Where can I learn Practical circuits for Cambridge 9702?

This free lesson on MarkScheme covers syllabus point 10.1 (Practical circuits) for Cambridge A-Level Physics. It includes visual revision, key points, and links to real past-paper questions with mark-scheme marking at markscheme.app/courses/9702/10-1-practical-circuits.

Is Practical circuits (10.1) on 9702 free to study?

Yes. The Physics 9702 course on MarkScheme is 100% free — including premium visual lessons, exam tips, and past-paper marking. No paywall for Practical circuits.

MarkScheme 9702

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10.1Physics25 min readPREMIUM

Practical circuits

Welcome to the world of practical circuits! This lesson dives into how real-world power sources behave, the fundamental Kirchhoff's Laws governing current and voltage, and how we combine components in series or parallel. You'll also learn the clever trick of potential dividers to get just the right voltage where you need it, even with sensors. Let's get started! This pilot aligns with Senpai Corner AS notes (2025–2027) for topic 10.1.

BY THE END, YOU CAN…

exam checklist — tick these off

1Explain and apply the concepts of electromotive force (e.m.f.) and internal resistance.
2Apply Kirchhoff's First and Second Laws to analyse both simple and complex circuits.
3Describe and calculate properties of series, parallel, and potential divider circuits, including sensor applications.

STUDY MODE

READING

TYPEFACE

Literata — a reading serif made for e-books; set like a textbook, sits well beside maths.

SIZE

AIRY SPACING

Wider letter and line spacing. The one change with solid evidence for readers who lose their place — worth a try whoever you are.

Pick whatever reads fastest for you — it differs from person to person, by up to a third.

EXPLAIN SIMPLER

The same notes in plain English — no jargon. Key points and exam tips stay.

DIAGRAM NOTES

A small sketch beside each block of notes.

In simple terms

A friendly intro before the formal notes — no formulas yet.

Practical circuits

Cambridge 9702 Paper 2 — Practical circuits (10.1). Senpai Corner diagram-backed pilot with premium structure and live visuals.

1
E.m.f. (ε) is the total energy supplied per unit charge by a source.
2
Potential difference (p.d.) is the energy converted per unit charge between two points in a circuit.
3
Internal resistance (r) is the opposition to current flow within the power source itself.
4
Terminal p.d. (V) is the voltage across the external circuit: V = ε - Ir.

What this topic covers

The official Cambridge syllabus points this lesson works through.

10.1.1
Recall and use the circuit symbols shown in section 6 of this syllabus
10.1.2
Draw and interpret circuit diagrams containing the circuit symbols shown in section 6 of this syllabus
10.1.3
Define and use the electromotive force (e.m.f.) of a source as energy transferred per unit charge in driving charge around a complete circuit
10.1.4
Distinguish between e.m.f. and potential difference (p.d.) in terms of energy considerations
10.1.5
Understand the effects of the internal resistance of a source of e.m.f. on the terminal potential difference

Explore the concept

Use the live diagram, PhET or GeoGebra sim, and synced steps — play it, drag controls, or tap a step.

Figure PhET simulation1 / 4

Loading simulation…

Fetching from PhET…

Circuit Construction Kit: DC — Virtual Lab

Drag out a battery — this is your e.m.f. source (10.1).

If the embed does not load, use Open on PhET.

Simulation by PhET Interactive Simulations, University of Colorado Boulder · Licensed to MarkScheme (public licence CC BY-NC 4.0 since 2026-03-30)

Step-synced diagram — highlights what to look for in the simulation above.

A power supply provides the e.m.f. that…

A power supply provides the e.m.f. that drives charge around the circuit.

14 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.

