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LearnYPH11WPH12 · Unit 2: Waves and ElectricityElectric circuitsResistance and resistivity
Electric circuits · Subtopic 5 of 6

Resistance and Resistivity

Resistance is R=VIR=\dfrac VI. A metal at constant temperature obeys Ohm's law: current is proportional to p.d. A wire's resistance depends on its material, length and area: R=ρLAR=\dfrac{\rho L}A, where the resistivity ρ\rho is a material property. Filament lamps, diodes, thermistors and LDRs have non-ohmic, changing resistances.

Cambridge 9702 Paper 1Cambridge 9702 Paper 2Edexcel YPH11 WPH12AQA 7408 Paper 1≈ 35 minRevision 6 · updated 2026-10-27
Section 1 of 14

Learning objectives

  • Use V=IRV=IR and state Ohm's law.
  • Use R=ρLAR=\dfrac{\rho L}A and describe how to measure resistivity.
  • Sketch and explain II–VV characteristics of a metal, a filament lamp and a diode.
  • Describe how thermistors and LDRs respond to temperature and light.
Pause and think

You stretch a wire to twice its length without changing its volume. What happens to its resistance?

Section 2 of 14

Core idea

Start hereCopper or nichrome?

House wiring uses copper; toaster elements use nichrome. A wire's resistance depends on its length and thickness, but also on the material itself. Resistivity captures the material part.

The big idea

R=VIR=\frac VI; R=ρLAR=\frac{\rho L}A, ρ\rho depends on material and temperature.

1. I–V characteristics

I–V characteristics
−6−4−2246−1−0.50.510V (V)I (A)ohmic resistorfilament lampdiode
Lamp: the filament heats, atoms vibrate more and impede electrons, so RR rises. Diode: conducts only above about 0.6 V forwards.
  • Metal at constant temperature: ohmic.
  • Filament lamp: RR rises as it heats.
  • Diode: conducts forward above ~0.6 V.

2. Resistivity

R=ρLAR=\frac{\rho L}A
where
ρ\rho
resistivity (Ω m).
LL
length.
AA
cross-sectional area.
Worked exampleNichrome wire

ρ=1.1×10−6\rho=1.1\times10^{-6} Ω m, L=1.5L=1.5 m, d=0.40d=0.40 mm.

Goal
RR.
Strategy
Area from radius.
  1. A=π(0.20×10−3)2=1.26×10−7 m2A=\pi(0.20\times10^{-3})^2=1.26\times10^{-7}\text{ m}^2
    Radius 0.20 mm.
  2. R=1.1×10−6×1.51.26×10−7=13 ΩR=\frac{1.1\times10^{-6}\times1.5}{1.26\times10^{-7}}=13\ \Omega
    Formula.
Answer13 Ω13\ \Omega.
✓ CheckCopper (ρ ~60× smaller) would be about 0.2 Ω ✓.
Worked exampleStretched wire

Stretched to twice its length, same volume.

Goal
New RR.
Strategy
L×2L\times2, A÷2A\div2.
  1. R′=ρ(2L)A/2R'=\frac{\rho(2L)}{A/2}
    Volume ALAL fixed.
  2. =4R=4R
    Simplify.
Answer×4\times4.
✓ CheckBoth changes increase RR ✓.

3. Sensors

Thermistor (NTC): resistance falls as it warms
20406080100246810120temperature (°C)resistance (kΩ)NTC thermistor
More charge carriers are released at higher temperature. An LDR behaves similarly with light intensity.
  • NTC thermistor: RR falls as temperature rises.
  • LDR: RR falls as light intensity rises.
Common misconceptionResistance vs resistivity Resistance belongs to the sample; resistivity to the material.

Summary

  • R=ρL/AR=\rho L/A.
  • I–V shapes.
Key words
Resistivity
Resistance of a 1 m cube of the material.
HistorySuperconductivity's surprise. In 19111911 Heike Kamerlingh Onnes cooled mercury to 4.24.2 K with liquid helium and found its resistance suddenly dropped to zero. Superconductivity wasn't explained until 19571957, and "high-temperature" superconductors discovered in 19861986 still need cooling below about −140-140 °C.
Fun factYour body as a resistor. Dry skin can have a resistance of 100 000100\,000 Ω, but wet skin drops to about 10001000 Ω. That's why electrical appliances and water are such a dangerous mix: the same voltage drives a hundred times the current.
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