In simple terms
A friendly intro before the formal notes — no formulas yet.
Resistance and resistivity
Cambridge 9702 Paper 2 — Resistance and resistivity (9.3). Senpai Corner diagram-backed pilot with premium structure and live visuals.
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9.3 Resistance and resistivity.
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Resistance , R of a conductor is the opposition to an electrical current.
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The higher the resistance of a conductor the more work needs to be applied to push the same amount of current through a conductor (Think friction when pushing a box).
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Resistance is measured in ohms, Ω.
What this topic covers
The official Cambridge syllabus points this lesson works through.
- 9.3.1
Define resistance
- 9.3.2
Recall and use
- 9.3.3
Sketch the I–V characteristics of a metallic conductor at constant temperature, a semiconductor diode and a filament lamp
- 9.3.4
Explain that the resistance of a filament lamp increases as current increases because its temperature increases
- 9.3.5
State Ohm's law
- 9.3.6
Recall and use
- 9.3.7
Understand that the resistance of a light-dependent resistor (LDR) decreases as the light intensity increases
- 9.3.8
Understand that the resistance of a thermistor decreases as the temperature increases (it will be assumed that thermistors have a negative temperature coefficient)
Explore the concept
Use the live diagram, PhET or GeoGebra sim, and synced steps — play it, drag controls, or tap a step.
Step-synced diagram — highlights what to look for in the simulation above.
Resistance R = V/I (Ohm’s law) for ohmic…
Resistance R = V/I (Ohm’s law) for ohmic conductors at constant temperature.
11 more simulations for this topic — run them in the Simulations section below
Simulations
Every simulation here runs the real model — try the steps on a card, then check what you see against the notes.
11 simulations · 5 to start with
Start herein this order — each one shows a different piece of the topic
- PhETStart here · 19702 9.2–9.3 · IB B.5
Ohm’s Law
Slide voltage and resistance; the current readout and formula resize live.
Why this one: I is proportional to V at fixed R; predict I for any pair, then check.
Try this
- Fix R = 500 Ω and double V — watch I double.
- Fix V = 4.5 V and double R — I halves.
- Pick any V and R, predict I, then check.
Look for I ∝ V at fixed R; I ∝ 1/R at fixed V.
Simulation by PhET Interactive Simulations, University of Colorado Boulder · Licensed to MarkScheme (public licence CC BY-NC 4.0 since 2026-03-30)
- 3JCN PhysicsStart here · 29702 9.2 · 9702 9.3 · IB B.5
Ohm's Law
Vary voltage and resistance; read current and plot V-I
Why this one: Plot V against I for a fixed resistor: a straight line through the origin with gradient R.
Try this
- Fix the resistance and double the voltage; read the current.
- Plot V against I and check for a straight line.
- Double the resistance and compare the gradient.
Look for For a fixed resistor V-I is a straight line through the origin with gradient R.
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
- 3JCN PhysicsStart here · 39702 9.3 · IB B.5
Heat Resistance
Heat a resistor and watch resistance change with temperature
Why this one: Heat the resistor and its resistance climbs, as a filament lamp's does once it glows.
Try this
- Heat the resistor and watch its resistance.
- Let it cool and compare.
Look for A metal's resistance rises with temperature because lattice vibrations scatter the electrons more.
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
- SimuPhysicsStart here · 49702 9.3 · IB B.5
Resistance, Collisions and Temperature
Inside a 3D copper sample an electron zig-zags between vibrating ion cores with its collisions counted; raise the temperature and watch R
Why this one: Count electron collisions as the ions vibrate harder: that is why a metal's R rises with temperature.
Try this
- Count the collisions at low temperature.
- Raise the temperature and count again.
- Read R against temperature.
Look for Resistance rises with temperature because the ion cores vibrate more and the electron collides more often.
Open on SimuPhysicsRuns on their siteSimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)
- PhETStart here · 5Java · best on a laptop9702 9.3 · IB B.5
Conductivity
Shine light on a metal, an insulator or a photoconductor and watch electrons move between energy bands and conduct.
