4.1.4 Current in a Current Carrying Conductor

• In a conductor, the current is due to the movement of charge carriers
• The charge carriers can be negative or positive, however, the current is always taken to be in the same direction
• In conductors, the charge carrier is usually free electrons
  • However, these electrons only travel a small difference before colliding with a metal ion
  • This means they have a relatively slow drift velocity, v

• In the diagram below, the current in each conductor is from right to left but the charge carriers move in opposite directions shown by the direction of the drift velocity v
  • In diagram A (positive charge carriers), the drift velocity is in the same direction as the current
  • In diagram B (negative charge carriers), the drift velocity is in the opposite direction to the current

Conduction in a current-carrying conductor

• The drift velocity is the average velocity of the charge carriers travelling through the conductor
  • You will find this value is relatively slow (∼ 10^-3 m s^-1)

• However, since the number density of charge carriers is so large, the current flow still seems to happen instantaneously

• The current can be expressed in terms of the number density (number of charge carriers per unit volume) n, the cross-sectional area A, the drift velocity v and the charge of the charge carriers q

Current in a conductor equation

• The same equation is used whether the charge carriers are positive or negative
  • The minus sign will indicate current in the opposite direction to the charge carriers

• The charge q will be e for electrons (-1.60 × 10^-19 C)
• The number density n represents the number of free charge carriers (electrons) per unit volume
  • Conductors, such as metals, have a high value of n
  • Insulators, such as plastics, have a small value of n

• The cross-sectional area A of a wire is the area of a circle

A = πr²

• Where:
  • r = radius of the wire (m)

• This equation shows:
  • v is inversely proportional to n meaning more charge carriers per unit volume will slow down their speed through the conductor
  • I is directly proportional to n since greater n means greater charge is flowing and therefore a larger current I. When the value of n is lower, the charge carriers must travel faster to carry the same current