Resistance and Resistivity
What is Resistance? ⚡️
Resistance is how much a material resists the flow of electric current. Think of it like a traffic jam for electrons – the more resistance, the fewer electrons can pass through.
Resistivity ρ 🔬
Resistivity is an intrinsic property of a material. It tells us how strongly the material opposes current, independent of its shape or size.
Formula: R = ρ L / A 📐
Where:
- \$R\$ = resistance (Ω)
- \$ρ\$ = resistivity (Ω·m)
- \$L\$ = length of the conductor (m)
- \$A\$ = cross‑sectional area (m²)
Example: A copper wire (ρ ≈ 1.68×10⁻⁸ Ω·m) 2 m long with a cross‑section of 1 mm² (1×10⁻⁶ m²) has
\$R = \frac{1.68\times10^{-8}\,\Omega\cdot m \times 2\,m}{1\times10^{-6}\,m^2} = 0.0336\,\Omega\$
Analogy: Water Flow 🚰
Imagine water flowing through a pipe:
- Length of pipe = \$L\$
- Pipe diameter = \$A\$ (cross‑section)
- Water viscosity = \$ρ\$ (resistivity)
- Pressure drop = \$R\$ (resistance)
Shorter, wider pipes (small \$L\$, large \$A\$) give less resistance.
Exam Tips 📚
- Always check units: \$ρ\$ in Ω·m, \$L\$ in m, \$A\$ in m² → \$R\$ in Ω.
- Convert mm² to m²: multiply by \$10^{-6}\$.
- Remember that \$ρ\$ is constant for a pure material at a given temperature.
- Use the formula in the correct order: first multiply \$ρ\$ and \$L\$, then divide by \$A\$.
- For multiple conductors in series, add resistances; in parallel, use reciprocal sum.
Common Resistivities (at 20 °C) 🔍
| Material | Resistivity (Ω·m) |
|---|
| Copper | 1.68×10⁻⁸ |
| Aluminium | 2.82×10⁻⁸ |
| Iron | 1.0×10⁻⁶ |
| Silver | 1.59×10⁻⁸ |