14 simulations · 5 to start with

Start herein this order — each one shows a different piece of the topic

PhysicsHubStart here · 19702 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: Raise the internal resistance and read the terminal voltage drop: lost volts equal Ir.
Try this
1. Pick the series circuit and read the current with the ammeter.
2. Switch to parallel and compare the currents in each branch.
3. 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.
Open on PhysicsHub
PhysicsHub (@mattqdev) · MIT
3JCN PhysicsStart here · 29702 10.1 · 9702 10.2 · IB B.5
Resistors in Series
Resistors in series: see current shared and voltage divided
Why this one: One current everywhere, and the p.d.s across the resistors add up to the supply.
Try this
1. Read the current at each point in the series circuit.
2. Read the voltage across each resistor and sum them.
Look for The same current flows through every series resistor and the voltages add to the supply.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
3JCN PhysicsStart here · 39702 10.1 · 9702 10.2 · IB B.5
Resistors in Parallel
Resistors in parallel: see voltage shared and current divided
Why this one: Each branch gets the full p.d.; the branch currents add to the total.
Try this
1. Read the voltage across each parallel resistor.
2. Read the branch currents and sum them.
Look for Each parallel branch sees the full voltage and the branch currents add to the total.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
oPhysicsStart here · 49702 10.1 · 9702 10.2 · IB B.5
Electric Circuit with Four Identical Lightbulbs
Combination circuit with four identical bulbs and three switches; predict then test brightness and current
Why this one: Predict the brightness before you close each switch, then test it.
Try this
1. Close one switch at a time and compare bulb brightness.
2. Close all three switches.
3. Open the switches in a different order.
Look for Bulbs in series share the current and glow dimmer; a parallel branch draws extra current from the source.
Open on oPhysics
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
SimuPhysicsStart here · 59702 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: Click each real component to see its circuit symbol, then share out 12 V with the rheostat.
Try this
1. Click each component to see its symbol.
2. Slide the rheostat and read the shared voltages.
3. 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 site
SimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)

More simulations9 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
1. Build a series circuit and read the ammeter.
2. Rebuild the same resistors in parallel and compare.
3. 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.
Open on The Physics Classroom
Physics Interactives by The Physics Classroom · Licensed to MarkScheme (site terms otherwise permit linking only)
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
1. Close the switch and record a V–I point.
2. Slide the rheostat and record several more.
3. 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 site
SimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)
SimuPhysicsCore9702 10.1 · IB B.5
Interactive Resistors Simulation
Build resistor networks and watch the live current and voltage readings update as you go
Try this
1. Build two resistors in series and read the current.
2. Rebuild them in parallel and compare.
3. Read the voltage across each resistor.
Look for Series resistances add and parallel resistances combine by reciprocals.
Open on SimuPhysicsRuns on their site
SimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)
SimuPhysicsCore9702 10.1 · 9702 10.2 · IB B.5
Parallel Connections: Wires and Nodes
Eight drawings of parallel resistors: gather every starting end at node a and every finishing end at node b and check each branch
Try this
1. Pick a drawing and gather the ends at node a and node b.
2. Check each branch connects to both nodes.
3. Try the Ladder and Diamond drawings.
Look for Resistors are in parallel when every branch connects the same two nodes.
Open on SimuPhysicsRuns on their site
SimuPhysics 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
1. Read each branch ammeter and the voltmeter.
2. Check V = IR for each branch.
3. 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.
Open on 3JCN Physics
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
1. Read the ammeter and each voltmeter.
2. Check V = IR for each resistor.
3. Check that the voltmeter readings sum to the supply voltage.
Look for One current, and the sum of the resistor voltages equals the emf.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0

Key formulas

Tap any symbol to reveal exactly what it means and its units.

KEY RELATION

$\varepsilon = \frac{W}{Q}$

Tap a symbol — great for exam definitions

KEY RELATION

$\varepsilon = V + Ir$

Tap a symbol — great for exam definitions

KEY RELATION

= r

Tap a symbol — great for exam definitions

KEY RELATION

$\sum I_{in} = \sum I_{out}$

KEY RELATION

$\sum \varepsilon = \sum IR$

Tap a symbol — great for exam definitions

KEY RELATION

$R_{total} = R_1 + R_2 + ...$

KEY RELATION

$\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + ...$

KEY RELATION

$V_{out} = V_{in} \times \frac{R_{out}}{R_{total}}$

Full topic notes

Formal explanation with the rigour you need for the exam.

Electromotive Force and Internal Resistance

Every power source, like a battery or power pack, has an electromotive force (e.m.f., ε). This is the total electrical energy it supplies per unit charge to drive current around a complete circuit. It’s like the 'push' for the charges, representing the maximum potential difference the source can provide when no current is drawn (on an open circuit).

$\varepsilon = \frac{W}{Q}$ (where W is energy/work done, Q is charge)

No power source is perfect. Inside, it has a small but significant internal resistance (r) due to the materials it's made from. This resistance causes some of the energy to be wasted as heat when current flows, creating a 'lost voltage' internally. This means the voltage available to your external circuit, called the terminal potential difference (V), is always less than the full e.m.f. when current is flowing.

