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.
- 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.
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.
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.
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 says that current is directly proportional to potential difference for an ohmic conductor, provided temperature and other physical conditions stay constant.
I–V characteristics
What the graphs mean
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.
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
What resistivity really means
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.
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.
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
Why the trends differ
An LDR changes resistance with light intensity. An NTC thermistor changes resistance with temperature. OCR expects you to recognise both as non-ohmic components.
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.
Worked examples
Knowledge Check
- Resistance depends on the component / dimensions as well as the material
- Resistivity is a property of the material itself
- Temperature / physical conditions must remain constant
- Resistance decreases
- The ions vibrate more strongly
- This causes more collisions for charge carriers / makes current harder to flow
Exam-Style Questions
- ρ = RA / L
- ρ = (4.8 × 2.0 × 10−6) / 1.5
- ρ = 6.4 × 10−6 Ω m
- 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
- 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
- Higher temperature frees / provides more charge carriers in the semiconductor
- This makes current easier to flow, so resistance decreases
Topic Summary
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.