Why this one: Metal, insulator, photoconductor: resistivity depends on how many carriers are free, and light can free them.
Try this
- Pick the metal and apply a voltage — electrons flow at once.
- Pick the insulator — no current even with the voltage up.
- Pick the photoconductor and turn on the light — electrons jump the gap and current flows.
Look for Resistivity depends on how many charge carriers are free: metals many, insulators none, photoconductors only when lit.
Simulation by PhET Interactive Simulations, University of Colorado Boulder · Licensed to MarkScheme (public licence CC BY-NC 4.0 since 2026-03-30)
More simulations6 more on this topic — core ones first
- PhETCoreJava · best on a laptop9702 9.1 · 9.3 · IB B.5
Battery-Resistor Circuit
Vary the battery voltage and the resistance; watch electrons move through the resistor and the resistor heat up.
Try this
- Raise the voltage — electrons move faster and the ammeter reads higher.
- Raise the resistance — the current falls and the atoms in the resistor jiggle more.
- Set the voltage to zero — electrons still move, but with no net drift.
Look for Current is the net drift of electrons; collisions with lattice atoms transfer energy and heat the resistor.
Simulation by PhET Interactive Simulations, University of Colorado Boulder · Licensed to MarkScheme (public licence CC BY-NC 4.0 since 2026-03-30)
- SimuPhysicsCore9702 9.3 · 9702 10.1 · IB B.5
Ohm's Law Lab — 3D Experiment
A 3D Ohm's law bench: switch, rheostat, ammeter and resistor in series, voltmeter across the resistor; each setting adds a V–I point
Try this
- Close the switch and record a V–I point.
- Slide the rheostat and record several more.
- Read the gradient of the V–I line.
Look for V is proportional to I for the resistor, and the gradient of the V–I line is its resistance.
Open on SimuPhysicsRuns on their siteSimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)
- 3JCN PhysicsCore9702 9.2 · 9702 9.3 · 9702 10.1
Ohm's Law - Resistors in Parallel
Ohm's law applied to resistors in parallel with meters
Try this
- Read each branch ammeter and the voltmeter.
- Check V = IR for each branch.
- Sum the branch currents and compare with the total.
Look for All branches share one voltage and the branch currents sum to the supply current.
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
- 3JCN PhysicsCore9702 9.2 · 9702 9.3 · 9702 10.1
Ohm's Law - Resistors in Series
Ohm's law applied to resistors in series with meters
Try this
- Read the ammeter and each voltmeter.
- Check V = IR for each resistor.
- Check that the voltmeter readings sum to the supply voltage.
Look for One current, and the sum of the resistor voltages equals the emf.
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
- 3JCN PhysicsCore9702 9.3 · IB B.5
Resistance & Resistivity
Vary wire length, area and material; read resistance and resistivity
Try this
- Double the wire length and read the resistance.
- Double the area and read it again.
- Change the material and compare the resistivity.
Look for R = ρL / A: resistance doubles with length and halves with area.
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
- SimuPhysics9702 9.1 · 9702 9.3 · IB B.5
Inside a Solid Conductor — Copper
A 3D copper lattice: Cu⁺ cores vibrate about fixed sites while free electrons move in the gaps between them
Try this
- Rotate the lattice and watch the cores vibrate.
- Follow one free electron.
- Compare the motion of cores and electrons.
Look for The ion cores stay in place while only the free electrons move through the lattice.
Open on SimuPhysicsRuns on their siteSimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)
Key formulas
Tap any symbol to reveal exactly what it means and its units.
Tap a symbol — great for exam definitions
Tap a symbol — great for exam definitions
Full topic notes
Formal explanation with the rigour you need for the exam.
Resistance: The Current's Obstacle Course
Resistance is a measure of how much a component opposes the flow of electric current. Imagine trying to run through a busy corridor – the more people (resistance), the harder it is to move quickly (current). A higher resistance means less current will flow for a given potential difference.