$\varepsilon = V + Ir$ OR $\varepsilon = I(R + r)$ (where V is terminal p.d., I is current, R is external resistance)

E.m.f. (ε) is the total energy supplied per unit charge by a source.
Potential difference (p.d.) is the energy converted per unit charge between two points in a circuit.
Internal resistance (r) is the opposition to current flow within the power source itself.
Terminal p.d. (V) is the voltage across the external circuit: V = ε - Ir.
The term 'lost volts' refers to the potential difference across the internal resistance (Ir).

Not clear?

Maximum Power Transfer

An important consequence of internal resistance is its effect on the power delivered to the external circuit. The power delivered to the external load resistor R is given by $P = I^2R$ . Since $I = \varepsilon / (R+r)$ , the power is $P = (\frac{\varepsilon}{R+r})^2 R$ . A key result from this relationship is the maximum power transfer theorem. This states that the maximum power is delivered to the external load when the load resistance R is equal to the internal resistance r of the source.

Condition for maximum power transfer: $R = r$

When this condition is met, the power delivered to the load is $P_{max} = \frac{\varepsilon^2}{4r}$ . However, note that under these conditions, an equal amount of power is dissipated as heat inside the source, making the process only 50% efficient.

Not clear?

Kirchhoff's Laws: The Circuit Rules

To analyse any complex circuit, we rely on Kirchhoff's Laws. His First Law, also known as the junction rule, is all about the conservation of charge. It simply states that charge cannot accumulate at a junction; the total current flowing into a junction must equal the total current flowing out.

$\sum I_{in} = \sum I_{out}$

Kirchhoff's Second Law, the loop rule, reflects the conservation of energy. It tells us that for any closed loop in a circuit, the algebraic sum of the e.m.f.s is equal to the algebraic sum of the potential differences (p.d.s) around that loop. A common sign convention is: e.m.f.s are positive if they drive current in the loop's direction, and p.d.s across resistors are negative as they represent an energy loss.

$\sum \varepsilon = \sum IR$

Kirchhoff's First Law: Sum of currents into a junction equals sum of currents out.
First Law is based on the principle of conservation of charge.
Kirchhoff's Second Law: The sum of e.m.f.s around any closed loop equals the sum of p.d.s.
Second Law is based on the principle of conservation of energy.
Consistent sign conventions are crucial when applying the Second Law.

Not clear?

Series and Parallel Circuits

When components are connected in series, they form a single path for the current. This means the current is the same through every component. The total voltage from the source is divided among them in proportion to their resistance ( $V_1/R_1 = V_2/R_2$ ), and the total resistance is the sum of individual resistances.

$R_{total} = R_1 + R_2 + ...$

In a parallel circuit, components are connected across the same two points, creating multiple paths for the current. Here, the potential difference (voltage) across each parallel branch is identical. The total current from the source splits, with each branch drawing current inversely proportional to its resistance. The total resistance is always less than the smallest individual resistance.

$\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + ...$

Series: Current is constant; voltage divides; resistances add directly.
Parallel: Voltage is constant; current divides; reciprocal resistances add.
Adding resistors in series increases the total resistance.
Adding resistors in parallel decreases the total resistance.
These rules are fundamental for simplifying complex circuits.

Not clear?

Potential Dividers and Sensing Circuits

A potential divider is a circuit using two or more series resistors to provide an output voltage ( $V_{out}$ ) that is a precise fraction of the input supply voltage ( $V_{in}$ ). By choosing the right resistance values, you can 'tap off' exactly the voltage you need for a specific part of your circuit. It's a very common and useful circuit configuration.

$V_{out} = V_{in} \times \frac{R_{out}}{R_{total}}$ (where $R_{out}$ is the resistance across which $V_{out}$ is measured)

You can make a potential divider variable using a potentiometer (a three-terminal resistor with a sliding contact) or a sensor like a thermistor (resistance depends on temperature) or Light Dependent Resistor (LDR) (resistance depends on light intensity). As the sensor's resistance changes, the output voltage of the divider changes, allowing it to act as a responsive sensing circuit for applications like thermostats or automatic lighting.

