Resistance and Resistivity — OCR A Level Physics
Module 4 · Electrons, waves and photons

Resistance and Resistivity

Specification: OCR A H556  |  Section: 4.2 Energy, power and resistance  |  Focus: resistance, Ohm’s law, I–V characteristics, LDRs, resistivity, temperature effects and NTC thermistors. Scope note: superconductivity is useful enrichment but is not explicitly listed in OCR H556 4.2.3–4.2.4, so it is included only as a short extension note.

By the end of this topic you should be able to…
  • define resistance using R = V / I and explain what it means physically
  • state and apply Ohm’s law for ohmic conductors
  • interpret I–V graphs for a resistor, filament lamp, diode and LED
  • use and rearrange ρ = RA / L and R = ρL / A
  • explain how length, area, material and temperature affect resistance
  • describe why metals and semiconductors behave differently with temperature

Big idea: resistance is about how hard it is for charge to pass through a component. Resistivity goes one layer deeper — it tells you how strongly the material itself resists current.

Part 1

Key ideas in pupil-friendly language

Resistance

Resistance tells you how much a component opposes the flow of charge. Large resistance means a given current needs a bigger potential difference.

Resistivity

Resistivity is a property of the material itself. It tells you how strongly that material resists current, independent of the wire’s exact dimensions.

Ohmic conductor

An ohmic conductor obeys Ohm’s law at constant temperature, so current is directly proportional to potential difference.

I–V characteristic

An I–V characteristic is a graph showing how current changes when the potential difference changes.

Negative temperature coefficient

A negative temperature coefficient means resistance decreases when temperature increases. NTC thermistors behave like this.

Part 2

Resistance and Ohm’s law

Resistance links potential difference and current. If a component has a larger resistance, the same current needs a larger potential difference across it.

Definition of resistanceR = V / I

Here R is resistance in ohms (Ω), V is potential difference in volts, and I is current in amperes. One ohm means one volt is needed to drive one ampere.

Ohm’s law

Ohm’s law says that current is directly proportional to potential difference for an ohmic conductor, provided temperature and other physical conditions stay constant.

I–V characteristics

Ohmic Conductor I V Filament Bulb I V Diode I V
An ohmic resistor gives a straight line through the origin. A filament lamp curves because heating changes resistance. A diode allows current mainly in one direction after a threshold.

What the graphs mean

Meaning of I-V graphs ohmic resistor constant temperature R stays constant filament lamp heats up as current rises R increases diode hardly any current until threshold one-way behaviour
The key exam skill is not just recognising the shape, but linking the shape to changing resistance inside the component.
Part 3

Resistivity and what controls resistance

Resistance depends on the dimensions of the wire as well as the material. A longer wire gives charges more collisions. A thicker wire gives more space for charge to pass through.

Resistivity equationR = ρL / A

ρ is resistivity in Ω m, L is length in m, and A is cross-sectional area in m². Rearranging gives ρ = RA / L.

Wire geometry: length and area

ρ = resistivity L = length A = area = R R = ρ L A
For the same material: increasing L increases resistance, while increasing A decreases resistance.

What resistivity really means

Low and high resistivity materials low ρ charges pass more easily high ρ material opposes current more
Low resistivity materials allow charge to move more easily. High resistivity materials give stronger opposition even if the wire sizes are the same.
Drift velocity explorer: see how L, A and ρ affect electron speed and resistance
R = 0.34 Ω
I = 35.3 A
Drift speed ∝ 1/R

Electrons drift faster when resistance is lower (shorter wire, larger area, lower resistivity). Watch how the particles speed up or slow down as you change each slider.

Part 4

Temperature effects

Temperature changes resistance because it changes how easily charge carriers move through the material. To understand this properly, you need the idea of number density.

Drift velocity equationI = n A v e

Here n is the number density of charge carriers in m−3, A is cross-sectional area, v is drift velocity, and e is the charge on an electron. The number density tells you how many free charge carriers are available per cubic metre.

Metals

n is very high and roughly constant with temperature. Higher temperature means more lattice vibration, so electrons collide more often and resistance increases.

Semiconductors

n is much smaller, but it increases strongly with temperature as more electrons are freed to conduct. This makes resistance decrease as temperature rises.

