Where can I learn Characteristics of alternating currents for Cambridge 9702?

This free lesson on MarkScheme covers syllabus point 21.1 (Characteristics of alternating currents) 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/9702/21-1-characteristics-of-alternating-currents.

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21.1Physics25 min readPREMIUM

Characteristics of alternating currents

Imagine the electricity powering your home; it’s an alternating current (AC). Unlike the steady flow from a battery (direct current, DC), AC constantly reverses direction and changes its strength. Understanding these "characteristics" is key to mastering how AC works in circuits. This pilot aligns with Senpai Corner A Level notes (2025–2027) for topic 21.1.

BY THE END, YOU CAN…

exam checklist — tick these off

1Define alternating current (AC) and contrast its characteristics with direct current (DC).
2Understand and apply instantaneous, peak, and Root Mean Square (RMS) values for AC voltage and current.
3Deduce that the mean power in a resistive load is half the maximum power for a sinusoidal alternating current.
4Calculate mean power dissipation in AC circuits using both peak and RMS values.

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.

Characteristics of alternating currents

Cambridge 9702 Paper 4 — Characteristics of alternating currents (21.1). Senpai Corner diagram-backed pilot with premium structure and live visuals.

1
Definition: An alternating current (AC) is one that periodically reverses its direction of flow.
2
Waveform: The magnitude of an AC also varies continuously with time, typically in a sinusoidal pattern.
3
Contrast with DC: Direct current (DC) flows in a single, constant direction with a steady magnitude.
4
Key Parameters: AC is described by its frequency, period, and amplitude (peak value).

What this topic covers

The official Cambridge syllabus points this lesson works through.

21.1.1
Understand and use the terms period, frequency and peak value as applied to an alternating current or voltage
21.1.2
Use equations of the form $x = x_0 \sin ωt$ representing a sinusoidally alternating current or voltage
21.1.3
Recall and use the fact that the mean power in a resistive load is half the maximum power for a sinusoidal alternating current
21.1.4
Distinguish between root-mean-square (r.m.s.) and peak values and recall and use $I_{r.m.s.} = I_0/\sqrt{2}$ and $V_{r.m.s.} = V_0/\sqrt{2}$ for a sinusoidal alternating current

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: AC

V = V₀ sin ωt; I and V peak together in a resistive circuit; r.m.s. = peak/√2.

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.

Step 1

Definition: An alternating current (AC) is one that periodically reverses its direction of flow.

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 · 4 to start with

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

3JCN PhysicsStart here · 19702 20.5 · 9702 21.1 · IB D.4
AC Generator
Spin a coil in a magnetic field and watch the sinusoidal emf
Why this one: Spin the coil and see where the sinusoidal emf comes from: fastest flux change gives the peak.
Try this
1. Spin the coil and watch the emf trace.
2. Spin it faster and compare the peak emf and the frequency.
3. Note the coil position when the emf is zero.
Look for The emf is sinusoidal, zero when the coil faces the field and largest when its flux is changing fastest.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
PhysicsHubStart here · 29702 17.1 · 9702 7.1 · 9702 21.1
Trigonometric Circle
Draggable angle on the unit circle; choose the function, rotation speed, initial angle, amplitude A, angular frequency ω and phase φ; see A·sin(ωθ+φ) plotted
Why this one: Set amplitude, ω and phase and see I = I₀ sin ωt built from the rotating circle.
Try this
1. Set ω = 1 and φ = 0 and drag the angle.
2. Change φ and watch the plot shift.
3. Double A.
Look for The sine plot is the projection of the rotating point; φ shifts it sideways and A scales its height.
Open on PhysicsHub
PhysicsHub (@mattqdev) · MIT
PhETStart here · 39702 20.5 · 21.1 · IB D.4
Generator
Spin a magnet near a coil with a water wheel and watch the induced current alternate.
Why this one: Turn the water wheel faster and watch both the frequency and the peak of the alternating current rise.
Try this
1. Turn the tap on gently — the bulb flickers twice per turn.
2. Show the voltmeter and speed up — the swing gets bigger and faster.
3. Increase the coil loops — the same spin gives a larger e.m.f.
Look for A rotating magnet gives a sinusoidal e.m.f. whose peak rises with speed and turns.
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)
SimuPhysicsStart here · 49702 20.5 · 9702 21.1 · IB D.4
3D AC Dynamo
A coil turns between magnet poles and the induced e.m.f. is drawn against angle; slip rings keep each brush on the same end of the coil
Why this one: Follow the emf against angle as the coil turns and see why slip rings give an alternating output.
Try this
1. Turn the coil and watch the e.m.f. trace.
2. Find the angle where the e.m.f. is largest.
3. Find where it reverses.
Look for The e.m.f. reverses every half turn, giving a sinusoidal output.
Open on SimuPhysicsRuns on their site
SimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)

