A wire is made of a material with a resistivity?

Question

A wire is made of a material with a resistivity
of 5.1043x10^-8 ­ ohms x m. It has length 6.09562m
and diameter 0.24907 mm.
What is the resistance of the wire? Answer
in units of ­ohms

Answer 1

For a wire of constant cross section radius (A), length (l), and resistivity (ρ), the total resistance (R) of the wire can be found as,
R = (ρ * l) / A

Unit-wise, we get,
Ohm meters * meters / meters^2 = Ohms * m^2 / m^2 = Ohms, which is the unit of electrical resistance.
Conceptually it also makes sense since the resistance of a wire is directly proportional to its length (the longer it is, the higher the resistance) and also the resistance is inversely proportional to its cross sectional area (the thinner it is, the higher the resistance).

We are told that,
ρ = 5.1043x10^-8 ¬ ohms x m
Diameter of the wire = 0.24907 mm
A = pi * (diameter / 2)^2 = 3.1415 * (2.24807 E-4 m / 2)^2 = 4.872677 E-8 m^2
l = 6.09562 m

R = (5.1043x10^-8 Ohm-meters) * (6.09562 meters) / (4.872677 E-8 m^2)
R = 6.3853 Ohms

So the resistance of the wire is about 6.4 Ohms.