Current in a Current Carrying Conductor (OCR A Level Physics)

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Mean Drift Velocity of Charge Carriers

  • 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

Charge carriers diagram, downloadable AS & A Level Physics revision notes

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

Calculating Current in a Current Carrying Conductor

  • 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 conductor equation, downloadable AS & A Level Physics revision notes

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 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

Worked example

A copper wire has 9.2 × 1028 free electrons m-3. The wire has a current of 3.5 A and a cross-sectional area of 1.5 mm2.Calculate the average drift speed of the electrons.

Examiner Tip

Remember that the cross-sectional area is in m2, the drift velocity is in m s-1 and the number density is in m-3. Therefore, sometimes unit conversions from cm or mm may be required, so make sure you're comfortable with these.

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Ashika

Author: Ashika

Expertise: Physics Project Lead

Ashika graduated with a first-class Physics degree from Manchester University and, having worked as a software engineer, focused on Physics education, creating engaging content to help students across all levels. Now an experienced GCSE and A Level Physics and Maths tutor, Ashika helps to grow and improve our Physics resources.