Electric Current, Ohm’s Law and Resistivity

Lesson

Part 1 — what really happens inside a wire when a current flows.

In this lesson you will

Explain conduction in metals using free electrons, relaxation time and drift velocity
Derive I = neAvd and define mobility
Derive J = σE and the expression ρ = m/(ne²τ)

Same random kicks in both; the field adds a steady drift opposite to E (checked).

Concept

Electric current

Current is the rate of flow of charge: $I = \dfrac{\Delta q}{\Delta t}$ , unit ampere (1 A = 1 C s⁻¹). Conventional current flows in the direction positive charge would move; in metals the carriers are electrons, moving the other way.

Current is a scalar (it obeys algebraic, not vector, addition at junctions) although it has a sense along a wire.
A steady current needs a source of emf to keep a field in the conductor.

Diagram

Free electrons and relaxation time

Same random kicks in both; the field adds a steady drift opposite to E (checked).

A metal holds a “gas” of free electrons moving randomly at about $10^5$ m s⁻¹, colliding with the vibrating ions. With no field their average velocity is zero.

The average time between successive collisions is the relaxation time τ (about $10^{-14}$ s in copper).
In a field E, each electron accelerates at $a = eE/m$ (opposite to E) between collisions, then loses that extra velocity in the next collision.

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