Potential dividers split a supply voltage into a smaller, desired output.
The output voltage depends on the ratio of resistances.
Potentiometers allow for continuously variable output voltages.
Thermistors and LDRs change resistance with environmental conditions.
Sensor placement determines how output voltage responds to stimuli (e.g., if $V_{out}$ is across an NTC thermistor, voltage will rise as temperature rises).

Not clear?

Worked examples

See the formulas applied — reveal one step at a time, like the exam.

reveal slowly — mark each step

EXAMPLE 1

A potential divider is constructed with a 12.0 V supply connected to two resistors in series, R₁ = 2.0 kΩ and R₂ = 4.0 kΩ. A high-resistance voltmeter is connected across R₂. What is the reading on the voltmeter?

1
Identify the known values: $V_{in} = 12.0 \text{ V}$ , $R_1 = 2.0 \text{ k}\Omega$ , $R_2 = 4.0 \text{ k}\Omega$ .

EXAMPLE 2

A cell with an e.m.f. of 1.5 V is connected to an external resistor of 4.0 Ω. The current flowing through the circuit is measured as 0.30 A. Calculate the internal resistance of the cell.

1
Identify the known values: $\varepsilon = 1.5 \text{ V}$ , $R = 4.0 \Omega$ , $I = 0.30 \text{ A}$ .

How it all connects

The big idea sits in the middle — tap a linked idea to explore the link.

MAIN IDEAPractical circuits

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.

electromotive force (e.m.f., ε): Every power source, like a battery or power pack, has an electromotive force (e.m.f., ε). This is the total electrical energy it supplies per unit charge to drive current around a complete circuit.
internal resistance (r): Inside, it has a small but significant internal resistance (r) due to the materials it's made from. This resistance causes some of the energy to be wasted as heat when current flows, creating a 'lost voltage' internally.
terminal potential difference (V): This means the voltage available to your external circuit, called the terminal potential difference (V), is always less than the full e.m.f. when current is flowing.
maximum power transfer theorem: A key result from this relationship is the maximum power transfer theorem. This states that the maximum power is delivered to the external load when the load resistance R is equal to the internal resistance r of the source.
series: When components are connected in series, they form a single path for the current. This means the current is the same through every component.
potential divider: A potential divider is a circuit using two or more series resistors to provide an output voltage ( $V_{out}$ ) that is a precise fraction of the input supply voltage ( $V_{in}$ ).
potentiometer: You can make a potential divider variable using a potentiometer (a three-terminal resistor with a sliding contact) or a sensor like a thermistor (resistance depends on temperature) or Light Dependent Resistor (LDR) (resistance depends on light intensity).

10Apply

Quick check

Write your answer first, then compare it with the model one — the gap is what you would have lost.

0 of 6 answered

11Understand

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.

Your explanation — no notes

12Remember

Revision flashcards

Guess first, then flip — retrieval beats re-reading.

Your guess — write it before you look

1 / 8 · ← → space

Key takeaways

Review these before you close the topic — retrieval beats re-reading.

close the tab only after these stick

E.m.f. (ε) is the total energy supplied per unit charge by a source.
Potential difference (p.d.) is the energy converted per unit charge between two points in a circuit.
Internal resistance (r) is the opposition to current flow within the power source itself.
Terminal p.d. (V) is the voltage across the external circuit: V = ε - Ir.
The term 'lost volts' refers to the potential difference across the internal resistance (Ir).

Practice — then mark it

The whole point: a real Cambridge question, marked mark-by-mark.

Question 1 of 29702/22 · Q5(b)(i)

PhysicsMay/June 2024

(b) (i)

The current in the circuit is 1.1 × 10⁻²A. The potential difference across Y is 4.0V.

Calculate the resistance of X.

resistance = .............................................................. Ω

Do it on paper → mark itMARKED MARK-BY-MARK · B1 / M1 / A1 · OFFICIAL SCHEME

9702/22/M/J/24

Question 2 of 29702/23 · Q5(c)(i)

PhysicsMay/June 2024

A third resistor is added in parallel with R₁ and R₂ in the circuit in Fig. 5.1. State and explain the effect, if any, of this change on: the current in the cell

Do it on paper → mark itMARKED MARK-BY-MARK · B1 / M1 / A1 · OFFICIAL SCHEME

9702/23/M/J/24

Extra simulations & links

PhET, GeoGebra and other curated tools — open in a new tab.