9.3 Resistance and resistivity.
Resistance , R of a conductor is the opposition to an electrical current.
The higher the resistance of a conductor the more work needs to be applied to push the same amount of current through a conductor (Think friction when pushing a box).
Resistance is measured in ohms, Ω.
Ohm’s Law states that the potential difference (V) is directly proportional to the Current (I) that flows through a conductor. 𝑅 = 𝑉 𝐼.
This law is only obeyed provided that the temperature and other physical properties remain constant and that the conductor is ohmic.
A Microscopic Look at Resistance
On a microscopic level, resistance in a metal conductor arises from collisions between the free-moving charge carriers (electrons) and the fixed positive ions that make up the crystal lattice. When a potential difference is applied, electrons are accelerated by the electric field, but these collisions hinder their overall progress, causing them to move with an average 'drift velocity'. The energy transferred during these collisions is dissipated as heat.
Resistance is caused by collisions between electrons and lattice ions.
These collisions convert electrical energy into thermal energy (Joule heating).
Increased temperature causes ions to vibrate with greater amplitude, increasing the frequency of collisions and thus increasing resistance.
Ohm's Law: The Golden Rule for Conductors
Ohm's Law describes a specific relationship where the current through a conductor is directly proportional to the potential difference across it, provided its temperature remains constant. Components that follow this rule are called ohmic conductors.
For ohmic conductors, (constant temperature).
An ohmic conductor's current-voltage (I-V) graph is a straight line through the origin.
This implies a constant resistance value for ohmic materials.
Crucially, temperature must remain constant for Ohm's Law to hold.
Non-Ohmic Conductors: Breaking the Linearity
Not all components obey Ohm's Law. Non-ohmic conductors have resistance values that change depending on factors like temperature or current. Their I-V graphs are not linear, showing how their resistance varies.
— Filament Lamps: Heat-Sensitive Resistance
A common example of a non-ohmic component is a filament lamp. As more current flows through the filament, it heats up significantly. This increase in temperature causes the metal atoms in the filament to vibrate more vigorously, making it harder for electrons to pass through.
Filament lamps are non-ohmic devices.
Their resistance increases as current (and thus temperature) rises.
Increased atomic vibrations impede electron flow.
This leads to a curve on their I-V graph, not a straight line.
— Semiconductor Diodes: Directional Flow
Semiconductor diodes are another key non-ohmic component. They allow current to flow easily in one direction (forward bias) once a small threshold voltage is overcome, but offer very high resistance to current flow in the opposite direction (reverse bias). They act like one-way valves for electricity.
Diodes are non-ohmic components, allowing current mainly one way.
They have very low resistance in 'forward bias' after a threshold voltage.
They exhibit extremely high resistance in 'reverse bias'.
Their I-V graph is distinctly non-linear and asymmetrical.
Resistivity: The Material's Inner Resistance
While resistance depends on a component's specific dimensions (length and cross-sectional area), resistivity is an intrinsic property of the material itself. It tells us how inherently good or bad a material is at conducting electricity, regardless of its shape or size. Think of it as a fingerprint for a material's electrical behaviour.
Resistivity () is a fundamental material property.
It measures a material's inherent ability to resist charge flow.
Independent of the conductor's length () or cross-sectional area ().
Unit: Ohm-metre (m).
Lower resistivity means a better conductor (e.g., copper).
Higher resistivity means a poorer conductor (e.g., nichrome).
Calculating Resistance from Resistivity
The formula can be rearranged to find the resistance of a specific wire or component if you know its material's resistivity, its length, and its cross-sectional area: . This is vital for designing circuits and selecting appropriate wires.
— Thermistors: Temperature-Sensitive Resistors
Thermistors are semiconductor devices whose resistance changes significantly with temperature. Unlike metals, most common thermistors (NTC - Negative Temperature Coefficient) experience a decrease in resistance as their temperature increases. This is because higher temperatures free more charge carriers, increasing conductivity.
Thermistors are semiconductor devices sensitive to temperature.
