understand that an electric current is a flow of charge carriers

Published by Patrick Mutisya · 14 days ago

Electric Current

Learning Objective

Understand that an electric current is a flow of charge carriers.

What is Electric Current?

Electric current, denoted by \$I\$, is the rate at which electric charge passes a given point in a circuit. It is defined mathematically as

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

where \$\Delta Q\$ is the amount of charge transferred in time interval \$\Delta t\$.

Charge Carriers

Different materials have different types of charge carriers that move to produce a current:

  • Metals (conductors): Free electrons are the primary charge carriers.

  • Semiconductors: Both electrons (in the conduction band) and holes (absence of electrons) act as charge carriers.

  • Electrolytes (ionic solutions): Positive and negative ions move in opposite directions.

  • Plasmas: Ions and free electrons both contribute.

Suggested diagram: Schematic showing flow of electrons in a metal wire versus flow of ions in an electrolyte.

Conventional Current vs. Electron Flow

Historically, current direction was defined before the electron was discovered. Therefore:

  • Conventional current: Direction of flow of positive charge (from higher to lower potential).

  • Electron flow: Actual motion of electrons, opposite to conventional current.

Both descriptions are valid, but most circuit analysis uses conventional current.

Units and Symbols

  • Current: \$I\$ measured in amperes (A).

  • Charge: \$Q\$ measured in coulombs (C).

  • Time: \$t\$ measured in seconds (s).

1 A = 1 C s\(^{-1}\).

Calculating Current

From the definition, the current can be calculated if the charge transferred and the time are known:

\$I = \frac{Q}{t}\$

Example: If \$5.0\times10^{-3}\,\text{C}\$ of charge passes a point in \$2.0\,\text{s}\$, the current is

\$I = \frac{5.0\times10^{-3}\,\text{C}}{2.0\,\text{s}} = 2.5\times10^{-3}\,\text{A}\$

Current in Different Media

MediumCharge Carrier(s)Typical Mobility (m² V⁻¹ s⁻¹)
Metal (e.g., copper)Free electrons\overline{4}.5×10⁻³
n‑type semiconductorElectrons\overline{0}.1–0.2
p‑type semiconductorHoles\overline{0}.05–0.1
Electrolyte (e.g., NaCl solution)Na⁺, Cl⁻ ions\overline{10}⁻⁴ (ions)

Key Relationships

  1. Ohm’s Law: \$V = IR\$, linking voltage \$V\$, current \$I\$, and resistance \$R\$.

  2. Power: \$P = VI = I^{2}R = \frac{V^{2}}{R}\$.

  3. Charge conservation: The total charge entering a junction equals the total charge leaving (Kirchhoff’s Current Law).

Summary

  • Electric current is the rate of flow of charge carriers.

  • In metals, electrons move; in electrolytes, ions move; in semiconductors, both electrons and holes contribute.

  • Current is measured in amperes, where 1 A = 1 C s\(^{-1}\).

  • Conventional current direction is defined as the direction positive charge would move.

  • Understanding the nature of charge carriers helps explain phenomena such as resistance, heating, and the operation of devices like diodes and transistors.

Practice Questions

  1. Calculate the current if \$1.2\times10^{-2}\,\text{C}\$ of charge passes a point in \$3.0\,\text{s}\$.

  2. In a copper wire, electrons drift with an average speed of \$2.2\times10^{-4}\,\text{m s}^{-1}\$. If the wire has a cross‑sectional area of \$1.0\times10^{-6}\,\text{m}^{2}\$ and each copper atom contributes one free electron, estimate the current. (Avogadro’s number \$N_A = 6.02\times10^{23}\,\text{mol}^{-1}\$, density of copper \$= 8.96\times10^{3}\,\text{kg m}^{-3}\$, atomic mass \$= 63.5\,\text{g mol}^{-1}\$.)

  3. Explain why the direction of conventional current is opposite to the direction of electron flow in a metal circuit.