Frequently asked

Why do voltmeters often read less than the stated EMF of a battery when current is flowing?

How do Kirchhoff's laws simplify the analysis of complex electrical circuits?

What is the role of sensors like LDRs and thermistors in practical potential divider circuits?

When is it desirable to match the load resistance to the internal resistance?

Checkpoint

One marked question is worth ten re-reads — close the loop before you move on.

Checkpoint

Reading it isn’t knowing it — prove it.

Before you move on: do 9702/22 · Q5(b)(i) on paper, snap a photo, and get examiner-style feedback on exactly where you win and lose marks.

Attempt & get marked →Takes about a minute · you’ll land back on this lesson

← PREVIOUS9.3 Resistance and resistivity NEXT →10.2 Kirchhoff's laws

Discuss Practical circuits

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Revise Practical circuits for Cambridge 9702 (10.1)

Looking for free Physics 9702 notes on Practical circuits? This A-Level lesson covers official syllabus point 10.1 on Paper 1: Multiple Choice / Paper 2: AS Level Structured Questions. Use the visual steps, key terms, and quick checks below — then practise a real 9702 past-paper question with mark-scheme marking. Built for students searching "Practical circuits 9702 revision", "9702 10.1 notes", or a free alternative to paid note sites.

Full Physics 9702 course Mark a past paper →9702 subject hub

10.1Physics25 min readPREMIUM

Practical circuits

BY THE END, YOU CAN…

exam checklist — tick these off

1Explain and apply the concepts of electromotive force (e.m.f.) and internal resistance.
2Apply Kirchhoff's First and Second Laws to analyse both simple and complex circuits.
3Describe and calculate properties of series, parallel, and potential divider circuits, including sensor applications.

STUDY MODE

READING

TYPEFACE

Literata — a reading serif made for e-books; set like a textbook, sits well beside maths.

SIZE

AIRY SPACING

Wider letter and line spacing. The one change with solid evidence for readers who lose their place — worth a try whoever you are.

Pick whatever reads fastest for you — it differs from person to person, by up to a third.

EXPLAIN SIMPLER

The same notes in plain English — no jargon. Key points and exam tips stay.

DIAGRAM NOTES

A small sketch beside each block of notes.

In simple terms

A friendly intro before the formal notes — no formulas yet.

Practical circuits

Cambridge 9702 Paper 2 — Practical circuits (10.1). Senpai Corner diagram-backed pilot with premium structure and live visuals.

1
E.m.f. (ε) is the total energy supplied per unit charge by a source.
2
Potential difference (p.d.) is the energy converted per unit charge between two points in a circuit.
3
Internal resistance (r) is the opposition to current flow within the power source itself.
4
Terminal p.d. (V) is the voltage across the external circuit: V = ε - Ir.

What this topic covers

The official Cambridge syllabus points this lesson works through.

10.1.1
Recall and use the circuit symbols shown in section 6 of this syllabus
10.1.2
Draw and interpret circuit diagrams containing the circuit symbols shown in section 6 of this syllabus
10.1.3
Define and use the electromotive force (e.m.f.) of a source as energy transferred per unit charge in driving charge around a complete circuit
10.1.4
Distinguish between e.m.f. and potential difference (p.d.) in terms of energy considerations
10.1.5
Understand the effects of the internal resistance of a source of e.m.f. on the terminal potential difference

Explore the concept

Use the live diagram, PhET or GeoGebra sim, and synced steps — play it, drag controls, or tap a step.

Figure PhET simulation1 / 4

Loading simulation…

Fetching from PhET…

Circuit Construction Kit: DC — Virtual Lab

Drag out a battery — this is your e.m.f. source (10.1).

If the embed does not load, use Open on PhET.

Simulation by PhET Interactive Simulations, University of Colorado Boulder · Licensed to MarkScheme (public licence CC BY-NC 4.0 since 2026-03-30)

Step-synced diagram — highlights what to look for in the simulation above.

A power supply provides the e.m.f. that…

A power supply provides the e.m.f. that drives charge around the circuit.

14 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.