Their resistance typically decreases as temperature increases.
Increased thermal energy releases more charge carriers.
Commonly used as temperature sensors in control systems (e.g., thermostats).
— Light-Dependent Resistors (LDRs): Light Sensors
Light-Dependent Resistors (LDRs) are semiconductor components whose resistance is influenced by light intensity. When exposed to brighter light, more electrons are excited and become free charge carriers, causing the LDR's resistance to decrease.
LDRs are semiconductor components sensitive to light intensity.
Their resistance decreases with increasing intensity of incident light.
More light energy frees up more charge carriers.
Used as light sensors in automatic lighting, security systems, etc.
— Superconductors: The Ultimate Conductors
Superconductors are extraordinary materials that exhibit absolutely zero electrical resistivity when cooled below a specific, material-dependent critical temperature. This means current can flow indefinitely without any energy loss due to resistance. While most have very low critical temperatures, research continues to find higher temperature superconductors.
Superconductors have zero electrical resistivity.
This occurs below a specific critical temperature, .
is unique to each superconducting material.
Potential uses include lossless power transmission and powerful electromagnets (e.g., in MRI scanners).
Ideal Measuring Instruments
When we analyse circuits, we often consider ideal measuring instruments to simplify calculations and understand their purpose. These ideals represent the perfect scenario for measurement.
Ideal ammeters are assumed to have zero resistance.
This ensures they accurately measure current without affecting the circuit.
Ideal voltmeters are assumed to have infinite resistance.
This prevents current from flowing through them, allowing accurate PD measurement.
Always remember the condition for Ohm's Law: constant temperature. If temperature changes, resistance might change, and the component is likely non-ohmic. Pay close attention to this detail in exam questions!
Worked examples
See the formulas applied — reveal one step at a time, like the exam.
A copper wire has a resistivity of . If the wire is 2.5 metres long and has a diameter of 0.5 mm, calculate its resistance.
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Convert diameter to radius and metres:
A 50.0 cm length of nichrome wire has a diameter of 0.80 mm. When a potential difference of 2.0 V is applied across its ends, a current of 1.83 A is measured. Calculate the resistivity of the nichrome.
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Calculate the wire's resistance () using Ohm's Law:
How it all connects
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Tap a linked idea to see how it connects back to the main topic — that connection is what examiners reward.
Glossary
Key terms for this topic — skim now; the Check step will test them.
- resistivity
While resistance depends on a component's specific dimensions (length and cross-sectional area), resistivity is an intrinsic property of the material itself.
- critical temperature
Superconductors are extraordinary materials that exhibit absolutely zero electrical resistivity when cooled below a specific, material-dependent critical temperature. This means current can flow indefinitely without any energy loss due to resistance.
Quick check
Write your answer first, then compare it with the model one — the gap is what you would have lost.
Teach it back
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Revision flashcards
Guess first, then flip — retrieval beats re-reading.
Key takeaways
Review these before you close the topic — retrieval beats re-reading.
9.3 Resistance and resistivity.
Resistance , R of a conductor is the opposition to an electrical current.
The higher the resistance of a conductor the more work needs to be applied to push the same amount of current through a conductor (Think friction when pushing a box).
Resistance is measured in ohms, Ω.
Ohm’s Law states that the potential difference (V) is directly proportional to the Current (I) that flows through a conductor. 𝑅 = 𝑉 𝐼.
This law is only obeyed provided that the temperature and other physical properties remain constant and that the conductor is ohmic.
Practice — then mark it
The whole point: a real Cambridge question, marked mark-by-mark.
the p.d. measured by the voltmeter.
Use Fig. 6.2 to determine: resistance R
Extra simulations & links
PhET, GeoGebra and other curated tools — open in a new tab.
Frequently asked
Checkpoint
One marked question is worth ten re-reads — close the loop before you move on.
Reading it isn’t knowing it — prove it.
Before you move on: do 9702/23 · Q5(c)(ii) on paper, snap a photo, and get examiner-style feedback on exactly where you win and lose marks.
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