Resistivity

Prof. Dr. Thorsten Jungmann (last updated 2025-09-03)

The resistivity (German: spezifischer Widerstand) describes the property of a material to oppose the electric current with a resistance. It is the reciprocal of the conductivity and a material property that you can read, for example, from the book of tables.

1 Quantity symbol and unit

The quantity symbol of the resistivity is the Greek lower-case letter $\rho$ (‘rho’). Its unit is ohm times metre with the unit symbol $\mathrm{\Omega }\cdot \mathrm{m}$.

$$[\rho ]=\mathrm{\Omega }\cdot \mathrm{m}$$

2 Practical and worked examples

The resistivity is the reciprocal of the conductivity:

$$\rho =\frac{1}{\sigma }$$

2.1 Resistance of a copper wire

The resistance of a conductor is calculated from:

$$R=\rho \cdot \frac{l}{A}$$

Example: copper electric line with $l=100\mathrm{m}$, $A=2.5\mathrm{m}{\mathrm{m}}^2$, ${\rho }_{Cu}=1.7\cdot 10^{-8}\mathrm{\Omega }\cdot \mathrm{m}$

$$R=1.7\cdot 10^{-8}\mathrm{\Omega }\cdot \mathrm{m}\cdot \frac{100\mathrm{m}}{2.5\cdot 10^{-6}{\mathrm{m}}^2}=\underline{0.68\mathrm{\Omega }}$$

2.2 Comparison of materials with identical geometry

Comparison of copper and aluminium for the same conductor ($l=50\mathrm{m}$, $A=1.5\mathrm{m}{\mathrm{m}}^2$):

Copper: ${\rho }_{Cu}=1.7\cdot 10^{-8}\mathrm{\Omega }\cdot \mathrm{m}$

$$R_{Cu}=1.7\cdot 10^{-8}\mathrm{\Omega }\cdot \mathrm{m}\cdot \frac{50\mathrm{m}}{1.5\cdot 10^{-6}{\mathrm{m}}^2}=\underline{0.567\mathrm{\Omega }}$$

Aluminium: ${\rho }_{Al}=2.7\cdot 10^{-8}\mathrm{\Omega }\cdot \mathrm{m}$

$$R_{Al}=2.7\cdot 10^{-8}\mathrm{\Omega }\cdot \mathrm{m}\cdot \frac{50\mathrm{m}}{1.5\cdot 10^{-6}{\mathrm{m}}^2}=\underline{0.900\mathrm{\Omega }}$$

2.3 Heating wire made of Nichrome

Calculation of a heating wire for $P=1000\mathrm{W}$ at $U=230\mathrm{V}$:

Required resistance: $R=\frac{U^2}{P}=\frac{(230\mathrm{V}{)}^2}{1000\mathrm{W}}=52.9\mathrm{\Omega }$

For Nichrome wire ($\rho =1.1\cdot 10^{-6}\mathrm{\Omega }\cdot \mathrm{m}$, $d=0.5\mathrm{mm}$):

$$l=\frac{R\cdot A}{\rho }=\frac{52.9\mathrm{\Omega }\cdot \pi \cdot (0.25\cdot 10^{-3}\mathrm{m}{)}^2}{1.1\cdot 10^{-6}\mathrm{\Omega }\cdot \mathrm{m}}=\underline{9.5\mathrm{m}}$$

Nichrome

Nichrome is a nickel-chromium alloy (typically 80 % nickel, 20 % chromium) that was developed specifically for resistance heating.

Important properties:

• High resistivity: $\rho \approx 1.1\cdot 10^{-6}\mathrm{\Omega }\cdot \mathrm{m}$
• High temperature resistance up to approx. 1 200 °C
• Resistant to oxidation thanks to a protective chromium oxide layer
• Mechanically stable even at high temperatures
• Low temperature coefficient of resistance

Typical applications:

• Heating wires in hair dryers, toasters, ovens
• Resistance furnaces in industry
• Heating coils in electric heating devices
• Glow wires in cigarette lighters

Advantage over other materials:
Whereas iron or copper oxidize at high temperatures and lose their properties, Nichrome remains stable and functional even at red heat.