More simulations7 more on this topic — core ones first

SimuPhysicsCore9702 21.1
AC Circuits Lab
Assemble resistors, capacitors and inductors into AC circuits and watch the voltage and current traces with their phase relationship
Try this
1. Build a resistor circuit and compare the traces.
2. Swap in a capacitor and compare.
3. Swap in an inductor.
Look for Current and voltage are in phase for a resistor and out of phase for a capacitor or inductor.
Open on SimuPhysicsRuns on their site
SimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)
3JCN PhysicsCore9702 20.5 · 9702 21.1 · 9702 21.2
DC Generator
Add a commutator to a generator and see the rectified DC output
Try this
1. Spin the coil and watch the commutator output.
2. Compare the output with the AC generator's trace.
Look for The commutator reverses the connections every half turn, so the output is a rectified, one-direction emf.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
PhET9702 21.1 · IB B.5
Circuit Construction Kit: AC — Virtual Lab
Build AC and DC circuits from batteries, AC sources, resistors, capacitors and inductors, measured with realistic meters only.
Try this
1. Wire an AC source to a resistor and clip the voltmeter across it — read the trace on the chart.
2. Swap the resistor for a capacitor — the current peaks before the voltage.
3. Add an inductor — now the current lags.
Look for Realistic meters load the circuit slightly; in AC, current and voltage can be out of phase.
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)
SimuPhysics9702 17.3 · 9702 21.1 · IB C.4
Wireless Radio Tuning
Several stations broadcast at once; tune the LC circuit and only the station matching its natural frequency comes through
Try this
1. Tune the circuit to one station.
2. Tune between stations and listen.
3. Compare the station frequency with the circuit frequency.
Look for A station comes through when its frequency matches the circuit's natural frequency.
Open on SimuPhysicsRuns on their site
SimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)
SimuPhysics9702 21.1
Hot Wire Ammeter (Thermal Ammeter)
The wire expands as it heats, the fine thread takes up the slack and the pointer swings; works on AC and DC alike
Try this
1. Pass a DC current and watch the pointer.
2. Switch to AC and compare.
3. Double the current and compare.
Look for The reading depends on heating, so it is the same for AC and DC of the same r.m.s. value.
Open on SimuPhysicsRuns on their site
SimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)
3JCN Physics9702 20.5 · 9702 21.1 · IB D.4
Transformer
Change turns ratio of a transformer; read primary and secondary voltages
Try this
1. Set a 1:2 turns ratio and read the primary and secondary voltages.
2. Reverse to 2:1 and compare.
Look for Vs / Vp equals Ns / Np.
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

$X = x_0\sin(\omega t)$

Tap a symbol — great for exam definitions

KEY RELATION

$\omega = 2\pi f$

Tap a symbol — great for exam definitions

KEY RELATION

$V_{rms} = \frac{V_{peak}}{\sqrt{2}}$

KEY RELATION

$I_{rms} = \frac{I_{peak}}{\sqrt{2}}$

KEY RELATION

$P(t) = (I_0 \sin(\omega t))^2 R = I_0^2 R \sin^2(\omega t)$

Tap a symbol — great for exam definitions

KEY RELATION

$\left = \text{average of } (I_0^2 R \sin^2(\omega t)) = I_0^2 R \times (\text{average of } \sin^2(\omega t)) = I_0^2 R \times \frac{1}{2}$

Tap a symbol — great for exam definitions

KEY RELATION

$\left = \frac{1}{2} P_{max} = \frac{1}{2} I_0^2 R = \frac{1}{2} \frac{V_0^2}{R}$

Tap a symbol — great for exam definitions

KEY RELATION

$\left = I_{rms}^2 R = \frac{V_{rms}^2}{R} = V_{rms} I_{rms}$

Tap a symbol — great for exam definitions

Full topic notes

Formal explanation with the rigour you need for the exam.

