Overview
This lecture explains current, drift velocity, resistance, resistivity, conductivity, current density, Ohm's law, and the effect of temperature in detail.
Current and Drift Velocity
- Current is the rate of flow of charge (dq/dt).
- Current in electron orbital motion = charge/time = e/T = ef = ev/2πr.
- Electric field, V/L, is set by the potential difference in the conductor.
- Two formulas for drift velocity: eEτ/m and I/nae.
Resistance, Resistivity, and Conductivity
- Resistance (R) = V/I = mL/(Ne²τA).
- R = ρL/A, where ρ (rho) is resistivity, which depends on material and temperature.
- Conductivity (σ) = 1/ρ and conductance (G) = 1/R.
- Units of resistivity are ohm-meter, units of conductivity are ohm⁻¹ meter⁻¹.
Current Density
- Current density (J) = I/A (where A is the normal area of current).
- If the area is not normal, then J = I/(A cosθ).
- I = J·A; current is a scalar, current density is a vector.
Ohm's Law, Graphs, and Conductors
- Ohm's law: V = IR, R = ρL/A.
- J = σE; this is the vector form of Ohm's law.
- Ohmic conductors: V-I graph is straight (linear).
- Non-ohmic conductors have a non-linear V-I graph.
- Slope of V-I graph = resistance, slope of I-V graph = conductance.
Effect of Temperature on Resistance
- Resistance of metallic conductors increases with temperature.
- Rₜ = R₀[1 + α(T - T₀)], where α is the temperature coefficient.
- Units of α are per °C or per K.
- α = (Rₜ - R₀)/(R₀(T - T₀)).
Important Equations of Resistance
- R ∝ length, R ∝ 1/area (condition: others remain constant).
- Resistance formulas: R = ρL/A, or R = ρL²/(V·d), or R = ρM/(dA²).
- When wire is stretched n times, new R = n²R.
- When wire is cut into n parts, new R = R/n.
Key Terms & Definitions
- Current — rate of flow of charge.
- Drift Velocity — average velocity of electrons.
- Resistance (R) — opposition to current.
- Resistivity (ρ) — material property, resistance per unit dimension.
- Conductivity (σ) — ability to conduct, 1/ρ.
- Current Density (J) — current flow per unit area.
- Ohmic Conductor — one that follows V = IR.
- Temperature Coefficient (α) — rate of increase in resistance per degree temperature rise.
Action Items / Next Steps
- Write all formulas in one place and make a list.
- Read notes and try solving examples.
- Prepare questions for the next session.