14 simulations · 5 to start with

Start herein this order — each one shows a different piece of the topic

PhysicsHubStart here · 19702 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: Raise the internal resistance and read the terminal voltage drop: lost volts equal Ir.
Try this
1. Pick the series circuit and read the current with the ammeter.
2. Switch to parallel and compare the currents in each branch.
3. 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.
Open on PhysicsHub
PhysicsHub (@mattqdev) · MIT
3JCN PhysicsStart here · 29702 10.1 · 9702 10.2 · IB B.5
Resistors in Series
Resistors in series: see current shared and voltage divided
Why this one: One current everywhere, and the p.d.s across the resistors add up to the supply.
Try this
1. Read the current at each point in the series circuit.
2. Read the voltage across each resistor and sum them.
Look for The same current flows through every series resistor and the voltages add to the supply.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
3JCN PhysicsStart here · 39702 10.1 · 9702 10.2 · IB B.5
Resistors in Parallel
Resistors in parallel: see voltage shared and current divided
Why this one: Each branch gets the full p.d.; the branch currents add to the total.
Try this
1. Read the voltage across each parallel resistor.
2. Read the branch currents and sum them.
Look for Each parallel branch sees the full voltage and the branch currents add to the total.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
oPhysicsStart here · 49702 10.1 · 9702 10.2 · IB B.5
Electric Circuit with Four Identical Lightbulbs
Combination circuit with four identical bulbs and three switches; predict then test brightness and current
Why this one: Predict the brightness before you close each switch, then test it.
Try this
1. Close one switch at a time and compare bulb brightness.
2. Close all three switches.
3. Open the switches in a different order.
Look for Bulbs in series share the current and glow dimmer; a parallel branch draws extra current from the source.
Open on oPhysics
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
SimuPhysicsStart here · 59702 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: Click each real component to see its circuit symbol, then share out 12 V with the rheostat.
Try this
1. Click each component to see its symbol.
2. Slide the rheostat and read the shared voltages.
3. 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 site
SimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)

More simulations9 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
1. Build a series circuit and read the ammeter.
2. Rebuild the same resistors in parallel and compare.
3. 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.
Open on The Physics Classroom
Physics Interactives by The Physics Classroom · Licensed to MarkScheme (site terms otherwise permit linking only)
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
1. Close the switch and record a V–I point.
2. Slide the rheostat and record several more.
3. 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 site
SimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)
SimuPhysicsCore9702 10.1 · IB B.5
Interactive Resistors Simulation
Build resistor networks and watch the live current and voltage readings update as you go
Try this
1. Build two resistors in series and read the current.
2. Rebuild them in parallel and compare.
3. Read the voltage across each resistor.
Look for Series resistances add and parallel resistances combine by reciprocals.
Open on SimuPhysicsRuns on their site
SimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)
SimuPhysicsCore9702 10.1 · 9702 10.2 · IB B.5
Parallel Connections: Wires and Nodes
Eight drawings of parallel resistors: gather every starting end at node a and every finishing end at node b and check each branch
Try this
1. Pick a drawing and gather the ends at node a and node b.
2. Check each branch connects to both nodes.
3. Try the Ladder and Diamond drawings.
Look for Resistors are in parallel when every branch connects the same two nodes.
Open on SimuPhysicsRuns on their site
SimuPhysics 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
1. Read each branch ammeter and the voltmeter.
2. Check V = IR for each branch.
3. 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.
Open on 3JCN Physics
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
1. Read the ammeter and each voltmeter.
2. Check V = IR for each resistor.
3. Check that the voltmeter readings sum to the supply voltage.
Look for One current, and the sum of the resistor voltages equals the emf.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0

Key formulas

Tap any symbol to reveal exactly what it means and its units.

KEY RELATION

$\varepsilon = \frac{W}{Q}$

Tap a symbol — great for exam definitions

KEY RELATION

$\varepsilon = V + Ir$

Tap a symbol — great for exam definitions

KEY RELATION

= r

Tap a symbol — great for exam definitions

KEY RELATION

$\sum I_{in} = \sum I_{out}$

KEY RELATION

$\sum \varepsilon = \sum IR$

Tap a symbol — great for exam definitions

KEY RELATION

$R_{total} = R_1 + R_2 + ...$

KEY RELATION

$\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + ...$

KEY RELATION

$V_{out} = V_{in} \times \frac{R_{out}}{R_{total}}$

Full topic notes

Formal explanation with the rigour you need for the exam.