What is Alternating Current (AC)?

Alternating current is an electrical current that continuously changes its magnitude and periodically reverses its direction of flow. This is fundamentally different from direct current (DC), which flows in a single, constant direction.

Definition: An alternating current (AC) is one that periodically reverses its direction of flow.
Waveform: The magnitude of an AC also varies continuously with time, typically in a sinusoidal pattern.
Contrast with DC: Direct current (DC) flows in a single, constant direction with a steady magnitude.
Key Parameters: AC is described by its frequency, period, and amplitude (peak value).

Not clear?

Understanding AC Values

Because AC varies, we need ways to describe its value at any moment, its maximum strength, and its overall "effectiveness". Let's start with a snapshot in time. For any sinusoidal AC quantity (current or voltage), its instantaneous value can be represented by:

$X = x_0\sin(\omega t)$

Here, $X$ is the instantaneous value (voltage or current) at time $t$ . $x_0$ is the peak value (or amplitude) – the absolute maximum magnitude reached. $\omega$ (omega) is the angular frequency, which tells us how quickly the AC oscillates.

$\omega = 2\pi f$

Instantaneous value ( $X$ ) is AC's value at a specific time.
Peak value ( $x_0$ ) is the maximum amplitude in a cycle.
Angular frequency ( $\omega$ ) determines oscillation speed.
Normal frequency ( $f$ ) is the number of cycles per second.

Not clear?

Peak vs. Root Mean Square (RMS)

While the peak value tells us the maximum, it doesn't represent the average power delivered. The average value of a sinusoidal current over a full cycle is zero. For practical purposes, like calculating power, we use the Root Mean Square (RMS) value.

The RMS value of an AC voltage or current is the equivalent DC value that would dissipate the same average power in a resistor. It's found by squaring all the instantaneous values, finding the mean (average) of those squares, and then taking the square root of that mean.

$V_{rms} = \frac{V_{peak}}{\sqrt{2}}$

$I_{rms} = \frac{I_{peak}}{\sqrt{2}}$

RMS value is the 'effective' value of AC.
It represents the DC equivalent for power dissipation.
For sinusoidal AC, $V_{rms}$ is $V_{peak}$ divided by $\sqrt{2}$ .
Similarly, $I_{rms}$ is $I_{peak}$ divided by $\sqrt{2}$ .

Not clear?

Power in AC Circuits

The instantaneous power in an AC circuit continuously varies because voltage and current are changing. However, we are usually interested in the mean power dissipated over a full cycle.

Not clear?

Deducing Mean Power

To understand why mean power is half the maximum power, let's look at the instantaneous power in a resistor. Power is given by $P = I^2R$ . Since the current is sinusoidal, $I = I_0 \sin(\omega t)$ , the instantaneous power is:

$P(t) = (I_0 \sin(\omega t))^2 R = I_0^2 R \sin^2(\omega t)$

From this equation, we can see that the maximum power, $P_{max}$ , occurs when $\sin^2(\omega t) = 1$ . So, $P_{max} = I_0^2 R$ . The power varies as $\sin^2(\omega t)$ , which is a function that oscillates between 0 and 1. Over a full cycle, the average value of $\sin^2(\omega t)$ is exactly $\frac{1}{2}$ .

Therefore, the mean power $\left$ is the average of the instantaneous power:

$\left = \text{average of } (I_0^2 R \sin^2(\omega t)) = I_0^2 R \times (\text{average of } \sin^2(\omega t)) = I_0^2 R \times \frac{1}{2}$

Since $P_{max} = I_0^2 R$ , we can conclude that:

$\left = \frac{1}{2} P_{max} = \frac{1}{2} I_0^2 R = \frac{1}{2} \frac{V_0^2}{R}$

A key advantage of using RMS values is that they simplify mean power calculations, making them identical to DC power calculations. This is precisely why RMS values are so useful!

$\left = I_{rms}^2 R = \frac{V_{rms}^2}{R} = V_{rms} I_{rms}$

Instantaneous power in AC varies continuously, but is always non-negative in a resistor.
Mean power over a cycle is half the peak power for sinusoidal AC.
This is because the average value of $\sin^2(\omega t)$ is 1/2.
RMS values allow for straightforward power calculations using DC-like formulas.

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 mains electricity supply has a peak voltage ( $V_{peak}$ ) of 325 V.

