1. Electric Current
Electric current I is the rate of flow of charge through a cross-section of a conductor:
SI unit: Ampere (A) = C/s | Scalar quantity (though it has direction, it does not follow vector addition laws in all situations)
Conventional current flows from + to −; electron flow is opposite (from − to +).
Current density J (A/m²): J = I/A = nev_d (current per unit area, a vector along E)
2. Drift Velocity
Free electrons in a conductor move randomly at high thermal speeds (~10⁶ m/s) with no net drift. When an electric field is applied, electrons gain a small net velocity in the direction opposite to E — the drift velocity v_d.
Where: e = charge of electron; τ = relaxation time (average time between collisions); m = electron mass.
Relation Between Current and Drift Velocity
Where: n = free electron density (number per m³); A = cross-sectional area; e = 1.6×10⁻¹⁹ C.
Example: Copper wire, n = 8.5×10²⁸ m⁻³, A = 1 mm² = 10⁻⁶ m², I = 1 A:
v_d = 1 / (8.5×10²⁸ × 10⁻⁶ × 1.6×10⁻¹⁹) = 7.4×10⁻⁵ m/s ≈ 0.07 mm/s
This is extremely slow — yet lights come on instantly because the electric field propagates at the speed of light.
3. Ohm's Law and Resistance
Ohm's Law (macroscopic): For ohmic conductors at constant temperature, V ∝ I:
Resistance R (Ω) is the ratio V/I. For a conductor of length L and cross-section A:
Where ρ = resistivity (Ω·m) — property of the material (not geometry).
Conductivity: σ = 1/ρ (S/m or Ω⁻¹m⁻¹). Ohm's law in microscopic form: J = σE.
Ohmic vs Non-Ohmic Conductors
| Ohmic | Non-Ohmic |
|---|---|
| V-I graph is a straight line through origin | V-I graph is not a straight line |
| R = constant (independent of V or I) | R varies with V or I |
| Examples: metallic wires at constant T | Examples: diode, thermistor, light bulb, LED |
4. Resistivity — Temperature Dependence
Where α = temperature coefficient of resistivity (K⁻¹ or °C⁻¹).
- Metals: α > 0 (resistivity increases with T — more collisions at higher T).
- Semiconductors: α < 0 (resistivity decreases with T — more charge carriers freed).
- Alloys (Nichrome, Manganin): very small α — used in standard resistors and heating elements.
| Material | ρ (Ω·m) | Use |
|---|---|---|
| Silver | 1.6 × 10⁻⁸ | Best conductor; contacts |
| Copper | 1.7 × 10⁻⁸ | Wiring |
| Nichrome | 1.0 × 10⁻⁶ | Heating elements |
| Silicon (semiconductor) | 6.4 × 10² | Transistors, ICs |
| Glass (insulator) | 10¹⁰–10¹⁴ | Insulation |
5. Mobility
Mobility μ is the magnitude of drift velocity per unit electric field:
SI unit: m²/V·s. Mobility is a material property — higher μ means electrons drift faster for the same field (better conductor).
