Resistance and resistivity

AS Level Physics · Electricity. A short explanation of the idea, the rules to remember, the mistake to avoid, a worked example and practice questions with answers.

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The idea

Resistance is the p.d. across a component divided by the current in it. It tells you how hard it is to drive current through that component. For a metal wire at constant temperature the resistance is constant, so current is proportional to p.d. This is Ohm's law.

Many components do not behave like this. A filament lamp gets hotter as the current rises, the metal ions vibrate more, electrons collide with them more often, and the resistance goes up. A diode conducts in one direction only.

The resistance of a wire depends on its size and on its material. Resistivity describes the material alone.

Rules to remember

Common mistake

Resistance is V ÷ I read at one point on the graph. It is not the gradient of an I–V graph (or its inverse) unless the graph is a straight line through the origin.

Worked example

A wire is 1.5 m long and has a cross-sectional area of 3.0 × 10−7 m2. Its material has resistivity 4.9 × 10−7 Ω m. What is its resistance?

  1. Use R = ρL/A.
  2. ρL = 4.9 × 10−7 × 1.5 = 7.35 × 10−7 Ω m2.
  3. R = 7.35 × 10−7 ÷ 3.0 × 10−7 = 2.45 Ω.

Answer: The resistance is 2.5 Ω (to 2 significant figures).

Practice questions

Try each one, then open the answer.

1. How is the resistance of a component defined?

  1. A
    the gradient of its I–V graph
  2. B
    the current in it divided by the p.d. across it
  3. C
    the p.d. across it divided by the current in it
  4. D
    the p.d. across it per unit length
Show answer

Answer: C. R = V/I at any point. The gradient of an I–V graph is ΔI/ΔV, which is not the resistance, especially for a non-ohmic component.

2. A metal wire of resistance R is stretched uniformly until its length is doubled. Its volume and resistivity stay the same. What is its new resistance?

  1. A
    R/2
  2. B
    2R
  3. C
    4R
  4. D
    8R
Show answer

Answer: C. Doubling the length at constant volume halves the area. R = ρL/A, so R is multiplied by 2 × 2 = 4.

3. Which statement is Ohm's law?

  1. A
    V = IR for every component
  2. B
    the current in a metallic conductor is proportional to the p.d. across it, provided temperature and other physical conditions are constant
  3. C
    resistance equals p.d. divided by current
  4. D
    power equals current times voltage
Show answer

Answer: B. V = IR defines resistance for any component; Ohm's law is the statement that I ∝ V for an ohmic conductor at constant temperature.

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