Calculate its Root Mean Square (RMS) voltage.
If this supply is connected to a heating element with a resistance of 60 \u03a9, what is the mean power dissipated by the element?

1
Calculate RMS voltage:

EXAMPLE 2

An AC source provides a current described by the equation $I = 5.0 \sin(100\pi t)$ , where $I$ is in amperes and $t$ is in seconds. The current flows through a 20 \u03a9 resistor.

What is the peak current?
What is the frequency of the supply?
Calculate the RMS current.
Determine the mean power dissipated in the resistor.

1
Identify Peak Current ( $I_0$ ):

How it all connects

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

MAIN IDEACharacteristics of alternating currents

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.

instantaneous value: Here, $X$ is the instantaneous value (voltage or current) at time $t$ . $x_0$ is the peak value (or amplitude) – the absolute maximum magnitude reached. $\omega$ (omega) is the angular frequency, which tells us how quickly the AC oscillates.
Alternating Current (AC): An electric current that periodically reverses its direction and continuously varies its magnitude over time.
AC differ from Direct: AC reverses direction and varies in magnitude, while DC flows in a constant direction with a steady magnitude.
Root Mean Square (RMS): The DC equivalent value that would dissipate the same average power in a resistor.

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 / 13 · ← → space

Key takeaways

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

close the tab only after these stick

Definition: An alternating current (AC) is one that periodically reverses its direction of flow.
Waveform: The magnitude of an AC also varies continuously with time, typically in a sinusoidal pattern.
Contrast with DC: Direct current (DC) flows in a single, constant direction with a steady magnitude.
Key Parameters: AC is described by its frequency, period, and amplitude (peak value).

Practice — then mark it

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

Question 1 of 29702/42 · Q8(b)(i)

PhysicsMay/June 2025

(b) (i)

Determine the peak power P₀ in the resistor.

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

9702/42/M/J/25

Question 2 of 29702/42 · Q8(b)(iii)

PhysicsMay/June 2025

(b) (iii)

Use the answer in (b)(ii) to explain why the mean power in the resistor is ¼ P₀.

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

9702/42/M/J/25

Extra simulations & links

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

Frequently asked

Why do countries use AC for mains electricity instead of DC?

What's the difference between frequency (

f

) and angular frequency (

\omega

Is the RMS value always

V_{peak}/\sqrt{2}

for any alternating current?

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 9702/42 · Q8(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

← PREVIOUS20.5 Electromagnetic induction NEXT →21.2 Rectification and smoothing

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Revise Characteristics of alternating currents for Cambridge 9702 (21.1)

Looking for free Physics 9702 notes on Characteristics of alternating currents? This A-Level lesson covers official syllabus point 21.1 on Paper 4: A 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 "Characteristics of alternating currents 9702 revision", "9702 21.1 notes", or a free alternative to paid note sites.

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

21.1Physics25 min readPREMIUM

Characteristics of alternating currents

BY THE END, YOU CAN…

exam checklist — tick these off

1Define alternating current (AC) and contrast its characteristics with direct current (DC).
2Understand and apply instantaneous, peak, and Root Mean Square (RMS) values for AC voltage and current.
3Deduce that the mean power in a resistive load is half the maximum power for a sinusoidal alternating current.
4Calculate mean power dissipation in AC circuits using both peak and RMS values.

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.

Characteristics of alternating currents

Cambridge 9702 Paper 4 — Characteristics of alternating currents (21.1). Senpai Corner diagram-backed pilot with premium structure and live visuals.

1
Definition: An alternating current (AC) is one that periodically reverses its direction of flow.
2
Waveform: The magnitude of an AC also varies continuously with time, typically in a sinusoidal pattern.
3
Contrast with DC: Direct current (DC) flows in a single, constant direction with a steady magnitude.
4
Key Parameters: AC is described by its frequency, period, and amplitude (peak value).

What this topic covers

The official Cambridge syllabus points this lesson works through.

21.1.1
Understand and use the terms period, frequency and peak value as applied to an alternating current or voltage
21.1.2
Use equations of the form $x = x_0 \sin ωt$ representing a sinusoidally alternating current or voltage
21.1.3
Recall and use the fact that the mean power in a resistive load is half the maximum power for a sinusoidal alternating current
21.1.4
Distinguish between root-mean-square (r.m.s.) and peak values and recall and use $I_{r.m.s.} = I_0/\sqrt{2}$ and $V_{r.m.s.} = V_0/\sqrt{2}$ for a sinusoidal alternating current

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: AC

V = V₀ sin ωt; I and V peak together in a resistive circuit; r.m.s. = peak/√2.

