Explain why the resistance of a metallic conductor increases as its temperature increases, using a model of charge carriers and the lattice structure of the metal.

IB DP Physics Higher 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)

Free electrons are the charge carriers in a metallic conductor. As the temperature rises the positive ions in the lattice vibrate with greater amplitude. The more vigorous lattice vibrations present a larger effective cross‑sectional obstruction, so the frequency of collisions between free electrons and the lattice ions increases. More frequent collisions reduce the mean drift velocity of the electrons for a given potential difference, and therefore the resistance V/I increases.

Examiner tips

  • Use the term "free electrons" and "lattice ions". Explain the link between vibration amplitude and collision frequency. Show that increased collisions lower drift velocity, leading to higher resistance. Keep the answer concise and to the points.

Common mistakes

  • Confusing electrons with ions as the charge carriers. Failing to mention the increase in lattice vibration amplitude. Not linking collisions to mean drift velocity and resistance.

Mark scheme (4 marks)

  1. Free electrons act as the charge carriers responsible for current in a metallic conductor.
  2. As temperature increases, the positive ions in the lattice vibrate with greater amplitude.
  3. The more vigorously vibrating ions present a larger effective cross-sectional obstruction, increasing the frequency of collisions between free electrons and the lattice ions.
  4. More frequent collisions reduce the mean drift velocity of the electrons for a given potential difference, so resistance (V/I) increases.

Key terms in this question

resistance

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