Electromotive Force and Internal Resistance

$\varepsilon = \frac{W}{Q}$ (where W is energy/work done, Q is charge)

$\varepsilon = V + Ir$ OR $\varepsilon = I(R + r)$ (where V is terminal p.d., I is current, R is external resistance)

E.m.f. (ε) is the total energy supplied per unit charge by a source.
Potential difference (p.d.) is the energy converted per unit charge between two points in a circuit.
Internal resistance (r) is the opposition to current flow within the power source itself.
Terminal p.d. (V) is the voltage across the external circuit: V = ε - Ir.
The term 'lost volts' refers to the potential difference across the internal resistance (Ir).

Not clear?

Maximum Power Transfer

Condition for maximum power transfer: $R = r$

Not clear?

Kirchhoff's Laws: The Circuit Rules

$\sum I_{in} = \sum I_{out}$

$\sum \varepsilon = \sum IR$

Kirchhoff's First Law: Sum of currents into a junction equals sum of currents out.
First Law is based on the principle of conservation of charge.
Kirchhoff's Second Law: The sum of e.m.f.s around any closed loop equals the sum of p.d.s.
Second Law is based on the principle of conservation of energy.
Consistent sign conventions are crucial when applying the Second Law.

Not clear?

Series and Parallel Circuits

$R_{total} = R_1 + R_2 + ...$

$\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + ...$

Series: Current is constant; voltage divides; resistances add directly.
Parallel: Voltage is constant; current divides; reciprocal resistances add.
Adding resistors in series increases the total resistance.
Adding resistors in parallel decreases the total resistance.
These rules are fundamental for simplifying complex circuits.

Not clear?

Potential Dividers and Sensing Circuits

$V_{out} = V_{in} \times \frac{R_{out}}{R_{total}}$ (where $R_{out}$ is the resistance across which $V_{out}$ is measured)

Potential dividers split a supply voltage into a smaller, desired output.
The output voltage depends on the ratio of resistances.
Potentiometers allow for continuously variable output voltages.
Thermistors and LDRs change resistance with environmental conditions.
Sensor placement determines how output voltage responds to stimuli (e.g., if $V_{out}$ is across an NTC thermistor, voltage will rise as temperature rises).

Not clear?

Worked examples

See the formulas applied — reveal one step at a time, like the exam.

reveal slowly — mark each step

EXAMPLE 1

1
Identify the known values: $V_{in} = 12.0 \text{ V}$ , $R_1 = 2.0 \text{ k}\Omega$ , $R_2 = 4.0 \text{ k}\Omega$ .

EXAMPLE 2

A cell with an e.m.f. of 1.5 V is connected to an external resistor of 4.0 Ω. The current flowing through the circuit is measured as 0.30 A. Calculate the internal resistance of the cell.

1
Identify the known values: $\varepsilon = 1.5 \text{ V}$ , $R = 4.0 \Omega$ , $I = 0.30 \text{ A}$ .

How it all connects

The big idea sits in the middle — tap a linked idea to explore the link.

MAIN IDEAPractical circuits

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.

electromotive force (e.m.f., ε): Every power source, like a battery or power pack, has an electromotive force (e.m.f., ε). This is the total electrical energy it supplies per unit charge to drive current around a complete circuit.
internal resistance (r): Inside, it has a small but significant internal resistance (r) due to the materials it's made from. This resistance causes some of the energy to be wasted as heat when current flows, creating a 'lost voltage' internally.
terminal potential difference (V): This means the voltage available to your external circuit, called the terminal potential difference (V), is always less than the full e.m.f. when current is flowing.
maximum power transfer theorem: A key result from this relationship is the maximum power transfer theorem. This states that the maximum power is delivered to the external load when the load resistance R is equal to the internal resistance r of the source.
series: When components are connected in series, they form a single path for the current. This means the current is the same through every component.
potential divider: A potential divider is a circuit using two or more series resistors to provide an output voltage ( $V_{out}$ ) that is a precise fraction of the input supply voltage ( $V_{in}$ ).
potentiometer: You can make a potential divider variable using a potentiometer (a three-terminal resistor with a sliding contact) or a sensor like a thermistor (resistance depends on temperature) or Light Dependent Resistor (LDR) (resistance depends on light intensity).

10Apply

Quick check

Write your answer first, then compare it with the model one — the gap is what you would have lost.

0 of 6 answered

11Understand

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.

Your explanation — no notes

12Remember

Revision flashcards

Guess first, then flip — retrieval beats re-reading.