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.

Step 1

Definition: An alternating current (AC) is one that periodically reverses its direction of flow.

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 · 4 to start with

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

3JCN PhysicsStart here · 19702 20.5 · 9702 21.1 · IB D.4
AC Generator
Spin a coil in a magnetic field and watch the sinusoidal emf
Why this one: Spin the coil and see where the sinusoidal emf comes from: fastest flux change gives the peak.
Try this
1. Spin the coil and watch the emf trace.
2. Spin it faster and compare the peak emf and the frequency.
3. Note the coil position when the emf is zero.
Look for The emf is sinusoidal, zero when the coil faces the field and largest when its flux is changing fastest.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
PhysicsHubStart here · 29702 17.1 · 9702 7.1 · 9702 21.1
Trigonometric Circle
Draggable angle on the unit circle; choose the function, rotation speed, initial angle, amplitude A, angular frequency ω and phase φ; see A·sin(ωθ+φ) plotted
Why this one: Set amplitude, ω and phase and see I = I₀ sin ωt built from the rotating circle.
Try this
1. Set ω = 1 and φ = 0 and drag the angle.
2. Change φ and watch the plot shift.
3. Double A.
Look for The sine plot is the projection of the rotating point; φ shifts it sideways and A scales its height.
Open on PhysicsHub
PhysicsHub (@mattqdev) · MIT
PhETStart here · 39702 20.5 · 21.1 · IB D.4
Generator
Spin a magnet near a coil with a water wheel and watch the induced current alternate.
Why this one: Turn the water wheel faster and watch both the frequency and the peak of the alternating current rise.
Try this
1. Turn the tap on gently — the bulb flickers twice per turn.
2. Show the voltmeter and speed up — the swing gets bigger and faster.
3. Increase the coil loops — the same spin gives a larger e.m.f.
Look for A rotating magnet gives a sinusoidal e.m.f. whose peak rises with speed and turns.
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)
SimuPhysicsStart here · 49702 20.5 · 9702 21.1 · IB D.4
3D AC Dynamo
A coil turns between magnet poles and the induced e.m.f. is drawn against angle; slip rings keep each brush on the same end of the coil
Why this one: Follow the emf against angle as the coil turns and see why slip rings give an alternating output.
Try this
1. Turn the coil and watch the e.m.f. trace.
2. Find the angle where the e.m.f. is largest.
3. Find where it reverses.
Look for The e.m.f. reverses every half turn, giving a sinusoidal output.
Open on SimuPhysicsRuns on their site
SimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)

More simulations7 more on this topic — core ones first

SimuPhysicsCore9702 21.1
AC Circuits Lab
Assemble resistors, capacitors and inductors into AC circuits and watch the voltage and current traces with their phase relationship
Try this
1. Build a resistor circuit and compare the traces.
2. Swap in a capacitor and compare.
3. Swap in an inductor.
Look for Current and voltage are in phase for a resistor and out of phase for a capacitor or inductor.
Open on SimuPhysicsRuns on their site
SimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)
3JCN PhysicsCore9702 20.5 · 9702 21.1 · 9702 21.2
DC Generator
Add a commutator to a generator and see the rectified DC output
Try this
1. Spin the coil and watch the commutator output.
2. Compare the output with the AC generator's trace.
Look for The commutator reverses the connections every half turn, so the output is a rectified, one-direction emf.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
PhET9702 21.1 · IB B.5
Circuit Construction Kit: AC — Virtual Lab
Build AC and DC circuits from batteries, AC sources, resistors, capacitors and inductors, measured with realistic meters only.
Try this
1. Wire an AC source to a resistor and clip the voltmeter across it — read the trace on the chart.
2. Swap the resistor for a capacitor — the current peaks before the voltage.
3. Add an inductor — now the current lags.
Look for Realistic meters load the circuit slightly; in AC, current and voltage can be out of phase.
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)
SimuPhysics9702 17.3 · 9702 21.1 · IB C.4
Wireless Radio Tuning
Several stations broadcast at once; tune the LC circuit and only the station matching its natural frequency comes through
Try this
1. Tune the circuit to one station.
2. Tune between stations and listen.
3. Compare the station frequency with the circuit frequency.
Look for A station comes through when its frequency matches the circuit's natural frequency.
Open on SimuPhysicsRuns on their site
SimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)
SimuPhysics9702 21.1
Hot Wire Ammeter (Thermal Ammeter)
The wire expands as it heats, the fine thread takes up the slack and the pointer swings; works on AC and DC alike
Try this
1. Pass a DC current and watch the pointer.
2. Switch to AC and compare.
3. Double the current and compare.
Look for The reading depends on heating, so it is the same for AC and DC of the same r.m.s. value.
Open on SimuPhysicsRuns on their site
SimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)
3JCN Physics9702 20.5 · 9702 21.1 · IB D.4
Transformer
Change turns ratio of a transformer; read primary and secondary voltages
Try this
1. Set a 1:2 turns ratio and read the primary and secondary voltages.
2. Reverse to 2:1 and compare.
Look for Vs / Vp equals Ns / Np.
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

