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:

• 
• ?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?n
  • 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

Resistivity

• 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

The resistivity of some materials at room temperature