Mobility, Relaxation Time, and Drude Conductivity
In the classical Drude model with field-independent relaxation time, mobility is drift speed per field and conductivity is nq times mobility; the electron form is ne squared tau over m.
Why this shows up in the exam
Estimating mobility from drift data · Relating mean free time to resistivity · Explaining material conductivity
Learn the idea
Carrier response links microscopic collisions to mobility, conductivity, and resistivity. An electric field accelerates a carrier between collisions. Frequent collisions limit the average drift, so longer relaxation time or more carriers makes the material more conductive.
🧠 Memory hook: More carriers or longer free time means easier conduction.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- mu = |v_d|/E = |q| tau/m — mobility in the low-field Drude model
- sigma = n |q| mu = n q² tau/m — conductivity for one carrier species
- rho = 1/sigma — resistivity of an isotropic ohmic material
How to approach it
- 1List n, q, tau, and m
- 2Choose mu, sigma, or rho relation
- 3Check SI units before substitution
Common slip-ups that cost marks
- •Dropping one factor of charge in sigma
- •Using the Drude formula for a strongly non-ohmic regime
- •Confusing mobility with drift speed
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A cell of emf 6 V and internal resistance 1 ohm is connected to a 2 ohm resistor. Find the circuit current.
More from Current Electricity
Resistivity, Conductivity, and Material Properties
Learn how resistivity and conductivity depend on material, length, area, and how resistance changes with dimensions and temperature.
Series and Parallel Combinations of Resistors
Master the calculation of equivalent resistance, voltage division, and current distribution in series and parallel resistor networks.
Electrical Energy, Power, and Heating Effect
Calculate electrical energy, power dissipation, and understand the heating effect of current in various circuit configurations.
EMF, Internal Resistance, and Terminal Voltage
Understand the concepts of EMF, internal resistance of cells, and how terminal voltage is affected in real circuits.
Drift Velocity and Microscopic View of Current
Explore the microscopic origin of current, including drift velocity, relaxation time, current density, and the effect of electric field in conductors.
Kirchhoff's Laws and Circuit Analysis
Apply Kirchhoff's current and voltage laws to analyze complex circuits and solve for unknowns.