Calculating Current & Drift Velocity(Edexcel International A Level Physics)

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Joanna

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Physics

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:

• 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.

Step 1: Consider the situation

• A copper wire is a conductor, and the free electrons are charge carriers
• Use the transport equation nqvA

Step 2: Rearrange the equation for drift speed v

Step 3: Substitute in values

• Current, I = 3.5 A
• Cross-sectional area, A = 1.5 mm2 = 1.5 ÷ 10002 = 1.5 × 10−6 m2
• Number density of conduction electrons, n = 9.2 × 1028 m−3
• Charge on an electron, q = 1.60 × 10−19 C (From the data sheet)

m s−1

mm s−1 (2 s.f.)

The Large Range of Material Resistivities

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

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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