Resistivity of Materials: Values, Formula and Examples
Electrical resistivity tells us how strongly a material opposes the flow of electric current. It helps us compare materials such as copper, aluminium, nichrome and glass, even when their sizes are different.
This lesson explains resistivity values at room temperature, the SI unit, the temperature formula and how to calculate the resistance of a wire.
1. What is electrical resistivity?
Resistivity, represented by the Greek letter rho (ρ), is a property of a material that describes how strongly it opposes electric current. A material with low resistivity allows current to flow more easily than a material with high resistivity under comparable conditions.
For a uniform conductor at a specified temperature, resistance is related to resistivity by this equation:
Rearranging gives:
ρ = RA/LHere:
- ρ (rho) = electrical resistivity, measured in ohm metres (Ω m).
- R = resistance, measured in ohms (Ω).
- L = conductor length, measured in metres (m).
- A = cross-sectional area, measured in square metres (m²).
For the same material at the same temperature, a longer wire has greater resistance, while a thicker wire has lower resistance. Resistivity describes the material itself rather than the dimensions of a particular wire.
Interactive SVG: Explore electrical resistance
Choose a material and change the wire dimensions to see how resistance changes. The calculation uses R = ρL/A.
The circles are illustrative symbols, not a simulation of actual electron speeds. Values are approximate and assume a uniform wire at constant temperature. Cross-sectional area is converted from mm² to m² for the calculation.
SI unit and dimensional formula
The SI unit of resistivity is the ohm metre (Ω m). From ρ = RA/L, its dimensional formula is [M L³ T⁻³ I⁻²].
2. Resistivity of different materials at 20°C
The following table gives approximate resistivity values for selected materials at or near 20°C. Actual values can vary with purity, composition and temperature.
| Material | Resistivity (Ω m) | Category |
|---|---|---|
| Silver | 1.59 × 10⁻⁸ | Metal |
| Copper | 1.68 × 10⁻⁸ | Metal |
| Gold | 2.44 × 10⁻⁸ | Metal |
| Aluminium | 2.65 × 10⁻⁸ | Metal |
| Tungsten | 5.60 × 10⁻⁸ | Metal |
| Iron | Approximately 1.0 × 10⁻⁷ | Metal |
| Lead | Approximately 2.2 × 10⁻⁷ | Metal |
| Nichrome | Approximately 1.1 × 10⁻⁶ | Alloy |
| Constantan | Approximately 4.9 × 10⁻⁷ | Alloy |
| Manganin | Approximately 4.8 × 10⁻⁷ | Alloy |
| Graphite | Material-dependent; commonly around 10⁻⁵ to 10⁻⁴ | Carbon material |
| Germanium | Approximately 0.46 | Semiconductor |
| Silicon | Highly dependent on purity and doping | Semiconductor |
| Glass | Often around 10¹⁰–10¹⁴ | Insulator |
| Hard rubber | Often around 10¹³–10¹⁶ | Insulator |
These are representative values, not universal constants for every sample. Resistivity ranges for insulators and semiconductors can be particularly wide. For precise engineering work, consult a material datasheet with specified measurement conditions.
What does the table tell us?
Good conductors
Silver and copper have very low resistivity. Copper is widely used for electrical wiring because it combines good conductivity with practical cost and availability.
Heating alloys
Nichrome has higher resistivity than copper and can withstand high temperatures, making it useful in heating elements.
Semiconductors
The resistivity of silicon and germanium depends strongly on temperature, impurities and doping.
Insulators
Glass and hard rubber usually have very high resistivity, so they restrict electric current under ordinary conditions.
3. Effect of temperature on resistivity
The resistivity of a material can change when its temperature changes. The direction and size of the change depend on the type of material.
Why does metal resistivity usually increase?
When a metal is heated, its atoms vibrate more strongly about their usual positions in the crystal lattice. Conduction electrons scatter more frequently from the vibrating lattice, making it harder for current to flow. As a result, the resistivity of most pure metals increases with temperature.
For small temperature changes, resistivity can often be approximated by a linear relationship:
In this equation:
- ρ(T) = resistivity at final temperature T.
- ρ(T₀) = resistivity at reference temperature T₀.
- α = temperature coefficient of resistivity at the reference temperature, in °C⁻¹ or K⁻¹.
- T − T₀ = temperature change in °C or K.
Do all materials behave like metals?
No. Many semiconductors have a negative temperature coefficient over ordinary operating ranges: their resistivity often decreases as temperature rises because more charge carriers become available. Some alloys, such as manganin and constantan, have relatively small temperature coefficients over useful temperature ranges.
4. Interactive resistivity temperature calculator
Enter the initial resistivity, temperature coefficient and two temperatures to estimate the new resistivity using the linear approximation.
The default values are an illustrative approximation for copper. This calculator assumes a constant temperature coefficient and is intended for small-to-moderate temperature changes.
5. Solved numerical example
Question: A copper wire has a resistivity of 1.68 × 10⁻⁸ Ω m at 20°C. If its temperature coefficient is 0.0039 °C⁻¹, estimate its resistivity at 80°C.
Step 1: Write the given values
ρ(T₀) = 1.68 × 10⁻⁸ Ω m
α = 0.0039 °C⁻¹, T₀ = 20°C, T = 80°C
Step 2: Calculate the temperature change
ΔT = T − T₀ = 80 − 20 = 60°C
Step 3: Apply the formula
ρ(T) = 1.68 × 10⁻⁸ [1 + (0.0039 × 60)]
ρ(T) = 1.68 × 10⁻⁸ × 1.234
ρ(T) ≈ 2.07 × 10⁻⁸ Ω mAnswer: The estimated resistivity at 80°C is 2.07 × 10⁻⁸ Ω m.
The value is higher than at 20°C because copper is a metal whose resistivity normally increases with temperature.
6. Why is resistivity useful in practical applications?
- Electrical wiring: Low-resistivity copper and aluminium reduce electrical losses in conductors.
- Heating elements: Nichrome's relatively high resistivity and heat resistance make it useful in heaters and toasters.
- Precision resistors: Alloys with small temperature coefficients help produce more stable resistance values.
- Insulation: Materials with high resistivity help prevent unwanted current leakage.
- Semiconductor devices: Controlling resistivity through doping is essential in electronic components.
Quick revision
- Resistivity is represented by ρ (rho).
- Its SI unit is Ω m.
- For a uniform conductor, R = ρL/A.
- For many metals, resistivity increases as temperature rises.
- The temperature equation is an approximation for a limited temperature range.
7. Frequently asked questions
What is the SI unit of electrical resistivity?
The SI unit is the ohm metre (Ω m). It is different from the ohm (Ω), which is the unit of resistance.
Which common metal has the lowest resistivity?
Silver has lower resistivity than copper among the common pure metals listed here at approximately 20°C. Copper is more commonly used for wiring because it is generally more economical.
Why does the resistivity of metals increase with temperature?
Heating increases lattice vibrations, which usually increases electron scattering in metals and therefore increases resistivity.
What is the difference between resistance and resistivity?
Resistance depends on the material, dimensions and temperature of a conductor. Resistivity is a material property at a specified temperature and is independent of the conductor's dimensions for a uniform material.
What is the formula for temperature-dependent resistivity?
For small temperature changes, ρ(T) = ρ(T₀)[1 + α(T − T₀)], where α is the temperature coefficient at the reference temperature.
Why is nichrome used in heating elements?
Nichrome has relatively high resistivity and good resistance to high-temperature operation and oxidation, making it useful for heating elements.
For further study, see the related topics on Ohm's law and electric current.