use, for a current-carrying conductor, the expression I = Anvq , where n is the number density of charge carriers

Electric Current: The Flow of Charge

What is Electric Current?

Electric current, denoted by the symbol \$I\$, is the rate at which electric charge flows through a conductor. Think of it like a stream of tiny cars (the charge carriers) moving along a road (the conductor). The faster and more cars that pass a point, the higher the current. 🚗

Key Formula

For a uniform, straight conductor the current can be calculated using:

\$I = A\,n\,v\,q\$

  • \$A\$ – Cross‑sectional area of the conductor (m²)
  • \$n\$ – Number density of charge carriers (m⁻³)
  • \$v\$ – Drift velocity of the carriers (m/s)
  • \$q\$ – Charge of one carrier (C)

Analogy: Water Flow

Imagine a pipe filled with water. The amount of water that passes a cross‑section per second is analogous to current. The pipe’s width (\$A\$) determines how many water molecules can flow side‑by‑side, the density of molecules (\$n\$) tells how many are in the water, their speed (\$v\$) is like the water’s velocity, and each molecule carries a tiny charge (\$q\$). The product of all four gives the total charge flow per second. 💧

Variable Summary Table

SymbolDescriptionUnits
\$A\$Cross‑sectional area of the wire
\$n\$Number density of free electronsm⁻³
\$v\$Drift velocity of electronsm/s
\$q\$Charge of one electronC
\$I\$Electric currentA (ampere)

Worked Example

Calculate the current in a copper wire that is 1 mm² in cross‑section, carries electrons with a drift velocity of \$1.0\times10^{-4}\,\text{m/s}\$, and has a free‑electron density of \$8.5\times10^{28}\,\text{m}^{-3}\$. The charge of an electron is \$q = 1.6\times10^{-19}\,\text{C}\$.

  1. Convert the area to square metres:

    \$A = 1\,\text{mm}^2 = 1\times10^{-6}\,\text{m}^2\$

  2. Plug values into the formula:

    \$I = (1\times10^{-6})\,(8.5\times10^{28})\,(1.0\times10^{-4})\,(1.6\times10^{-19})\$

  3. Compute step by step:

    1. \$8.5\times10^{28}\times1.0\times10^{-4}=8.5\times10^{24}\$
    2. \$8.5\times10^{24}\times1.6\times10^{-19}=13.6\times10^{5}\$
    3. \$13.6\times10^{5}\times1\times10^{-6}=1.36\times10^{0}=1.36\$ A

  4. Result: The current is approximately \$1.4\,\text{A}\$.

Quick Recap

  • Current \$I\$ is the flow of charge per second.
  • Formula \$I = A\,n\,v\,q\$ links geometry, material properties, and motion.
  • Remember: \$A\$ (area) and \$n\$ (density) set how many carriers can move, \$v\$ (velocity) sets how fast, and \$q\$ (charge) tells how much charge each carrier carries.
  • Use the example as a template for any conductor you encounter.