Edexcel International A Level Physics

Revision Notes

2.42 Calculating Current & Drift Velocity

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Calculating Current & Drift Velocity

Drift Velocity

  • In a conductor, the current is due to the movement of charge carriers
    • The charge carriers can be negative or positive
    • However current is always taken to be in the same direction

  • Drift velocity is the average velocity of the charge carriers travelling through the conductor
  • In conductors, the charge carrier is usually free electrons
    • Free electrons only travel small distances before colliding with a metal ion
    • Therefore they have a relatively slow drift velocity of ∼ 10−3 m s−1

  • In the diagram below, the current in each conductor is from right to left
    • 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 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 low value of n
  • Since the density of charge carriers is so large in conductors, the flow of current flow appears to happen instantaneously

The Transport Equation

  • The current can be expressed in the transport equation:

I space equals space n q v A

  • Where:
    • I = current (A)
    • n = number density (m−3)
    • q = the charge of the charge carrier (C)
    • v = drift velocity (m s−1)
    • A = cross sectional area of the wire (m2), calculated using A = πr2
  • The same equation is used whether the charge carriers are positive or negative
    • A negative value for v will indicate current in the opposite direction to the charge carriers
  • The transport equation shows that v is inversely proportional to n
    • Since the more charge carriers available per unit volume the more the density will slow down their speed through the conductor
  • The transport equation also shows that I is directly proportional to 
    • Greater n means a 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

The number density of conduction electrons in a copper wire is 9.2 × 1028 m−3.  The wire carries a current of 3.5 A and it has a cross-sectional area of 1.5 mm2.

Determine the average drift velocity of the electrons.


The Large Range of Material Resistivities


  • The transport equation tells us that current, I ∝ number of charge carriers, n
    • Therefore, the larger the number of charge carriers, the greater the current will be for the same applied voltage
    • This is because resistivity has decreased with more charge carriers available
  • Different materials have different numbers of charge carriers

  • Insulators have few charge carriers:
    • They have such a high resistivity that virtually no current will flow through them
    • A perfect insulator would have no charge carriers, n = 0 
    • A perfect insulator would have a current of zero regardless of the voltage applied

  • Conductors have a large number of charge carriers
    • Metals are good conductors because they have free electrons
    • Free electrons are the atoms from the outer shell of each atom
    • Therefore there are lots of charge carriers per unit volume
    • This means resistivity is low

  • Semiconductors have a small number of free electrons
    • There are fewer delocalised electrons in a semiconductor than in a metal 
    • There are a greater number of free electrons at a higher temperature
    • Resistivity changes in a semiconductor, due to the variation with temperature in free electrons which are available as charge carriers 
    • Silicon is an example of a semiconductor

Table of resistivity of materials at room temperature, downloadable AS & A Level Physics revision notes

The resistivity of some materials at room temperature

Exam 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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