What the Resistivity of a Wire Depends On: Material and Temperature

The resistivity of a wire depends on two fundamental factors: the intrinsic atomic structure of the conductor material and its current temperature, completely independent of the wire's physical length or thickness. While hobbyists and trade students often use the terms 'resistance' and 'resistivity' interchangeably on the bench, confusing the two leads to critical errors in voltage drop calculations, heat dissipation planning, and breaker sizing. Resistivity (denoted by the Greek letter rho, ρ) is an inherent material property, whereas resistance is a component property determined by both the material and the physical geometry of the wire.

Resistance vs. Resistivity: The Most Common Confusion

Before calculating voltage drop or sizing a feeder, you must separate what the material does from what the geometry does. The most common mistake in DIY electrical work is assuming that cutting a wire in half changes its resistivity. It does not; it only changes its resistance.

The relationship is defined by the formula:

R = ρ × (L / A)

• R = Resistance (measured in Ohms, Ω)
• ρ (rho) = Resistivity (measured in Ohm-meters, Ω·m)
• L = Length of the wire (meters)
• A = Cross-sectional area (square meters)

What resistivity changes in a real circuit is the baseline voltage drop and heat generation (I²R losses) for a given physical footprint. If you swap a 6 AWG copper wire for a 6 AWG aluminum wire of the exact same length, the geometry (L and A) remains identical, but the circuit's total resistance increases because aluminum has a higher intrinsic resistivity than copper. This forces you to either accept a higher voltage drop or upsize the aluminum wire to compensate.

The Two Variables: Material Composition and Temperature

Since geometry is excluded from the definition of resistivity, we are left with only two variables that dictate the value of ρ in any standard residential or commercial conductor.

1. The Conductor Material

Every conductive element has a unique atomic lattice that dictates how easily free electrons can flow through it. In home wiring, you are almost exclusively choosing between copper and aluminum. According to data from The Engineering Toolbox, the baseline resistivity of these materials at a standard room temperature of 20°C (68°F) is:

• Copper (Annealed): 1.68 × 10⁻⁸ Ω·m
• Aluminum (99.5% pure): 2.65 × 10⁻⁸ Ω·m

Because aluminum's resistivity is roughly 58% higher than copper's, an aluminum conductor must have a cross-sectional area about 1.6 times larger than a copper conductor to achieve the exact same resistance over the same distance.

2. Temperature Fluctuations

As a conductor heats up, its atomic lattice vibrates more intensely (a phenomenon known as phonon scattering). These vibrations physically obstruct the flow of electrons, increasing the material's resistivity. This is quantified by the temperature coefficient of resistance (α). For copper, α is approximately 0.00393 per °C at 20°C.

Worked Numeric Example: 50A EV Charger Feeder at 20°C vs 75°C

Let's look at how temperature-dependent resistivity impacts a real-world installation. Suppose you are running a 240V, 50A Level 2 EV charger feeder using 6 AWG Copper THHN in a conduit, with a one-way distance of 100 feet (200 feet total loop length).

Wire Geometry:

• Cross-sectional area (A) of 6 AWG = 13.3 mm² (13.3 × 10⁻⁶ m²)
• Total loop length (L) = 200 ft = 60.96 meters

Scenario A: Cold Wire at 20°C

Using the baseline copper resistivity (ρ = 1.68 × 10⁻⁸ Ω·m):

R = (1.68 × 10⁻⁸ × 60.96) / (13.3 × 10⁻⁶) = 0.0768 Ω

Voltage Drop = 50A × 0.0768 Ω = 3.84V (1.6% drop)

Scenario B: Hot Wire at 75°C Under Load

First, we calculate the new resistivity at 75°C using the formula: ρ_T = ρ_20 [1 + α(T - 20)]

ρ_75 = 1.68 × 10⁻⁸ [1 + 0.00393(55)] = 1.68 × 10⁻⁸ [1.2165] = 2.04 × 10⁻⁸ Ω·m

Now, recalculate the resistance:

R = 0.0768 Ω × 1.2165 = 0.0934 Ω

Voltage Drop = 50A × 0.0934 Ω = 4.67V (1.94% drop)

While both scenarios keep you well under the NEC recommended 3% branch circuit voltage drop limit, this 21% swing in voltage drop purely due to temperature-altered resistivity is exactly why the NFPA 70 (National Electrical Code) mandates specific temperature columns for ampacity derating.

Where You Meet This In Practice

You rarely calculate raw resistivity formulas on the jobsite; instead, you interact with its effects through standardized tables and physical sizing rules.

• NEC 310.16 Ampacity Tables: The ampacity tables in the NEC are not arbitrary. They are derived from the Neher-McGrath equation, which heavily factors in the temperature-dependent resistivity of the conductor alongside the thermal resistance of the insulation and surrounding environment. When you select the 75°C column for a breaker termination, you are implicitly acknowledging the increased resistivity of the copper at that operating temperature.
• Aluminum vs. Copper Sizing: Because aluminum's resistivity is higher, the NEC requires larger aluminum wires for the same ampacity. For a standard 100A residential service panel feeder, you can use 4 AWG Copper, but you must step up to 2 AWG Aluminum to achieve the necessary cross-sectional area to offset the higher resistivity.
• Lug Terminations and Oxidation: While not strictly bulk resistivity, aluminum rapidly forms an oxide layer when exposed to air. Aluminum oxide is an insulator with massive resistivity. This is why aluminum branch circuit wiring failed in the 1970s (leading to modern AFCI/CO-ALR requirements) and why you must use antioxidant compound (like Noalox) on modern aluminum feeder terminations to keep contact resistance low.