# Resistance & Temperature(Edexcel International A Level Physics)

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Joanna

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Physics

## 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 ∝ (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

#### 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

• 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

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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