R = (ρ ℓ) / A
- ℓ length wire in m
- A cross sectional area in m2
- ρ resistivity of the material in Ωm
Example
50.0 cm of a constantan wire has a electric resistance of 1.125 Ω
Find the diameter of the wire
ρ of constantan : 0.45 x 10-6 Ωm
R = (ρ ℓ)/A
R A = ρ ℓ
A = (ρ ℓ)/R = ((0.45 x 10-6)( 0.50)) /1.125 = 2.0 x 10-7 m2 = 2.0 x 10-1 mm2
A = π r2
2.0 x 10-1 = πr2
r2 = (2.0 x10-1)/π = 0.06366
r = 0.25 mm
d = 2r = 2 x 0.25 = 0.50 mm