Wire Resistance
Resistance from resistivity, length and area.
Formula
Variables
How it works
A wire’s resistance grows when charge carriers have to travel farther, so it is proportional to the length L. It also falls when the wire has a larger cross-sectional area A, because there are more parallel paths for current to flow; the material property \u03c1 (resistivity) sets how strongly the material opposes current in the first place. This relation comes from combining the material’s intrinsic resistivity with the geometry of a uniform wire.
When to use it
Use this formula when you know the material of a uniform wire or conductor and want to estimate its resistance from its dimensions. It is common in circuit design, power transmission, and comparing how different wire gauges or materials affect current flow.
Worked example, step by step
A nichrome wire has resistivity \u03c1 = 1.1 \u00d7 10^-6 \u03a9\u22c5m, length L = 2.5 m, and cross-sectional area A = 0.50 mm^2. Step 1: Convert the area to square metres: 0.50 mm^2 = 0.50 \u00d7 10^-6 m^2 = 5.0 \u00d7 10^-7 m^2. Step 2: Substitute into R = \u03c1L/A: R = (1.1 \u00d7 10^-6 \u03a9\u22c5m)(2.5 m) / (5.0 \u00d7 10^-7 m^2). Step 3: Calculate the numerator: 1.1 \u00d7 10^-6 \u00d7 2.5 = 2.75 \u00d7 10^-6. Step 4: Divide: R = (2.75 \u00d7 10^-6) / (5.0 \u00d7 10^-7) = 5.5 \u03a9. Final answer: The wire’s resistance is 5.5 \u03a9.
Common mistakes to avoid
- Using the wire diameter directly instead of converting it to cross-sectional area
- Forgetting to convert mm^2 or cm^2 into m^2 before calculating
- Mixing up resistivity \u03c1 with resistance R, which are different quantities
Did You Know?
Thicker or shorter wires have less resistance, which is why heavy appliances need chunky power cords.
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