$X = x_0\sin(\omega t)$

Tap a symbol — great for exam definitions

KEY RELATION

$\omega = 2\pi f$

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KEY RELATION

$V_{rms} = \frac{V_{peak}}{\sqrt{2}}$

KEY RELATION

$I_{rms} = \frac{I_{peak}}{\sqrt{2}}$

KEY RELATION

$P(t) = (I_0 \sin(\omega t))^2 R = I_0^2 R \sin^2(\omega t)$

Tap a symbol — great for exam definitions

KEY RELATION

$\left = \text{average of } (I_0^2 R \sin^2(\omega t)) = I_0^2 R \times (\text{average of } \sin^2(\omega t)) = I_0^2 R \times \frac{1}{2}$

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KEY RELATION

$\left = \frac{1}{2} P_{max} = \frac{1}{2} I_0^2 R = \frac{1}{2} \frac{V_0^2}{R}$

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KEY RELATION

$\left = I_{rms}^2 R = \frac{V_{rms}^2}{R} = V_{rms} I_{rms}$

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Full topic notes

Formal explanation with the rigour you need for the exam.

What is Alternating Current (AC)?

Definition: An alternating current (AC) is one that periodically reverses its direction of flow.
Waveform: The magnitude of an AC also varies continuously with time, typically in a sinusoidal pattern.
Contrast with DC: Direct current (DC) flows in a single, constant direction with a steady magnitude.
Key Parameters: AC is described by its frequency, period, and amplitude (peak value).

Not clear?

Understanding AC Values

$X = x_0\sin(\omega t)$

$\omega = 2\pi f$

Instantaneous value ( $X$ ) is AC's value at a specific time.
Peak value ( $x_0$ ) is the maximum amplitude in a cycle.
Angular frequency ( $\omega$ ) determines oscillation speed.
Normal frequency ( $f$ ) is the number of cycles per second.

Not clear?

Peak vs. Root Mean Square (RMS)

$V_{rms} = \frac{V_{peak}}{\sqrt{2}}$

$I_{rms} = \frac{I_{peak}}{\sqrt{2}}$

RMS value is the 'effective' value of AC.
It represents the DC equivalent for power dissipation.
For sinusoidal AC, $V_{rms}$ is $V_{peak}$ divided by $\sqrt{2}$ .
Similarly, $I_{rms}$ is $I_{peak}$ divided by $\sqrt{2}$ .

Not clear?

Power in AC Circuits

The instantaneous power in an AC circuit continuously varies because voltage and current are changing. However, we are usually interested in the mean power dissipated over a full cycle.

Not clear?

Deducing Mean Power

$P(t) = (I_0 \sin(\omega t))^2 R = I_0^2 R \sin^2(\omega t)$

Therefore, the mean power $\left$ is the average of the instantaneous power:

$\left = \text{average of } (I_0^2 R \sin^2(\omega t)) = I_0^2 R \times (\text{average of } \sin^2(\omega t)) = I_0^2 R \times \frac{1}{2}$

Since $P_{max} = I_0^2 R$ , we can conclude that:

$\left = \frac{1}{2} P_{max} = \frac{1}{2} I_0^2 R = \frac{1}{2} \frac{V_0^2}{R}$

A key advantage of using RMS values is that they simplify mean power calculations, making them identical to DC power calculations. This is precisely why RMS values are so useful!

