Edexcel A Level Physics

Revision Notes

3.19 Resistance & Temperature

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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

Electrons and resistance, downloadable AS & A Level Physics revision notes

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

Resistance & Temperature in a Metal, downloadable AS & A Level Physics revision notes

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 ∝ (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

Filament lamp IV graph, downloadable AS & A Level Physics revision notes

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

Worked example

The temperature of a non-ohmic resistor increases as the current through it increases.

Explain this is terms of the structure of a metal.

Step 1: Consider the effect on rate of electron flow:

    • Rate of flow of electrons increases

Step 2: Consider the effect on number of collisions of conduction electrons with the lattice

    • This increases the number of collisions of conduction electrons with the ions in the lattice

Step 3: Describe what happens to the vibrations of the lattice

    • Therefore vibrations of the lattice ions increase

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

Thermistor graph, downloadable AS & A Level Physics revision notes

  • 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

Thermistor diagram, downloadable AS & A Level Physics revision notes

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

Worked example

A thermistor is connected in series with a resistor R and a battery.WE - thermistor in circuit question image, downloadable AS & A Level Physics revision notesThe resistance of the thermistor is equal to the resistance of R at room temperature.

Which statement describes the effect when the temperature of the thermistor decreases?

A.     The p.d across the thermistor increases

B.     The current in R increases

C.     The current through the thermistor decreases

D.     The p.d across R increases

ANSWER: A

Step 1: Outline the nature of a thermistor

  • The resistance of the thermistor increases as the temperature decreases

Step 2: Consider the properties of current in a series circuit

  • Since the thermistor and resistor R are connected in series, the current I in both of them is the same

Step 3: Consider a relevant equation

  • Ohm’s law states that V = IR
  • Since the resistance of the thermistor increases, and I is the same, the potential difference V across it increases

Step 4: State the conclusion

  • Therefore, statement A is correct

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