4.2.5 Resistivity

• All materials have some resistance to the flow of charge
• As free electrons move through a metal wire, they collide with ions which get in their way
• As a result, they transfer some, or all, of their kinetic energy on collision, which causes electrical heating

Free electrons collide with ions which resist their flow

• Since current is the flow of charge, the ions resisting their flow causes resistance
• Resistance depends on the length of the wire, the cross-sectional area through which the current is passing and the resistivity of the material

• The resistivity equation shows that:
  • The longer the wire, the greater its resistance
  • The thicker the wire, the smaller its resistance

The length and width of the wire affect its resistance

• Resistivity is a property that describes the extent to which a material opposes the flow of electric current through it
• It is a property of the material, and is dependent on temperature
• Resistivity is measured in Ω m

Resistivity of some materials at room temperature

• The higher the resistivity of a material, the higher its resistance
  • This is why copper, with its relatively low resistivity at room temperature, is used for electrical wires — current flows through it very easily

• Insulators have such a high resistivity that virtually no current will flow through them

• The resistivity of a material depends on its temperature
  • How it varies depends on whether the material is a metal or a semiconductor

Metals

• All solids are made up of vibrating atoms
• As the temperature rises, the ions vibrate with a greater frequency and amplitude
• Electric current is the flow of free electrons in a material
  • The electrons collide with the vibrating atoms which impede their flow, hence the current decreases

Metal atoms and free electrons at low and high temperatures

• So, if the current decreases, then the resistance will increase (from V = IR)
  • Therefore, its resistivity will increase since ρ ∝ R (if the area A and length L is constant)

• For a metallic conductor which obeys Ohm's law:
  • An increase in temperature causes an increase in resistance and resistivity
  • A decrease in temperature causes a decrease in resistance and resistivity

Semiconductors

• The resistivity of semiconductors behaves in the opposite way to metals
• The number density of charge carriers (such as electrons) increases with increasing temperature
• Therefore, for a semiconductor:
  • An increase in temperature causes a decrease in resistance and resistivity
  • A decrease in temperature causes an increase in resistance and resistivity

• One example of this is a thermistor
  • This is often used in temperature sensing circuits such as thermometers and thermostats

• This is only for semiconductors with a negative temperature coefficient (NTC)