$\left = I_{rms}^2 R = \frac{V_{rms}^2}{R} = V_{rms} I_{rms}$

Instantaneous power in AC varies continuously, but is always non-negative in a resistor.
Mean power over a cycle is half the peak power for sinusoidal AC.
This is because the average value of $\sin^2(\omega t)$ is 1/2.
RMS values allow for straightforward power calculations using DC-like formulas.

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 mains electricity supply has a peak voltage ( $V_{peak}$ ) of 325 V.

Calculate its Root Mean Square (RMS) voltage.
If this supply is connected to a heating element with a resistance of 60 \u03a9, what is the mean power dissipated by the element?

1
Calculate RMS voltage:

EXAMPLE 2

An AC source provides a current described by the equation $I = 5.0 \sin(100\pi t)$ , where $I$ is in amperes and $t$ is in seconds. The current flows through a 20 \u03a9 resistor.

What is the peak current?
What is the frequency of the supply?
Calculate the RMS current.
Determine the mean power dissipated in the resistor.

1
Identify Peak Current ( $I_0$ ):

How it all connects

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

MAIN IDEACharacteristics of alternating currents

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Glossary

Key terms for this topic — skim now; the Check step will test them.

instantaneous value: Here, $X$ is the instantaneous value (voltage or current) at time $t$ . $x_0$ is the peak value (or amplitude) – the absolute maximum magnitude reached. $\omega$ (omega) is the angular frequency, which tells us how quickly the AC oscillates.
Alternating Current (AC): An electric current that periodically reverses its direction and continuously varies its magnitude over time.
AC differ from Direct: AC reverses direction and varies in magnitude, while DC flows in a constant direction with a steady magnitude.
Root Mean Square (RMS): The DC equivalent value that would dissipate the same average power in a resistor.

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

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Your guess — write it before you look

1 / 13 · ← → space

Key takeaways

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

close the tab only after these stick

Definition: An alternating current (AC) is one that periodically reverses its direction of flow.
Waveform: The magnitude of an AC also varies continuously with time, typically in a sinusoidal pattern.
Contrast with DC: Direct current (DC) flows in a single, constant direction with a steady magnitude.
Key Parameters: AC is described by its frequency, period, and amplitude (peak value).

Practice — then mark it

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

Question 1 of 29702/42 · Q8(b)(i)

PhysicsMay/June 2025

(b) (i)

Determine the peak power P₀ in the resistor.

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

9702/42/M/J/25

Question 2 of 29702/42 · Q8(b)(iii)

PhysicsMay/June 2025

(b) (iii)

Use the answer in (b)(ii) to explain why the mean power in the resistor is ¼ P₀.

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

9702/42/M/J/25

Extra simulations & links

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

Frequently asked

Why do countries use AC for mains electricity instead of DC?

What's the difference between frequency (

f

) and angular frequency (

\omega

Is the RMS value always

V_{peak}/\sqrt{2}

for any alternating current?

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 9702/42 · Q8(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

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Revise Characteristics of alternating currents for Cambridge 9702 (21.1)

In simple terms

What this topic covers

Explore the concept

Simulations

AC Generator

Trigonometric Circle

Generator

3D AC Dynamo

AC Circuits Lab

DC Generator

Circuit Construction Kit: AC — Virtual Lab

Wireless Radio Tuning

Hot Wire Ammeter (Thermal Ammeter)

Transformer

Key formulas

Full topic notes

What is Alternating Current (AC)?

Understanding AC Values

Peak vs. Root Mean Square (RMS)

Power in AC Circuits

Deducing Mean Power

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 Characteristics of alternating currents

Revise Characteristics of alternating currents for Cambridge 9702 (21.1)

In simple terms

What this topic covers

Explore the concept

Simulations

AC Generator

Trigonometric Circle

Generator

3D AC Dynamo

AC Circuits Lab

DC Generator

Circuit Construction Kit: AC — Virtual Lab

Wireless Radio Tuning

Hot Wire Ammeter (Thermal Ammeter)

Transformer

Key formulas

Full topic notes

What is Alternating Current (AC)?

Understanding AC Values

Peak vs. Root Mean Square (RMS)

Power in AC Circuits

Deducing Mean Power

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 Characteristics of alternating currents