In simple terms
A friendly intro before the formal notes — no formulas yet.
The 'Push' and 'Speed' of Electricity
Potential difference (voltage) is like the 'push' given to each unit of charge, telling us how much energy it gains or loses. Power then describes how quickly this electrical energy is being moved or converted into other forms.
Imagine a water slide. Potential difference is like the height difference the water gets at the top, giving each litre of water a certain amount of potential energy. Power is how many litres per second rush down the slide, indicating how quickly that energy is being converted into kinetic energy and heat.
- 1
Define the 'Push': Potential Difference (V) measures the energy transferred per unit charge.
- 2
Define the 'Speed': Power (P) measures the rate at which energy is transferred or dissipated.
- 3
Connect Them: Electrical power is the product of potential difference and current ().
- 4
Calculate Total Energy: Total electrical energy is power multiplied by the time it's transferred ().
What this topic covers
The official Cambridge syllabus points this lesson works through.
- 9.2.1
Define the potential difference across a component as the energy transferred per unit charge
- 9.2.2
Recall and use
- 9.2.3
Recall and use , and
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.
Step 1
Define the 'Push': Potential Difference (V) measures the energy transferred per unit charge.
10 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.
10 simulations · 4 to start with
Start herein this order — each one shows a different piece of the topic
- 3JCN PhysicsStart here · 19702 9.2 · 9702 9.3 · 9702 10.1
Ohm's Law - Resistors in Series
Ohm's law applied to resistors in series with meters
Why this one: The voltmeter readings across the resistors add up to the e.m.f.: energy per coulomb is shared out.
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
- SimuPhysicsStart here · 29702 9.2 · IB B.5
Electric Power and Energy
A 3D bench of appliances: read each rating plate, work out R from V²/P, and compare the three power formulae, including the motor
Why this one: Read a rating plate, find R from V²/P and check P = VI = I²R agree for the heater.
Try this
- Read the lamp's rating plate and work out R.
- Compare the three power formulae for the heater.
- Select the motor and compare again.
Look for P = VI = I²R = V²/R for a resistor, while a motor's V is not IR.
Open on SimuPhysicsRuns on their siteSimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)
- PhETStart here · 39702 9.2–9.3 · IB B.5
Ohm’s Law
Slide voltage and resistance; the current readout and formula resize live.
Why this one: Fix R and double V: I doubles, so P = IV goes up four times.
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)
- PhETStart here · 4Java · best on a laptop9702 9.2 · IB B.5
Battery Voltage
Turn the battery voltage up and down and watch charges separate onto the two terminals.
Why this one: Turn the voltage up and more charge separates: e.m.f. is the energy spent per coulomb.
Try this
- Set a small voltage — a few charges collect on each terminal.
- Turn it up — more charge separates and the terminals grow more positive and negative.
- Reverse the voltage — the terminals swap sign.
Look for EMF is the energy per coulomb the battery spends separating charge: higher voltage, more separation.
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
- The Physics ClassroomCore9702 9.1 · 9702 9.2 · 9702 10.1
DC Circuit Builder
A virtual circuit board: add resistors, bulbs, wires and ammeters, use a voltmeter, and build series, parallel and combination circuits
Try this
- Build a series circuit and read the ammeter.
- Rebuild the same resistors in parallel and compare.
- Measure the voltage across each resistor with the voltmeter.
Look for Current is the same everywhere in series, and voltage is the same across parallel branches.
Physics Interactives by The Physics Classroom · Licensed to MarkScheme (site terms otherwise permit linking only)
- SimuPhysicsCore9702 9.2 · 9702 10.3 · IB B.5
Potential Difference and the Earthed Point
A 3D circuit with an earth rod and a landscape of potential above it; move the earth clip and the landscape slides without any difference changing
Try this
- Read the potential at each node.
- Move the earth clip and read them again.
- Compare the differences between nodes.
Look for Moving the earthed point shifts every potential by the same amount and leaves every potential difference unchanged.
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 · IB B.5
Ohm's Law
Vary voltage and resistance; read current and plot V-I
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 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
- PhysicsHubCore9702 10.2 · 9702 10.1 · 9702 9.2
Kirchhoff's Circuit Laws
Four DC circuits; set each EMF, internal resistance and the three resistances, drag a voltmeter and ammeter on; watch the KCL and KVL sums balance to zero
Try this
- Pick the series circuit and read the current with the ammeter.
- Switch to parallel and compare the currents in each branch.
- Raise the internal resistance and read the terminal voltage.
Look for Currents into each junction sum to zero and the voltages around each loop sum to the EMF.
PhysicsHub (@mattqdev) · MIT
- SimuPhysics9702 9.1 · 9702 9.2 · IB B.5
Electric Circuit Analogy
A water circuit runs alongside an electric one: pumps for cells, narrow pipes for resistors, flow rate for current
Try this
- Compare the pump with the cell.
