Resistivity — Quick Revision

Mr Toogood's Physics · Electricity basics

AQA 3.5.1.3
R = ρl/A
Resistivity
ρ = RA/l
Rearranged
Ω m
Units of ρ
R = 0
Superconductor, T≤T꜀

Resistivity basics

Resistance depends on a material's resistivity (ρ) and the conductor's dimensions: longer wires collide electrons more; thicker wires give more paths for charge to flow.

Resistance increasing with the length of a conductor

Resistance increases with length, decreases with cross-sectional area.

  • R ∝ l — double the length, double the resistance.
  • R ∝ 1/A — double the area, halve the resistance.
  • ρ is a fixed material property at constant temperature — not dependent on shape.
Choosing conductors: lower ρ = better conductor (e.g. copper < aluminium), but real choices trade off ρ against other properties — aluminium for power lines (lighter, stretches less), gold for contacts (unreactive, won't tarnish).

Semiconductors & thermistors

Semiconductors conduct better when given energy (heat or light), freeing more charge carriers from the valence band into the conduction band.

NTC thermistor resistance against temperature graph

NTC thermistor: resistance falls sharply as temperature rises.

  • NTC thermistor (only type in this spec): resistance decreases as temperature increases.
  • Intrinsic semiconductors (thermistor, LDR): undoped; equal holes & conduction electrons.
  • Extrinsic semiconductors (diode, LED): doped N-type/P-type; conduct above ~0.7 V threshold.

Superconductors

YBCO resistance dropping to zero at its critical temperature

Resistance drops to exactly zero at the critical temperature, T꜀.

A superconductor has zero resistivity at or below its critical temperature T꜀. E.g. mercury: 4.2 K; YBCO ceramic: 92 K. The Meissner effect excludes magnetic fields, enabling levitation (MAGLEV).

Exam essentials

How R changes with T

  • Metals: R increases with T (more ion vibration → more collisions).
  • NTC thermistor: R decreases with T (more charge carriers freed).
  • Superconductor: R = 0 exactly, at or below T꜀.

Superconductor uses

  • Strong magnetic fields with no energy loss: MRI scanners, particle accelerators.
  • Zero-loss power transmission (if room-temp superconductors are developed).

Common slips

  • Convert mm → m before substituting into ρ = RA/l.
  • Use A = πD²/4 directly from a given diameter — no need to halve first.
  • Don't confuse resistivity (material property) with resistance (also depends on shape).