4.2ElectricityCore

Resistivity

Resistance depends on shape — a long, thin wire always resists current more than a short, thick one made of exactly the same metal. Strip that shape-dependence away, and you’re left with a number that describes the material alone: resistivity.

35 min Video by vt.physics Module 4.2 Energy, power and resistance

Resistivity — A Level PhysicsWatch the full walkthrough before the notes below.

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What you'll be able to do

Use the resistivity equation $R = \frac{ρ L}{A}$
Explain how the resistance of a metal changes with temperature
Explain how the resistance of an NTC thermistor changes with temperature
Describe superconductivity

The resistivity equation

$Resistivity$ , $ρ$ , describes a material’s intrinsic opposition to current flow, independent of the sample’s length or cross-sectional area, measured in ohm-metres.

R = \frac{ρ L}{A}

Resistance from resistivity, length and cross-sectional area.

1Use

R = \frac{ρ L}{A}

R = \frac{4.9 \times 1 0 ^{- 7} \times 3.0}{2.0 \times 1 0 ^{- 7}}

Answer

R \approx 7.4 Ω

Temperature dependence of metals

As a metal’s temperature rises, its positive ions vibrate more vigorously, so free electrons collide with them more frequently as they drift through the material. More frequent collisions mean greater resistivity, and hence greater resistance, as temperature rises.

NTC thermistors

An NTC (negative temperature coefficient) thermistor behaves oppositely to a metal: rising temperature frees many more charge carriers within its semiconductor material, and this large increase in available carriers outweighs the increased collision rate, so its resistance falls sharply as temperature rises.

Tip — Metal: resistance rises with temperature. NTC thermistor: resistance falls with temperature. The two behave in exactly opposite ways, for opposite underlying reasons.

Superconductivity

Certain materials, cooled below a very low critical temperature, undergo a sudden transition to exactly zero resistivity — a genuinely different regime from simply "very low resistance". Below this temperature, current flows with no energy dissipated as heat at all, a property exploited in powerful electromagnets such as those used in MRI scanners.

Equation recap

R = \frac{ρ L}{A}

Resistance from resistivity.

Common mistakes to avoid

Believing resistivity changes if a wire is cut shorter.

Resistivity is a property of the material only; cutting the wire changes its resistance (via L) but not its resistivity.

Assuming an NTC thermistor behaves like a metal as temperature rises.

A thermistor’s resistance DECREASES with rising temperature, the opposite of a metal, because far more charge carriers become available.

Describing a superconductor as having "very low" resistance.

Below its critical temperature, resistivity is exactly zero — a distinct physical state, not merely a small value on the usual scale.

Key takeaways

Resistance R = ρL/A; resistivity ρ is a property of the material alone.
A metal’s resistance increases with temperature (more frequent lattice collisions).
An NTC thermistor’s resistance decreases sharply with temperature (more charge carriers freed).
Below its critical temperature, a superconductor has exactly zero resistivity.

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Resistivity

35 min Video by vt.physics Module 4.2 Energy, power and resistance