The resistance of a constant-diameter length of conductive material is:
R = ρL/A
R is the resistance, ρ is the material's resistivity, L is the length, and A is the cross-sectional area.
We know that a cylindrical bar's cross sectional area A is given by:
A = πr²
where r is the radius.
The resistance is then given by:
R = ρL/(πr²)
Copper bar:
ρ = 1.72×10⁻⁸Ωm
r = 1.20×10⁻²m (half of its diameter 2.40cm)
L = 0.330m
R = (1.72×10⁻⁸)(0.330)/(π(1.20×10⁻²)²)
R = 1.25×10⁻⁵Ω
Platinum bar:
ρ = 10.60×10⁻⁸Ωm
r = 1.20×10⁻²m (half of its diameter 2.40cm)
L = 0.125m
R = (10.60×10⁻⁸)(0.125)/(π(1.20×10⁻²)²)
R = 2.93×10⁻⁵Ω
Add up the resistances to find the total resistance:
1.25×10⁻⁵Ω + 2.93×10⁻⁵Ω
= 4.18×10⁻⁵Ω
=