Your guess — write it before you look

1 / 8 · ← → space

Key takeaways

Review these before you close the topic — retrieval beats re-reading.

close the tab only after these stick

E.m.f. (ε) is the total energy supplied per unit charge by a source.
Potential difference (p.d.) is the energy converted per unit charge between two points in a circuit.
Internal resistance (r) is the opposition to current flow within the power source itself.
Terminal p.d. (V) is the voltage across the external circuit: V = ε - Ir.
The term 'lost volts' refers to the potential difference across the internal resistance (Ir).

Practice — then mark it

The whole point: a real Cambridge question, marked mark-by-mark.

Question 1 of 29702/22 · Q5(b)(i)

PhysicsMay/June 2024

(b) (i)

The current in the circuit is 1.1 × 10⁻²A. The potential difference across Y is 4.0V.

Calculate the resistance of X.

resistance = .............................................................. Ω

Do it on paper → mark itMARKED MARK-BY-MARK · B1 / M1 / A1 · OFFICIAL SCHEME

9702/22/M/J/24

Question 2 of 29702/23 · Q5(c)(i)

PhysicsMay/June 2024

A third resistor is added in parallel with R₁ and R₂ in the circuit in Fig. 5.1. State and explain the effect, if any, of this change on: the current in the cell

Do it on paper → mark itMARKED MARK-BY-MARK · B1 / M1 / A1 · OFFICIAL SCHEME

9702/23/M/J/24

Extra simulations & links

PhET, GeoGebra and other curated tools — open in a new tab.

Frequently asked

Why do voltmeters often read less than the stated EMF of a battery when current is flowing?

How do Kirchhoff's laws simplify the analysis of complex electrical circuits?

What is the role of sensors like LDRs and thermistors in practical potential divider circuits?

When is it desirable to match the load resistance to the internal resistance?

Checkpoint

One marked question is worth ten re-reads — close the loop before you move on.

Checkpoint

Reading it isn’t knowing it — prove it.

Before you move on: do 9702/22 · Q5(b)(i) on paper, snap a photo, and get examiner-style feedback on exactly where you win and lose marks.

Attempt & get marked →Takes about a minute · you’ll land back on this lesson

← PREVIOUS9.3 Resistance and resistivity NEXT →10.2 Kirchhoff's laws

Discuss Practical circuits

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Revise Practical circuits for Cambridge 9702 (10.1)

In simple terms

What this topic covers

Explore the concept

Simulations

Kirchhoff's Circuit Laws

Resistors in Series

Resistors in Parallel

Electric Circuit with Four Identical Lightbulbs

Circuit Symbols and the Voltage Divider

DC Circuit Builder

Ohm's Law Lab — 3D Experiment

Interactive Resistors Simulation

Parallel Connections: Wires and Nodes

Ohm's Law - Resistors in Parallel

Ohm's Law - Resistors in Series

Key formulas

Full topic notes

Electromotive Force and Internal Resistance

Maximum Power Transfer

Kirchhoff's Laws: The Circuit Rules

Series and Parallel Circuits

Potential Dividers and Sensing Circuits

Worked examples

How it all connects

Glossary

Quick check

Teach it back

Revision flashcards

Key takeaways

Practice — then mark it

Extra simulations & links

Frequently asked

Checkpoint

Reading it isn’t knowing it — prove it.

Discuss Practical circuits

Revise Practical circuits for Cambridge 9702 (10.1)

In simple terms

What this topic covers

Explore the concept

Simulations

Kirchhoff's Circuit Laws

Resistors in Series

Resistors in Parallel

Electric Circuit with Four Identical Lightbulbs

Circuit Symbols and the Voltage Divider

DC Circuit Builder

Ohm's Law Lab — 3D Experiment

Interactive Resistors Simulation

Parallel Connections: Wires and Nodes

Ohm's Law - Resistors in Parallel

Ohm's Law - Resistors in Series

Key formulas

Full topic notes

Electromotive Force and Internal Resistance

Maximum Power Transfer

Kirchhoff's Laws: The Circuit Rules

Series and Parallel Circuits

Potential Dividers and Sensing Circuits

Worked examples

How it all connects

Glossary

Quick check

Teach it back

Revision flashcards

Key takeaways

Practice — then mark it

Extra simulations & links

Frequently asked

Checkpoint

Reading it isn’t knowing it — prove it.

Discuss Practical circuits