NTC thermistor

A negative temperature coefficient thermistor is made from semiconductor material. Its resistance falls as temperature rises because n increases faster than any extra scattering.

Resistance against temperature

Resistance and temperature temperature R metal semiconductor NTC thermistor
Metals usually show increasing resistance as temperature rises. Semiconductors and NTC thermistors show decreasing resistance because more charge carriers become available.

Why the trends differ

Why temperature trends differ metal higher temperature → ions vibrate more → more collisions → n constant, R increases semiconductor / NTC higher temperature → more charge carriers freed → n increases strongly → R decreases
In metals, extra scattering dominates. In semiconductors, the increase in number density n dominates and reduces the overall resistance.
LDR and thermistor

An LDR changes resistance with light intensity. An NTC thermistor changes resistance with temperature. OCR expects you to recognise both as non-ohmic components.

Extension note

Superconductivity is a state where resistance falls to zero below a critical temperature in certain materials. This is useful enrichment, but it is not a named OCR H556 4.2.3–4.2.4 requirement, so do not let it replace the core exam content above.

Part 5

Worked examples

Worked example 1
A resistor has a potential difference of 6.0 V across it and a current of 0.30 A through it. Calculate the resistance.
Use R = V / I
R = 6.0 / 0.30
R = 20 Ω
Worked example 2
A metal wire has length 2.5 m, cross-sectional area 1.2 × 10−6 m² and resistivity 1.7 × 10−8 Ω m. Calculate its resistance.
Use R = ρL / A
R = (1.7 × 10−8 × 2.5) / (1.2 × 10−6)
R = 3.54 × 10−2 Ω
R ≈ 0.035 Ω
Worked example 3
A student measures the resistance of a thermistor as temperature rises. The resistance falls. Explain why this means the thermistor has a negative temperature coefficient.
Negative temperature coefficient means resistance decreases when temperature increases.
That is exactly the trend described.
So the thermistor is an NTC thermistor.
Knowledge

Knowledge Check

1
What is the difference between resistance and resistivity?
2 marks
  • Resistance depends on the component / dimensions as well as the material
  • Resistivity is a property of the material itself
2
State the condition needed for Ohm’s law to hold.
1 mark
  • Temperature / physical conditions must remain constant
3
How does increasing cross-sectional area affect resistance for the same material and length?
1 mark
  • Resistance decreases
4
Why does the resistance of a metal usually increase with temperature?
2 marks
  • The ions vibrate more strongly
  • This causes more collisions for charge carriers / makes current harder to flow
Exam Practice

Exam-Style Questions

1
A metal wire has resistance 4.8 Ω, length 1.5 m and cross-sectional area 2.0 × 10−6 m². Calculate the resistivity of the material. adapted from local OCR question-bank theme: resistivity
3 marks
  • ρ = RA / L
  • ρ = (4.8 × 2.0 × 10−6) / 1.5
  • ρ = 6.4 × 10−6 Ω m
2
Describe and explain the shape of the I–V graph for a filament lamp. real OCR-style theme found in local bank
3 marks
  • It is curved / not a straight line
  • As current increases the filament heats up
  • Its resistance increases, so current rises less quickly for each extra volt
3
A student says “if a wire has high resistance then the material must have high resistivity”. Explain why this is not always true. generated exam-style
3 marks
  • Resistance also depends on length and cross-sectional area
  • A long thin wire can have large resistance even if resistivity is modest
  • Resistivity is the material property, not the whole component property
4
Explain why the resistance of an NTC thermistor decreases when temperature increases. generated exam-style
2 marks
  • Higher temperature frees / provides more charge carriers in the semiconductor
  • This makes current easier to flow, so resistance decreases
Summary

Topic Summary

Resistance and Resistivity

Resistance

R = V / I. It measures how much a component opposes current.

Ohm’s law

For an ohmic conductor at constant temperature, current is directly proportional to potential difference.

Resistivity

R = ρL / A. Longer wires have larger resistance, thicker wires have smaller resistance.

Temperature

Metals usually gain resistance as temperature rises. Semiconductors and NTC thermistors usually lose resistance.

4.2.3 resistance 4.2.4 resistivity I–V characteristics NTC thermistor