3 Typical orders of magnitude

Very good conductors:

• Silver (Ag): $\rho \approx 1.6\cdot 10^{-8}\mathrm{\Omega }\cdot \mathrm{m}$
• Copper (Cu): $\rho \approx 1.7\cdot 10^{-8}\mathrm{\Omega }\cdot \mathrm{m}$
• Gold (Au): $\rho \approx 2.4\cdot 10^{-8}\mathrm{\Omega }\cdot \mathrm{m}$
• Aluminium (Al): $\rho \approx 2.7\cdot 10^{-8}\mathrm{\Omega }\cdot \mathrm{m}$

Resistance materials:

• Tungsten (W): $\rho \approx 5.6\cdot 10^{-8}\mathrm{\Omega }\cdot \mathrm{m}$ (incandescent bulbs)
• Iron (Fe): $\rho \approx 1.0\cdot 10^{-7}\mathrm{\Omega }\cdot \mathrm{m}$
• Constantan (CuNi): $\rho \approx 5.0\cdot 10^{-7}\mathrm{\Omega }\cdot \mathrm{m}$ (precision resistors)
• Nichrome (NiCr): $\rho \approx 1.1\cdot 10^{-6}\mathrm{\Omega }\cdot \mathrm{m}$ (heating wires)

Carbon materials:

• Graphite: $\rho \approx 2\cdot 10^{-5}\mathrm{\Omega }\cdot \mathrm{m}$ (parallel to the layers)
• Carbon: $\rho \approx 5\cdot 10^{-5}\mathrm{\Omega }\cdot \mathrm{m}$ (carbon brushes)

Semiconductors (pure material at 20 °C):

• Germanium (Ge): $\rho \approx 0.5\mathrm{\Omega }\cdot \mathrm{m}$
• Silicon (Si): $\rho \approx 2.3\cdot 10^3\mathrm{\Omega }\cdot \mathrm{m}$
• Gallium arsenide (GaAs): $\rho \approx 10^6\mathrm{\Omega }\cdot \mathrm{m}$

Insulators:

• PVC: $\rho \approx 10^9\text{...}10^{16}\mathrm{\Omega }\cdot \mathrm{m}$
• Glass: $\rho \approx 10^{11}\text{...}10^{13}\mathrm{\Omega }\cdot \mathrm{m}$
• Porcelain: $\rho \approx 10^{12}\text{...}10^{14}\mathrm{\Omega }\cdot \mathrm{m}$
• Teflon (PTFE): $\rho \approx 10^{16}\text{...}10^{18}\mathrm{\Omega }\cdot \mathrm{m}$

Rules of thumb:

• Very good conductors: $\rho <10^{-7}\mathrm{\Omega }\cdot \mathrm{m}$
• Semiconductors: $\rho \approx 10^{-3}\text{...}10^6\mathrm{\Omega }\cdot \mathrm{m}$
• Insulators: $\rho >10^8\mathrm{\Omega }\cdot \mathrm{m}$

4 Example phrasings

• ‘Copper has a resistivity of $1.7\cdot 10^{-8}\mathrm{\Omega }\cdot \mathrm{m}$ at 20 °C.’
• ‘Because of its high resistivity and its temperature resistance, Nichrome is well suited for heating wires.’
• ‘The resistivity of silicon depends strongly on temperature and doping.’
• ‘For insulators, the resistivity is above $10^8\mathrm{\Omega }\cdot \mathrm{m}$.’

5 Related quantities

• Resistance of a conductor:

$$R=\rho \cdot \frac{l}{A}$$

• Conductivity:

$$\sigma =\frac{1}{\rho }$$

• Conductance:

$$G=\frac{1}{R}=\sigma \cdot \frac{A}{l}$$

• Current density and electric field strength:

$$\vec{J}=\sigma \cdot \vec{E}=\frac{1}{\rho }\cdot \vec{E}$$

6 Related components

• Conductor, electric line, cable: the choice of material determines losses and cross-section
• Resistor: choice of material for the desired resistance
• Heating device: high-resistance materials for generating heat
• Insulator: high-resistance materials for electrical insulation