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Resistance

Resistivity and the equation R = ρl/A

  • 3 things to know
  • Component 2

Overview

Resistivity of a material and typical value for the resistivity of copper at room temperature.

What you need to know

Answer each one before you reveal it.

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Key term

State the equation for the resistance of a uniform wire in terms of resistivity, defining every symbol and its unit.

Key term

Outline how the resistivity of a metal in the form of a wire is determined experimentally.

Key term

Why is the diameter of the wire measured at several places along it in a resistivity experiment?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    State the equation for the resistance of a uniform wire in terms of resistivity, defining every symbol and its unit.

    Model answer

    The equation is R = ρl/A, where R is the resistance in ohms (Ω), ρ is the resistivity in ohm metres (Ω m), l is the length in metres (m) and A is the cross-sectional area in square metres (m²).

  2. 2

    Define the resistivity of a material.

    Model answer

    The resistivity of a material is the resistance of a sample of it of unit length and unit cross-sectional area, and it is given by ρ = RA/l.

  3. 3

    Derive the unit of resistivity from R = ρl/A.

    Model answer

    Rearranging gives ρ = RA/l, so the unit is Ω × m² ÷ m. That simplifies to Ω m.

  4. 4

    Why is resistivity a more useful quantity than resistance when comparing two materials?

    Model answer

    Resistance depends on the size and shape of the sample, whereas resistivity is a property of the material alone at a given temperature.

  5. 5

    What is a typical value for the resistivity of copper at room temperature?

    Model answer

    Copper has a resistivity of about 1.7 × 10⁻⁸ Ω m at room temperature.

  6. 6

    A copper cable of length 50 m has a cross-sectional area of 2.5 mm². Calculate its resistance, taking ρ = 1.7 × 10⁻⁸ Ω m.

    Model answer

    The resistance is R = (1.7 × 10⁻⁸ × 50) ÷ (2.5 × 10⁻⁶) = 0.34 Ω. Substituting back, ρ = RA/l = 0.34 × 2.5 × 10⁻⁶ ÷ 50 = 1.7 × 10⁻⁸ Ω m.

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