp * l / Ssection = ρsp * l / Ssection.
3. Let us express from this the cross-sectional area of the aluminum wire:
Ssection = ρsp * l * Ssechm / ρsdm * l = ρspa * Ssecm / ρsdm.
4. Substitute the numerical values:
Ssection = ρsp * Ssection / ρsdm = 0.028 * 6.8 / 0.0175 = 10.88 mm².
Answer: 10.88 mm².