Resistivity example
R = ρl/A
| symbol | quantity | unit | unit symbol |
|---|---|---|---|
| R | resistance | ohm | Ω |
| ρ | resistivity | ohm metre | Ω m |
| l | length | metre | m |
| A | cross-sectional area | square metre | m² |
ρ is the Greek letter rho.
Question
Calculate the resistance of a one metre length of 24 SWG Nichrome wire.
Answer
The key to getting the correct value is to make sure you use consistent units for the values of resistivity, area and length. In this example SI units are used throughout.
There is one other formula that is needed. To calculate the cross-sectional area of the wire we will assume that the wire is circular. So the cross-sectional area, A, is the area of a circle with a radius r.
A = π × r²
Resistivity of Nichrome = 110 × 10-8 Ω m
Length = 1.00 m
Diameter of 24 SWG wire = 0.559 mm
Radius = 0.559/2 = .2795 mm = 2.795 × 10-4 m
Cross-sectional area = π × (2.795 × 10-4)2 = 2.45 × 10-7 m²
R = [(110 × 10-8) × 1.00] / [π × (2.795 × 10-4)2]
R = 4.48 Ω
©8886 4-Jan-2004