Resistance & Temperature (Edexcel IAL Physics)

Modelling the Variation of Resistance with Temperature

Spec point — 79

• 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

Spec point — 79

• 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:

  • an increase in temperature leads to an increase in resistance and resistivity
  • a decrease in temperature leads to 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 leads to increased vibrations in the lattice of ions

  • As a result, the frequency of collisions between free electrons and the ions increases, which leads to an increase in resistance

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

  • This is seen on the I-V graph as a curve with a decreasing gradient

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.

Answer:

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

Spec point — 79

• 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

Worked Example A thermistor is connected in series with a resistor R and a battery.

The 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