Current Electricity

Lesson

Part 1 — what happens inside a wire when current flows, why materials resist it, and how much power that resistance turns into heat.

In this lesson you will

Derive the relation between current and drift velocity and define mobility
Distinguish ohmic and non-ohmic conductors; use resistivity and conductivity
Explain how resistivity depends on temperature
Calculate the power dissipated in resistors

Concept

Electric current

Current is the rate of flow of charge through a cross-section: $I = \dfrac{\Delta q}{\Delta t}\ \ (\text{steady}),\qquad I = \dfrac{dq}{dt},\qquad 1\ \text{A} = 1\ \text{C s}^{-1}$ Its direction (conventional current) is the direction in which positive charge would flow; in metals the electrons move the other way.

Current is a scalar: it has a sense along the wire but does not add as a vector.
Charge carriers: electrons in metals, ions in electrolytes, electrons and holes in semiconductors.

Table of typical currents from lightning to nerve signals
Situation	Typical current
Lightning stroke	tens of thousands of amperes
Room heater	about 5 to 10 A
Phone charging	about 1 to 3 A
Nerve signal	microamperes

Diagram

Drift velocity

Free electrons move randomly at high speed, but with no field their average velocity is zero. A field $\vec E$ gives each electron an acceleration $-e\vec E/m$ between collisions. The average velocity gained is the drift velocity: $\vec v_d = -\dfrac{e\vec E}{m}\,\tau$ where $\tau$ is the average time between collisions (relaxation time).

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