B.5.9—Direct current and charge flow

Current

Electric current is charge passing a point per unit time:

$$I=\frac{\Delta q}{\Delta t}$$

The SI unit is the ampere, $$1\,\mathrm A=1\,\mathrm{C\,s^{-1}}$$.

Find charge or carrier count

$$\Delta q=I\Delta t$$

If each carrier has charge magnitude e, the number of carriers passing is $$N=\Delta q/e$$.

Microscopic picture

Metal electrons move randomly with a small drift superimposed when current flows. Current measures net charge flow, not the total random motion of every electron.

Worked example from the mapped local textbook

A lamp carries $50\,\mathrm{mA}=0.050\,\mathrm{A}$ for $1.0\,\mathrm{min}=60\,\mathrm{s}$.

$$q=It=(0.050)(60)=3.0\,\mathrm{C}$$

$$N=\frac{q}{e}=\frac{3.0}{1.60\times10^{-19}}=1.9\times10^{19}\ \text{electrons}$$

Use the electron charge magnitude for the carrier count; direction is handled separately by current convention.

Common trap

Use time in seconds and charge in coulombs. Do not use I/t for charge; current is already charge divided by time.