Electrical conductivity measures how easily a material allows electrons to flow through it, while electrical resistivity is the exact inverse, quantifying how strongly that same material opposes current.
The Core Definitions and Material Data
When you select a wire for a branch circuit or a trace for a PCB, you are betting on the atomic structure of the metal. Resistivity ($\rho$) is an intrinsic property of the material itself, measured in ohm-meters ($\Omega\cdot m$). It tells you how much resistance a 1-meter cube of that material will exhibit. Conductivity ($\sigma$) is simply the reciprocal of resistivity ($\sigma = 1/\rho$), measured in siemens per meter (S/m). Think of resistivity as the inherent 'friction' the material applies to electrons, regardless of the wire's length or thickness.
Below is the reference data you need when calculating voltage drop or designing custom busbars. All values are standardized at 20°C (68°F), as resistivity increases linearly with temperature for most metals.
| Material | Resistivity ($\rho$) at 20°C ($\Omega\cdot m$) | Conductivity ($\sigma$) at 20°C (MS/m) | Temp Coefficient ($\alpha$) per °C |
|---|---|---|---|
| Silver (Annealed) | $1.59 \times 10^{-8}$ | 62.9 | 0.00380 |
| Copper (Annealed) | $1.724 \times 10^{-8}$ | 58.0 | 0.00393 |
| Gold | $2.44 \times 10^{-8}$ | 41.0 | 0.00340 |
| Aluminum (1350 Alloy) | $2.82 \times 10^{-8}$ | 35.5 | 0.00403 |
| Iron (Pure) | $1.00 \times 10^{-7}$ | 10.0 | 0.00500 |
| Nichrome 80/20 | $1.10 \times 10^{-6}$ | 0.91 | 0.00040 |
Source: Standard reference values via Georgia State University HyperPhysics.
Worked Numeric Example: 12V Solar Branch Circuit
Let’s look at how resistivity forces your hand in a real-world installation. Low-voltage DC systems are unforgiving; because the voltage is low, even a fraction of an ohm of resistance causes massive percentage-based voltage drops.
The Scenario: You are wiring a 12V nominal LiFePO4 battery bank to a 12V, 20A DC water pump. The one-way wire length is 50 feet, meaning the total circuit loop (positive and negative) is 100 feet (30.48 meters). Your target is to keep the voltage drop under 3% (0.36V) to prevent the pump's internal low-voltage cutoff from tripping.
The formula for resistance based on material resistivity is $R = \rho \cdot \frac{L}{A}$, where $L$ is length and $A$ is cross-sectional area. Rearranging to solve for the required area: $A = \frac{\rho \cdot L}{R}$.
Sizing with Copper
Using annealed copper ($\rho = 1.724 \times 10^{-8}\,\Omega\cdot m$):
$A_{cu} = \frac{(1.724 \times 10^{-8}) \cdot 30.48}{0.018} = 2.917 \times 10^{-5}\,m^2$ (or $29.17\,mm^2$).
Looking at standard wire gauges, 2 AWG copper has an area of $33.6\,mm^2$. This exceeds our requirement, yielding an actual voltage drop of about 0.31V (2.6%).
Sizing with Aluminum
If you try to save money by using 1350 Aluminum ($\rho = 2.82 \times 10^{-8}\,\Omega\cdot m$):
$A_{al} = \frac{(2.82 \times 10^{-8}) \cdot 30.48}{0.018} = 4.775 \times 10^{-5}\,m^2$ (or $47.75\,mm^2$).
2 AWG aluminum ($33.6\,mm^2$) will result in a 4.3% voltage drop—too high. You must step up to 1/0 AWG aluminum ($53.5\,mm^2$) to safely carry this 20A load over 50 feet while maintaining the 3% drop threshold.
Where You Meet This in Practice
Resistivity isn't just a textbook variable; it drives purchasing and installation decisions across three major domains in electrical work and electronics design.
1. Mains Service Entrance Feeders (AL vs. CU)
When upgrading a residential panel to 200A, you will notice aluminum SER (Service Entrance Cable) is significantly cheaper and lighter than copper. Because aluminum has roughly 61% of the conductivity of copper, the NFPA 70 (NEC) ampacity tables require you to upsize. For a 200A residential service, 2/0 AWG copper is sufficient, but you must use 4/0 AWG aluminum to achieve the same ampacity and voltage drop characteristics. Always use anti-oxidant paste (like Noalox) on aluminum terminations to prevent high-resistance oxide layers from forming over time.
2. PCB Trace Width and Copper Weight
In embedded hardware design, the copper traces on your PCB act as microscopic wires. Standard FR4 boards use 1 oz/ft² copper, which is roughly 35 µm thick. If you are routing a 5A power line to a motor driver on an ESP32 carrier board, you cannot use a standard 10-mil signal trace. Using the resistivity of copper, PCB trace width calculators will dictate a minimum trace width of roughly 50 mils for a 10°C temperature rise. If you ignore this, the trace's resistance will cause localized heating, potentially delaminating the board or triggering a brownout on your microcontroller.
3. Heating Elements and High-Resistivity Alloys
Sometimes, high resistivity is exactly what you want. Nichrome (an alloy of nickel and chromium) has a resistivity roughly 64 times higher than copper. More importantly, its temperature coefficient ($\alpha$) is nearly flat, and it forms a protective chromium oxide layer when heated. This makes it the mandatory choice for toaster elements, 3D printer hotends, and dummy loads for testing power supplies, as it converts electrical energy directly into heat without melting or oxidizing away.
Common Confusions: Resistance vs. Resistivity
The most frequent mistake hobbyists and junior technicians make is using the terms resistance and resistivity interchangeably. They are fundamentally different concepts.
What is the exact difference between resistance and resistivity?
Resistance ($R$) is a property of a specific object (like a 50-foot spool of 12 AWG wire or a 100-ohm resistor). It changes if you cut the wire in half or change its thickness. Resistivity ($\rho$) is a property of the material (like copper or aluminum). A 1-inch cube of copper and a 1-mile spool of copper wire have vastly different resistances, but they share the exact same resistivity.
Does conductivity mean a material is a superconductor?
No. Conductivity simply means the material allows current to flow with some efficiency. Silver has the highest natural conductivity of any room-temperature metal, but it still has resistance. Superconductors have exactly zero resistivity, but they only operate at extreme cryogenic temperatures, far outside the scope of standard electrical installations.
Why do we use copper instead of silver if silver has higher conductivity?
Silver's conductivity is only about 5% higher than copper's, but its cost is exponentially higher. Copper provides the optimal intersection of high conductivity, mechanical tensile strength, and solderability. Gold is sometimes used for connector plating not because it is the most conductive (it's actually worse than both silver and copper), but because it is highly inert and will not form a resistive oxide layer in humid environments.
