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Course: OCR A Level Physics A H556
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OCR A Level Physics A H556

1. Development of Practical Skills in Physics

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2. Foundations in Physics

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3. Forces and Motion

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4. Electrons, Waves and Photons

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OCR H556 chapter questions and answers

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Text lesson

4.2.5 Resistivity

4.2.5 Resistivity: Define resistivity, use R = ρL/A to find the resistance of wires, and compare materials.

4.2.5 Resistivity
Length
  • For a given material and cross-section, resistance is proportional to the length of the conductor.
Cross-sectional area
  • Resistance is inversely proportional to the area, because a wider wire gives more paths for charge flow.
Material
  • Different materials have different numbers of charge carriers, which is accounted for by resistivity.
Temperature
  • For a metal, resistance rises with temperature as ions vibrate more and impede the electrons.
The Resistivity Equation
Equation
  • R = ρL/A, where R is resistance, L is length, A is cross-sectional area and ρ is resistivity.
Rearranging
  • The resistivity can be found from ρ = RA/L.
Unit
  • Resistivity is measured in ohm metres, written Ω m.
Meaning
  • Resistivity is a property of the material, equal to the resistance of a sample of unit length and unit area.
Material Resistivity (Ω m) Note
Copper 1.7 × 10⁻⁸ Very good conductor
Constantan 4.9 × 10⁻⁷ Used in resistance wire
1

Write down the known quantities and convert them to SI units.
2

For a round wire, find the area from A = πd²/4 or πr², using a diameter in metres.
3

Substitute into R = ρL/A, or rearrange to find another quantity.
4

Check the unit, since a diameter given in mm must be converted to metres before squaring.
5

Comment on the size of the answer, such as whether the resistance is small for a short copper wire.
Double the length
  • Doubling the length of a wire doubles its resistance because ρ and A stay unchanged.
Double the diameter
  • Doubling the diameter multiplies the area by four, so the resistance falls to a quarter.
Same wire, new material
  • A material with a higher resistivity gives a proportionally higher resistance for the same dimensions.
Choosing materials
  • Cables use low-resistivity copper while heating elements use higher-resistivity alloys.

Question: A copper wire of length 2.5 m has diameter 0.30 mm. The resistivity of copper is 1.7 × 10⁻⁸ Ω m. Calculate its resistance.

  1. Diameter = 0.30 × 10⁻³ m, so area A = π d² / 4 = π × (0.30 × 10⁻³)² / 4 = 7.07 × 10⁻⁸ m².
  2. R = ρL/A = 1.7 × 10⁻⁸ × 2.5 / 7.07 × 10⁻⁸.
    What the symbols mean: R = resistance (Ω) · ρ = resistivity (Ω m) · L = length (m) · A = cross-sectional area (m2)
  3. R = 4.25 × 10⁻⁸ / 7.07 × 10⁻⁸ = 0.60 Ω.

Answer: The resistance is 0.60 Ω.

4.2.5 – Key Points for the Exam

  • Resistivity: A property of a material equal to RA/L, measured in Ω m.
  • Resistance: The ratio of potential difference to current, R = V/I.
  • Cross-sectional area: The area of the end face of a wire, π d²/4 for a circular wire.
  • Ohm metre: The SI unit of resistivity.
  • Conductor: A material that allows charge to flow easily.

Common Mistakes

  • Using the diameter instead of the area, or forgetting the factor of one quarter in A = πd²/4.
  • Not converting millimetres to metres before calculating the area.
  • Quoting the resistivity in ohms rather than ohm metres.
  • Thinking resistivity depends on the length of the particular wire; it depends on the material only.
YOUR STUDY PATH

4.2.5 Resistivity

OCR A Level Physics A H556 / 4. Electrons, Waves and Photons

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