Explain why the resistance of a metallic conductor increases as its temperature increases.

IB DP Physics Standard Level (2023 syllabus) — B.5 Current and circuits · Explain · 4 marks · View as Markdown

Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).

Model answer (4 marks)

A metallic conductor consists of a lattice of positive ions with a sea of delocalised electrons.

When the temperature rises the ions vibrate with greater amplitude.

The increased vibration gives the ions a larger effective cross‑sectional area, so the free electrons collide with them more often.

More frequent collisions lower the mean drift velocity for a given applied potential, so the current decreases.

Since R = V/I, a lower I for the same V means a higher resistance.

Examiner tips

Use the term "lattice of positive ions" and "sea of delocalised electrons". Show the chain: ↑T → ↑ion vibration → ↑electron‑ion collisions → ↓drift velocity → ↓I → ↑R. Mention the equation R = V/I to link current and resistance.

Common mistakes

Failing to mention the lattice of ions and delocalised electrons. Confusing temperature with applied voltage. Omitting the link between collisions and mean drift velocity.

Mark scheme (4 marks)

A metallic conductor contains a lattice of positive ions (and a 'sea' of delocalised/free electrons).
As temperature increases, the positive ions vibrate with greater amplitude.
The more vigorously vibrating ions present a greater effective cross-sectional obstruction, so free electrons collide with (or are scattered by) the ions more frequently.
More frequent collisions reduce the mean drift velocity of the electrons for the same applied potential difference, meaning the current decreases and hence resistance (R = V/I) increases.

Key terms in this question

resistance · metallic conductor