Resistance & Temperature (Edexcel A Level Physics): Revision Note

Modelling the Variation of Resistance with Temperature

• 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

•  As temperature increases, the vibrations of the ions in the lattice also increase

  • This increases the chance of collisions between the conduction electrons and the ions

• Since current is the flow of charge, the ions resisting the flow of electrons cause resistance

• Therefore as temperature increases so does resistance

  • At small increases of temperature this increase is linear

• A higher current will cause temperature to rise 

  • This is due to more collisions between free electrons and ions

  • The collisions cause the ions to vibrate more

Resistance & Temperature for Metallic Conductors

• All solids are made up of vibrating atoms

  • This includes metal solids

• As the temperature in a metal rises, the ions vibrate with a greater frequency and amplitude

  • The electrons collide with the vibrating atoms which impede their flow, hence the current decreases

  • electric current is the flow of free electrons in a material

Metal atoms and free electrons at low and high temperatures

• Current decreases because the resistance has increased (from V = IR)

  • This is because resistivity has increased

  • This is from 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

• The I-V graph for a filament lamp shows this effect

I-V characteristics for a filament lamp

• As the current increases, the number of collisions between free electrons and the lattice of ions increases

  • This increases the temperature of the filament in the lamp 

• An increase in temperature:

  • Causes greater vibrations in the lattice of ions

  •  Therefore increased collisions between free electrons and the ions

  • And so an increased resistance

• Resistance opposes the current, causing the current to increase at a slower rate

  • This is seen as a curve in the graph

Resistance & Temperature for Thermistors

• The resistivity of a thermistor behaves in the opposite way to metals

  • This is because it is a type of semiconductor

  • Semiconductors behave in a different way to metals

• The number density of charge carriers (such as electrons) increases with increasing temperature

• Therefore, for a thermistor:

  • An increase in temperature causes a decrease in resistance and resistivity

  • A decrease in temperature causes an increase in resistance and resistivity

• Thermistors are often used in temperature sensing circuits such as thermometers and thermostats

• A thermistor is a non-ohmic conductor and sensory resistor whose resistance varies with temperature

  • Most thermistors are negative temperature coefficient ntc) components.

  • This means that if the temperature increases, the resistance of the thermistor decreases (and vice versa)

• The temperature-resistance graph for a thermistor is shown below

• Thermistors are temperature sensors and are used in circuits in ovens, fire alarms and digital thermometers

  • As the thermistor gets hotter, its resistance decreases

  • As the thermistor gets cooler, its resistance increases

The resistance through a thermistor is dependent on the temperature of it