How will the resistance of the rheostat change if a nickel wire is taken instead of a constantan wire?

Let’s write an expression to determine the resistivity of the wire:
ρsp = R * Ssech / l, where R is the resistance of the wire, l is the length of the wire, Ssech is the cross-sectional area.
Let us express R from here:
R = ρsp * l / Ssection
For a constantan wire rheostat, the resistance is:
R1 = ρcon * l / Ssection
For a rheostat with a nickel wire resistance:
R2 = ρnik * l / Ssection
The length of the wire and the cross-section are considered the same, we divide R2 / R1:
R1 / R2 = (ρsp * l / Ssech1) / (ρsp * l / Ssech2) = ρfin / ρnik
According to the reference book, we determine:
ρnik = 6.8 * 10-8 Ohm * m
ρcon = 50 * 10-8 Ohm * m
Let’s calculate:
R1 / R2 = 50 * 10-8 / 6.8 * 10-8 = 7.35
Answer: the resistance of the rheostat will decrease by 7.35 times, because the resistance of nickel is less.