Electrical Resistivity (SL IB Physics)

• The resistance of a sample depends on:
  • The material it is made of
  • The length of the sample
  • The cross-sectional area of the sample

• The resistance of a conductor (e.g. a wire) is:
  • Directly proportional to its length
  • Inversely proportional to its cross-sectional area 

How the dimensions of a wire (i.e. length and width) affect its resistance

• The cross-sectional area of a wire is always modelled as a circle
  • Therefore, the cross-sectional area is πr², where r is the radius of the wire

Resistivity

• This leads to the definition of a new quantity, called resistivity
• Resistivity is a property describing the extent to which a material opposes the flow of electric current through it
• It is defined as follows:

The resistivity of a material is equal to the resistance per unit length of a material with unit cross-sectional area 

• The equation for the resistivity is:

• Where:
  • ρ = resistivity in ohm-metres (Ω m)
  • R = resistance in ohms (Ω)
  • A = cross-sectional area of material in square metres (m²)
  • L = length of material in meres (m)

• Resistivity is measured in ohm-metres (Ω m)

• Resistivity is the property of a material

Resistivity of Materials Table

• Conductors, such as metals, have low values of resistivity
  • This makes metals, such as copper and aluminium, ideal for making wires as they have low values of resistance, which is why they are excellent conductors

• Whereas insulators have such high values of resistivity that virtually no current will flow through them
  • This is why insulating materials, such as plastic and rubber, are ideal for housing electrical wires, as they keep current flowing within the circuit and prevent users from receiving dangerous electric shocks