Free electron theory of metals
Solid state phenomena · Physics
Study notes
**Worked Example – Resistance of a Copper Wire** 1. **Given**: Length L = 2.0 m, cross‑section A = 1.0×10⁻⁶ m², electron density n = 8.5×10²⁸ electrons/m³, mean free time τ = 2.5×10⁻¹⁴ s, electron charge e = 1.6×10⁻¹⁹ C, electron mass m = 9.1×10⁻³¹ kg. 2. **Calculate conductivity σ** using Drude formula: σ = ne²τ/m. σ = (8.5×10²⁸)(1.6×10⁻¹⁹)²(2.5×10⁻¹⁴)/(9.1×10⁻³¹) ≈ 5.8×10⁷ S/m. 3. **Find resistivity ρ**: ρ = 1/σ ≈ 1.72×10⁻⁸ Ω·m. 4. **Compute resistance R**: R = ρL/A = (1.72×10⁻⁸)(2.0)/(1.0×10⁻⁶) ≈ 0.034 Ω. 5. **Result**: The copper wire has a resistance of about 0.034 ohms.