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Electric Current

Source lecture(s): SC134 Lec1, Lec8

Intuition

Current is the flow rate of charge—like water current, but with electrons (or ions).

Formal Definition

\[I = \frac{dq}{dt}\]

Mathematical Formulation

Current density: \(\vec{J} = nq\vec{v}_d\) Drift speed: \(v_d = I/(nqA)\)

Derivation

Count charges passing a cross-section per unit time; multiply by charge magnitude.

Worked Example

2 A through a wire of area \(1\,\text{mm}^2\) with \(n\approx 8.5\times10^{28}\,\text{m}^{-3}\) gives \(v_d\approx 1.5\times10^{-4}\,\text{m/s}\).

Common Mistakes

  • Confusing drift speed with signal speed.
  • Using wrong cross-sectional area in \(J\).

Quiz

Q1. Does conventional current flow in the direction of electron drift?

Answer

No—opposite direction.