- Narrow a pipe and compare with a resistor.
- Compare the flow rate with the current.
Look for Flow rate matches current and the pump's pressure matches the cell's e.m.f.
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
Tap a symbol — great for exam definitions
Tap a symbol — great for exam definitions
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.
What is Potential Difference (p.d.)?
Potential difference, often shortened to p.d. or simply voltage, tells us how much energy is transferred when a unit of charge moves between two points in a circuit. Essentially, it quantifies the "energy push" that charges receive (e.g., from a battery) or the "energy drop" as they pass through a component (e.g., a resistor).
9.2 Potential difference and power.
Potential difference is defined as the work done to transfer one unit of charge across two points of different potential (charge). 𝑉 = 𝑊 𝑄.
Here V is the potential difference in volts (V), W is the work done in joules and Q is the charge in coulombs.
Recall that power is the rate of work done or rate of energy transferred i.e. 𝑃 = 𝑊 𝑡.
Depending on the info given in the question, the above equation can be written in many forms e.g. 𝑃 = 𝑄𝑉 𝑡 𝑃 = 𝑉𝐼 𝑃 = 𝐼 2 𝑅.
What is Electrical Power?
Electrical power is all about speed – specifically, the rate at which electrical energy is transferred, supplied, or dissipated within a circuit. It measures how quickly electrical energy transforms into other forms, such as heat, light, or mechanical energy in devices like motors.
Represents the rate of energy transfer or conversion.
The SI unit is the Watt (W).
1 Watt is equivalent to 1 Joule of energy transferred every second (1 J/s).
A higher power rating means a faster rate of energy conversion or delivery.
The Electrical Power Formulas
We can combine the definitions of potential difference, current, and Ohm's Law to derive several crucial formulas for electrical power. These equations are fundamental for analysing circuits and calculating power dissipation or supply based on the known quantities.
This is the most fundamental formula for electrical power.
It directly shows power is proportional to both voltage (potential difference) and current.
Can be derived by substituting and into .
Always choose the power formula (, , or ) that uses the known quantities in your problem. This simplifies calculations and reduces the chance of errors by avoiding intermediate steps.
Total Electrical Energy Transferred
While power describes the rate of energy transfer, sometimes you need to know the total amount of energy transferred over a specific period. This is simply the power multiplied by the duration for which the component or circuit was operating.
Total energy transferred is the product of power and time, .
The formula is derived by substituting into .
The SI unit for total energy is the Joule (J).
Worked examples
See the formulas applied — reveal one step at a time, like the exam.
A light bulb is connected across a 12 V power supply, drawing a current of 0.5 A for 10 minutes.
- Calculate the electrical power dissipated by the bulb.
- Calculate the total electrical energy converted by the bulb in this time.
- 1
To find the power (P), we use the formula :
A resistor of carries a current of . Find the potential difference across it and the power dissipated using and .
- 1
How it all connects
The big idea sits in the middle — tap a linked idea to explore the link.
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.
- Potential difference (p.d.)
The energy transferred or work done per unit charge as it moves between two points in a circuit.
- SI unit for potential
The Volt (V), defined as one Joule per Coulomb (1 J/C).
- SI unit for power
The Watt (W), which is equivalent to one Joule per second (1 J/s).
Quick check
Write your answer first, then compare it with the model one — the gap is what you would have lost.
Teach it back
If you can explain it simply, you own it — gaps here are marks you’d lose.
Teach it back
Explain this topic as if teaching a friend. We name the gaps an examiner would still dock.
Revision flashcards
Guess first, then flip — retrieval beats re-reading.
Key takeaways
Review these before you close the topic — retrieval beats re-reading.
9.2 Potential difference and power.
Potential difference is defined as the work done to transfer one unit of charge across two points of different potential (charge). 𝑉 = 𝑊 𝑄.
Here V is the potential difference in volts (V), W is the work done in joules and Q is the charge in coulombs.
Recall that power is the rate of work done or rate of energy transferred i.e. 𝑃 = 𝑊 𝑡.
Depending on the info given in the question, the above equation can be written in many forms e.g. 𝑃 = 𝑄𝑉 𝑡 𝑃 = 𝑉𝐼 𝑃 = 𝐼 2 𝑅.
Practice — then mark it
The whole point: a real Cambridge question, marked mark-by-mark.
The load resistor R has a resistance of 370 Ω. Show that the maximum power dissipated in R is 0.22 W.
The potential difference between the ground and the atmosphere is 3.0 × 10^7 V.
Calculate the average power, in GW, transferred during the lightning strike.
power = ................................................................ GW
Extra simulations & links
PhET, GeoGebra and other curated tools — open in a new tab.
Frequently asked
Checkpoint
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Reading it isn’t knowing it — prove it.
Before you move on: do 9702/41 · Q7(b)(i) on paper, snap a photo, and get examiner-style feedback on exactly where you win and lose marks.
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