The resistivity of copper is a fundamental material property that quantifies how strongly pure copper opposes the flow of electric current, measured at approximately 1.68 × 10⁻⁸ Ω·m (ohm-meters) at 20°C. While conductivity gets the marketing glory in product descriptions, resistivity is the raw number that actually dictates voltage drop, heat generation, and the physical wire gauge you must pull to keep a circuit safe and code-compliant. When you are sizing a feeder for a subpanel or calculating trace widths for a custom PCB, this single constant is the starting point for every calculation.
Resistivity vs. Resistance: The Most Common Confusion
People frequently confuse resistivity with resistance, but they describe two completely different things. Resistivity (ρ) is an intrinsic property of the material itself, much like density. A microscopic flake of copper and a massive copper busbar share the exact same resistivity. Resistance (R), on the other hand, is a property of a specific object—like a 50-foot spool of 12 AWG THHN wire.
The relationship between the two is defined by the formula:
R = ρ × (L / A)
- R = Resistance in Ohms (Ω)
- ρ = Resistivity of the material (Ω·m)
- L = Length of the conductor (meters)
- A = Cross-sectional area of the conductor (square meters)
Because resistivity is fixed for copper at a given temperature, the only ways you can change the resistance in your installation are by altering the length of the wire run or changing the wire gauge (cross-sectional area).
Worked Numeric Example: Calculating Copper Wire Voltage Drop
Let us look at a real-world scenario to see how the resistivity of copper impacts a standard residential branch circuit. Suppose you are wiring a 120V dedicated outlet for a heavy appliance, and you need to pull 10 AWG solid copper wire (THHN) from the panel to an outlet 100 feet away. You plan to run a continuous 30A load.
1. Define the Variables:
- Resistivity of copper (ρ) at 20°C = 1.68 × 10⁻⁸ Ω·m
- Length (L) = 100 feet = 30.48 meters (one-way)
- Cross-sectional Area (A) of 10 AWG = 5.26 mm² = 5.26 × 10⁻⁶ m²
2. Calculate One-Way Resistance:
R = (1.68 × 10⁻⁸ × 30.48) / (5.26 × 10⁻⁶) = 0.0973 Ω
3. Calculate Round-Trip Voltage Drop:
Current must travel to the load and return to the panel, so we double the resistance for a single-phase circuit: 0.0973 Ω × 2 = 0.1946 Ω total loop resistance.
Using Ohm's Law (V = I × R), the voltage drop at 30A is:
V_drop = 30A × 0.1946 Ω = 5.84 Volts
Where You Meet Copper Resistivity in Practice
You will run into the practical limits of copper's resistivity across several different domains in electrical and electronics work:
Branch Circuit Wiring and Feeders
When pulling NM-B or THHN through conduit, resistivity is the reason long runs require upsizing. If you ignore it, motors will draw higher amperage to compensate for low voltage, overheat, and trip breakers or burn out windings.
PCB Trace Routing
In custom PCB design, the copper layer is typically 1 oz/ft² (about 35 µm thick). Because the cross-sectional area of a trace is so tiny, the resistivity of copper forces you to use trace width calculators (like the Saturn PCB Toolkit) to ensure a 5A trace does not act like a fuse and melt off the board.
High-Current DC Busbars (Solar and LiFePO4)
When building 48V battery banks or solar combiner boxes, you will choose between copper and aluminum busbars. Copper's resistivity is roughly 60% lower than aluminum's. While aluminum is lighter and cheaper, you must use physically thicker aluminum bars to achieve the same resistance and prevent thermal runaway at the lugs.
Temperature Coefficient: Why 20°C Is Not the Whole Story
The standard value of 1.68 × 10⁻⁸ Ω·m is only valid at 20°C (68°F). In a real electrical panel or inside a conduit bundled with other current-carrying conductors, wires get hot. Copper has a positive temperature coefficient of approximately 0.00393 per °C, meaning its resistivity increases as it heats up. According to Georgia State University's HyperPhysics database, this thermal drift fundamentally alters your voltage drop calculations in high-ambient environments.
| Temperature | Typical Scenario | Resistivity (Ω·m) | Resistance Increase |
|---|---|---|---|
| 20°C (68°F) | Bench testing / Datasheet baseline | 1.68 × 10⁻⁸ | 0% (Baseline) |
| 60°C (140°F) | Warm NM-B cable / 60°C terminal rating | 1.94 × 10⁻⁸ | +15.5% |
| 75°C (167°F) | Standard THHN under load / 75°C lugs | 2.01 × 10⁻⁸ | +19.6% |
| 90°C (194°F) | Max THHN rating / High ambient attic | 2.11 × 10⁻⁸ | +25.6% |
As detailed in standard engineering references like All About Circuits, failing to account for this 20% to 25% increase in resistivity at operating temperature is a primary reason why calculated voltage drops often fail to match field measurements on a hot summer day.
Frequently Asked Questions
What is the electrical resistivity of copper compared to aluminum?
At 20°C, the resistivity of pure copper is 1.68 × 10⁻⁸ Ω·m, while pure aluminum is significantly higher at 2.65 × 10⁻⁸ Ω·m. This means copper is about 36% more conductive than aluminum by volume. However, because aluminum is much lighter, it actually has better conductivity by weight, which is why high-voltage transmission lines use aluminum despite its higher volumetric resistivity.
How does the resistivity of copper change with temperature?
Copper has a positive temperature coefficient, meaning its resistivity increases as it gets hotter. For every 1°C rise in temperature above 20°C, the resistivity of copper increases by approximately 0.393%. In practical terms, a copper wire operating at its 75°C thermal limit will have roughly 20% higher resistance than the same wire measured at room temperature.
Why is the resistivity of copper important for solar panel wiring?
Solar arrays operate at low DC voltages (often 12V, 24V, or 48V for off-grid, or up to 600V for string inverters) where even a small absolute voltage drop represents a massive percentage of power loss. Because power loss scales with the square of the current (P = I²R), the low resistivity of copper is critical to minimize I²R heating and ensure maximum wattage actually reaches the charge controller or inverter rather than being wasted as heat in the wire.
What is the difference between copper resistivity and conductivity?
They are exact mathematical inverses of one another. Resistivity (measured in ohm-meters) defines how much a material blocks current, while conductivity (measured in siemens per meter) defines how easily it passes current. If copper's resistivity is 1.68 × 10⁻⁸ Ω·m, its conductivity is simply 1 divided by that number, which equals roughly 5.96 × 10⁷ S/m. Wire manufacturers usually market conductivity, while engineers calculate with resistivity.
