Current Electricity

Syllabus Unit: Electrodynamics

Why it matters

Chapter overview

Current electricity examines the steady flow of charge through conductors — starting from the microscopic picture of drifting electrons, through Ohm's law and resistivity, to how resistors combine in real circuits, and finally to how Kirchhoff's laws, the Wheatstone bridge and the potentiometer let NEET-level circuits be solved exactly rather than approximately.

Physics Syllabus Electrodynamics 25%–30% weightage

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1Random Thermal MotionFree electrons move randomly, no net drift

2Field E AppliedElectrons accelerate opposite to E

3Collisions Limit DriftAverage relaxation time τ sets vd = eEτ/m

4Ordered Drift = CurrentI = nAvde

1Current, Drift Velocity & Resistance

Electric current is the ordered drift of free electrons superimposed on their random thermal motion — this microscopic picture explains why conductors resist current flow.

Learning Objectives

Define electric current I = dQ/dt and relate it to drift velocity via I = nAvd e.
Explain why drift velocity is only mm/s while the 'signal' that lights a bulb travels near light speed.
State the microscopic origin of resistance via relaxation time, R = ml/(ne²τA).
Distinguish resistance R (property of a specific conductor) from resistivity ρ (property of the material).

Key Terms

Drift Velocity (vd)The small average net velocity gained by free electrons opposite to the applied field, from acceleration between collisions with lattice ions.

Relaxation Time (τ)The average time between successive collisions of a free electron with the lattice, roughly 10^-14 s in metals.

Mobility (μ)Drift velocity per unit electric field, μ = vd/E = eτ/m.

Free Electron Density (n)Number of conduction electrons per unit volume of the conductor, of order 10^28 per m³ for copper.

With no applied field, free electrons in a conductor move randomly at high thermal speeds (~10^5 m/s) with zero net displacement. Applying an electric field superimposes a slow, ordered **drift** opposite to E (electrons are negative) — this ordered drift is what constitutes electric current.

Current from drift velocity

I = n A vd e

n = free electron density
A = cross-sectional area of the conductor
vd = drift velocity of electrons
e = magnitude of electronic charge

Key Pointvd itself is tiny (~10^-4 m/s), yet a bulb lights up almost instantly — because the electric field (and the drift response) propagates through the wire near the speed of light, not because individual electrons race across the circuit.

Microscopic origin of resistance

Between collisions with vibrating lattice ions, an electron accelerates under E for an average relaxation time τ, gaining vd = eEτ/m. Substituting into I = nAvde reproduces Ohm's law microscopically and gives resistivity ρ = m/(ne²τ).

R = ρl/A = ml / (ne²τA)

Common MistakeTrap: resistivity ρ depends only on the material and temperature — not on the conductor's length or area. Resistance R depends on both the material and the geometry, R = ρl/A.