Edexcel A Level (IAL) Physics-2.50 Resistance & Temperature- Study Notes- New Syllabus
Edexcel A Level (IAL) Physics -2.50 Resistance & Temperature- Study Notes- New syllabus
Edexcel A Level (IAL) Physics -2.50 Resistance & Temperature- Study Notes -Edexcel A level Physics – per latest Syllabus.
Key Concepts:
- understand how changes of resistance with temperature may be modelled in terms of lattice vibrations and number of conduction electrons and understand how to apply this model to metallic conductors and negative temperature coefficient thermistors
Temperature Dependence of Resistance: Lattice Vibrations and Conduction Electrons
Electrical resistance depends strongly on temperature. This behaviour can be explained using a microscopic model involving lattice vibrations and the number of conduction electrons. Different materials behave differently — especially metals and NTC thermistors.
Metallic Conductors — Why Resistance Increases with Temperature
In metals, conduction is due to free electrons moving through a lattice of positive ions.
When temperature increases:
- The metal ions vibrate more vigorously (increased lattice vibrations).
- Electrons collide more frequently with the vibrating ions.
- More collisions → electrons lose momentum more often.
- Drift velocity decreases for the same applied voltage.
Result: Resistance increases with temperature.
\( R \uparrow \quad \text{as} \quad T \uparrow \)
Reason (microscopic): increased electron–ion collisions.
NTC Thermistors — Why Resistance Decreases with Temperature
In semiconductors (including NTC thermistors), conduction works differently.
When temperature increases:
- More electrons gain enough energy to enter the conduction band.
- This increases the number of charge carriers \( n \).
- More carriers → higher current for the same voltage.
- Thus resistance decreases.
Result: Resistance decreases with temperature.
\( R \downarrow \quad \text{as} \quad T \uparrow \)
Reason (microscopic): increase in charge carriers dominates over increase in vibrations.
Comparing Metals and Thermistors
| Material | Effect of Temperature | Microscopic Reason |
|---|---|---|
| Metallic conductor | Resistance increases | More lattice vibrations → more electron collisions |
| NTC thermistor | Resistance decreases | More electrons released (increase in \( n \)) |
Using the Drift Velocity Model
The drift velocity equation:
\( I = nqvA \)
Helps us understand behaviour:
- Metals: \( n \) is constant (number of free electrons doesn’t change); temperature increases → lower \( v \) (more collisions) → resistance increases.
- Thermistors: \( n \) increases dramatically with temperature; this overwhelms effect of collisions → resistance decreases.
Applying the Model
A. Metallic Conductor
- Initial temperature rise → slight increase in \( n \) but negligible.
- Main effect: increased lattice vibrations.
- Thus \( R \propto T \) approximately linearly at moderate temperatures.
B. NTC Thermistor
- At low temperatures, few carriers are available → high resistance.
- With temperature rise, many electrons jump to conduction band.
- Thus resistance drops rapidly (non-linear behaviour).
Example (Easy)
Why does the resistance of a copper wire increase as it gets hotter?
▶️ Answer / Explanation
- More lattice vibrations at higher temperature.
- Electrons collide more often.
- More collisions → greater resistance.
Example (Medium)
Explain why the resistance of an NTC thermistor falls rapidly with temperature.
▶️ Answer / Explanation
- Temperature increases release many more charge carriers.
- Thus \( n \) rises dramatically.
- More electrons available to carry current → lower resistance.
- This effect is stronger than increased lattice vibrations.
Example (Hard)
Describe how the drift velocity model explains the opposite temperature behaviour of metals and thermistors.
▶️ Answer / Explanation
Metal:
- Number of charge carriers \( n \) is constant.
- Higher temperature → more ion vibrations → more collisions.
- More collisions → lower drift velocity \( v \).
- Lower \( v \) → resistance increases.
Thermistor:
- Heating releases more electrons → \( n \) increases greatly.
- Higher \( n \) increases current even if collisions increase.
- Thus drift velocity behaviour is dominated by the rise in electron number.
- Overall effect → resistance decreases.