Resistance Resisitivity

Overview

Engineering reference data for Resistance Resisitivity in electrical engineering.

Key Formulas

Ohm's Law

$V = IR$

Voltage = Current × Resistance.

Power

$P = VI = I^2R = V^2/R$

Electrical power.

Energy

$E = Pt$

Energy = Power × Time.

Variables

Symbol	Description	Unit
$V$	Voltage	V
$I$	Current	A
$R$	Resistance	Ω
$P$	Power	W

Common Resistivity Values

Conductors at 20°C

Good conductors have low resistivity. Values below are for temperatures around 20°C.

Insulators

Good insulators have high resistivity.

Resistivity Comparison (Relative to Copper)

This table shows how the resistivity of various metals compares to that of annealed copper (which is set as 1.00). A lower number indicates better conductivity.

Practical Example: Wire Resistance Calculation

The fundamental relationship $R = \rho L / A$ allows you to calculate the resistance of a wire if you know its material properties and dimensions.

Example 1: 10 m of 17-gauge Copper Wire Given:

• Length, $L = 10\,\text{m}$
• Cross-sectional area, $A = 1.04\,\text{mm}^2 = 1.04 \times 10^{-6}\,\text{m}^2$
• Copper resistivity, $\rho = 1.7 \times 10^{-8}\,\Omega\cdot\text{m}$

Calculation: $R = \frac{\rho L}{A} = \frac{(1.7 \times 10^{-8}\,\Omega\cdot\text{m})(10\,\text{m})}{1.04 \times 10^{-6}\,\text{m}^2} \approx 0.16\,\Omega$

Example 2: Effect of Reducing Wire Gauge (to 24-gauge) The same 10 m length of copper wire is now 24-gauge with $A = 0.205\,\text{mm}^2$.

$R = \frac{(1.7 \times 10^{-8}\,\Omega\cdot\text{m})(10\,\text{m})}{0.205 \times 10^{-6}\,\text{m}^2} \approx 0.83\,\Omega$

This demonstrates how significantly resistance increases as the cross-sectional area decreases.

Unit Conversion

Conversions for the SI unit of resistivity (ohm metre, Ω·m): $1\,\Omega\cdot\text{m} = 10^2\,\Omega\cdot\text{cm} = 39.37\,\Omega\cdot\text{inch} = 3.28\,\Omega\cdot\text{foot}$

References

• Original Source