In simple terms
A friendly intro before the formal notes — no formulas yet.
Potential dividers
Cambridge 9702 Paper 2 — Potential dividers (10.3). Senpai Corner diagram-backed pilot with premium structure and live visuals.
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10.3 Potential dividers.
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According to Kirchhoff’s Second Law, the potential difference across a power source is divided when two resistors are connected in series.
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The larger the resistance the larger the voltage share (the big eater gets more pie!).
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A potentiometer is a type of variable resistor used as a potential divider.
What this topic covers
The official Cambridge syllabus points this lesson works through.
- 10.3.1
Understand the principle of a potential divider circuit
- 10.3.2
Recall and use the principle of the potentiometer as a means of comparing potential differences
- 10.3.3
Understand the use of a galvanometer in null methods
- 10.3.4
Explain the use of thermistors and light-dependent resistors in potential dividers to provide a potential difference that is dependent on temperature and light intensity
Explore the concept
Use the live diagram and synced steps — play it or tap a step card to walk through.
The divider Two resistors in series share the supply voltage between them.
5 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.
5 simulations · 4 to start with
Start herein this order — each one shows a different piece of the topic
- PhETStart here · 19702 10.3
Circuit Construction Kit: DC
Two resistors in series as a divider; move the voltmeter to read the share across each.
Why this one: Put 10 Ω and 30 Ω in series on 12 V and read 9 V across the 30 Ω; add a load and watch the output fall.
Try this
- Series 10 Ω and 30 Ω on 12 V — read V across the 30 Ω (expect 9 V).
- Swap the 30 Ω for 10 Ω — the output drops to 6 V.
- Add a 10 Ω load across the output — why does the reading fall?
Look for V_out = V_in · R₂/(R₁+R₂); a load in parallel lowers the effective R₂.
Simulation by PhET Interactive Simulations, University of Colorado Boulder · Licensed to MarkScheme (public licence CC BY-NC 4.0 since 2026-03-30)
- PhysicsHubStart here · 29702 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
Why this one: Read the p.d. across each series resistor: the share is in proportion to its resistance.
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
- SimuPhysicsStart here · 39702 10.1 · 9702 10.3 · IB B.5
Circuit Symbols and the Voltage Divider
Real components on a bench: click any one to see its symbol, slide the rheostat to share out the 12 V, and push the current through
Why this one: Slide the rheostat and the two output voltages always add back to the 12 V supply.
Try this
- Click each component to see its symbol.
- Slide the rheostat and read the shared voltages.
- Compare the two voltages with the 12 V supply.
Look for The two output voltages always add up to the 12 V supply.
Open on SimuPhysicsRuns on their siteSimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)
- 3JCN PhysicsStart here · 49702 10.3 · 9702 10.2 · IB B.5
Wheatstone Bridge for Resistors
Balance a Wheatstone bridge to find an unknown resistance
Why this one: A balanced bridge is two dividers with equal output: no current crosses when R1/R2 = R3/R4.
Try this
- Adjust the variable arm until the bridge balances.
- Use the ratio of the arms to find the unknown resistance.
Look for At balance no current crosses the bridge and R1/R2 = R3/R4.
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
More simulations1 more on this topic — core ones first
- 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)
Key formulas
Tap any symbol to reveal exactly what it means and its units.
Full topic notes
Formal explanation with the rigour you need for the exam.
The Core Concept: Voltage Division
At its heart, a potential divider is a simple series circuit. When resistors are connected in series across a voltage source, the total voltage supplied is distributed amongst them. This distribution isn't random; it's directly proportional to each resistor's individual resistance. The larger the resistance, the greater the share of the total voltage it "drops" across itself.
The Potential Divider Formula
In a series circuit, the current () is the same through every component. According to Ohm's Law (), the voltage drop across a resistor is proportional to its resistance. For two resistors, and , in series with an input voltage , the output voltage () across is given by:
10.3 Potential dividers.
According to Kirchhoff’s Second Law, the potential difference across a power source is divided when two resistors are connected in series.
The larger the resistance the larger the voltage share (the big eater gets more pie!).
A potentiometer is a type of variable resistor used as a potential divider.
In the diagram above, the total resistance of the potentiometer is R.
When the slider is moved it divides R into R1 and R2.
Variable Output: Potentiometers and Sensors
To create an output voltage that isn't fixed, we can incorporate a variable resistor. A potentiometer is a three-terminal variable resistor, often wired into a potential divider circuit. By sliding its contact (wiper), the resistance ratio changes continuously, allowing for a continuously adjustable output voltage, perfect for volume controls or brightness adjustments.
Sensors like Light Dependent Resistors (LDRs) and thermistors can replace fixed resistors in a potential divider. An LDR's resistance decreases with more light, while an NTC thermistor's resistance drops with increasing temperature. This makes the output voltage responsive to environmental changes, forming the basis of many automatic control systems like streetlights or temperature alarms.
Null Measurements: Precision with Potentiometers
Potentiometers are also critical in highly accurate null measurement techniques. The key advantage is that at the null point (zero current flow), no current is drawn from the component being measured. This prevents the measurement device from altering the circuit's conditions, ensuring a more accurate determination of its actual potential difference. A galvanometer detects this precise null point.
Always clearly identify which resistor the output voltage is being taken across in the potential divider formula; a common mistake is using the wrong resistance in the numerator. Also, understand how sensors (LDRs, thermistors) change their resistance based on external conditions, and how this affects the overall resistance ratio and thus the output voltage.
Worked examples
See the formulas applied — reveal one step at a time, like the exam.
A 12V power supply is connected across two series resistors: R1 = 200Ω and R2 = 400Ω. Calculate the output voltage taken across R2.
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Identify the input voltage: .
A light-sensing circuit uses a 9.0 V supply, a fixed 10 kΩ resistor, and a Light Dependent Resistor (LDR) in series. The output voltage is taken across the LDR. A switch connected to the output is triggered when the voltage reaches 6.0 V, indicating it is dark. What is the resistance of the LDR at this point?
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Identify known values:
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.
- potentiometer
A potentiometer is a three-terminal variable resistor, often wired into a potential divider circuit.
- In a potential divider
As the room gets darker, the LDR's resistance increases. This increases its share of the total voltage, so increases.
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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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.
10.3 Potential dividers.
According to Kirchhoff’s Second Law, the potential difference across a power source is divided when two resistors are connected in series.
The larger the resistance the larger the voltage share (the big eater gets more pie!).
A potentiometer is a type of variable resistor used as a potential divider.
In the diagram above, the total resistance of the potentiometer is R.
When the slider is moved it divides R into R1 and R2.
Practice — then mark it
The whole point: a real Cambridge question, marked mark-by-mark.
The cell of e.m.f. 1.2V is replaced by a new cell with the same e.m.f. but with an internal resistance that is not negligible. State and explain the effect, if any, of the internal resistance of the new cell on the position of the null point.
With reference to ratios of resistances, explain how this circuit can be used to determine the resistance of X.
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 · Q7(b)(iii) on paper, snap a photo, and get examiner-style feedback on exactly where you win and lose marks.
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