Physics • Year 12 • Module 6 • Lesson 11
AC Generators — Changing Flux
Secure the core vocabulary, the flux and emf equations, the 90° phase relationship, and the role of slip rings before tackling calculations and graph analysis.
1. Term–definition match
The definitions below are shuffled. In the right-hand column write the matching term from this list: AC generator (alternator), slip rings, brushes, peak emf (ε0), angular frequency (ω), magnetic flux (Φ), Faraday’s Law, coil area (A), period (T), commutator. 10 marks (1 each)
| # | Definition | Matching term |
|---|---|---|
| 1.1 | A device that converts mechanical rotational energy into alternating current via electromagnetic induction. | |
| 1.2 | Continuous conducting rings that maintain electrical contact with a rotating coil without reversing the current direction. | |
| 1.3 | Carbon or graphite contacts that press against the rings to transfer current to the external circuit. | |
| 1.4 | The maximum value of induced emf in a rotating coil; equal to NBAω. | |
| 1.5 | The rate of rotation expressed in radians per second; related to frequency by ω = 2πf. | |
| 1.6 | The product of magnetic field strength, the number of turns, and the area component perpendicular to the field; measured in webers (Wb). | |
| 1.7 | The law stating that the induced emf in a circuit equals the negative rate of change of magnetic flux through it. | |
| 1.8 | The surface enclosed by the coil through which flux is calculated; maximum flux occurs when this faces the magnetic field perpendicularly. | |
| 1.9 | The time for one complete rotation of the coil; equal to 1/f. | |
| 1.10 | A split-ring device used in DC motors and generators to reverse the current direction every half-turn, producing rectified output — not used in AC generators. |
2. True or false — with correction
Circle T or F for each statement. If the statement is false, write the corrected version on the line below it. 12 marks (1 T/F + 1 correction each)
2.1 When the coil of an AC generator is perpendicular to the magnetic field, the flux through it is at a maximum and the induced emf is also at a maximum. T / F
2.2 The peak emf of an AC generator is given by ε0 = NBAω, where N is the number of turns, B is the field strength, A is the coil area, and ω is the angular frequency. T / F
2.3 Slip rings are used in AC generators to reverse the current direction every half-turn, converting the AC output to DC. T / F
2.4 Doubling the rotation frequency of an AC generator doubles both the peak emf and the frequency of the output voltage. T / F
2.5 The magnetic flux through a rotating coil varies as Φ = NBA sin(ωt) when the coil starts perpendicular to the magnetic field at t = 0. T / F
2.6 Flux and emf are 90° out of phase: when flux is at its maximum value, the rate of change of flux — and therefore the emf — is zero. T / F
3. Fill-in-the-blank paragraph
Use the word bank to complete the passage. Each word is used once. 8 marks (1 per blank)
Word bank:
alternating · cosine · flux · maximum · NBAω · parallel · sine · slip rings
In an AC generator, a rectangular coil rotates in a uniform magnetic field. The magnetic ___________ through the coil changes continuously and is described by the equation Φ = NBA ___________(ωt). Differentiating this expression gives the induced emf: ε = ___________ sin(ωt). The emf is at its ___________ value when the coil is ___________ to the magnetic field, because the coil sides are moving perpendicular to the field and cutting field lines at the greatest rate. The output of the generator is ___________ current because the emf reverses direction each half-turn. Continuous electrical contact between the rotating coil and the external circuit is maintained by ___________, which do not reverse the current. The emf follows a ___________ wave pattern over time.
4. Function recall
Answer each question in 1–2 sentences using precise terms from the lesson. 8 marks (2 each)
4.1 Explain why the induced emf in an AC generator is zero when the coil is perpendicular to the magnetic field.
4.2 What is the function of slip rings in an AC generator, and how do they differ from a split-ring commutator?
4.3 State the relationship between peak emf and each of the four variables N, B, A, and ω. What would happen to peak emf if the coil area were halved?
4.4 Describe the phase relationship between the flux graph and the emf graph for a rotating coil. At what coil orientation is each quantity at its maximum?
5. Formula recall and symbol identification
Complete the table below for the two key AC generator equations. 8 marks (1 per cell)
| Equation | What it calculates | SI unit of the quantity on the left | One factor that doubles the result |
|---|---|---|---|
| Φ = NBA cos(ωt) | |||
| ε = NBAω sin(ωt) |
5.1 In the formula ε0 = NBAω, what does each letter stand for? Write the name and SI unit for each symbol.
6. Build a concept map
Draw labelled arrows between the six terms below to show how they are connected. Each arrow must carry a linking phrase (e.g. “determines”, “is 90° out of phase with”, “is maximised when”). Aim for at least 6 labelled arrows. 6 marks (1 per valid labelled arrow)
Supplied terms: magnetic flux · induced emf · coil orientation · angular frequency · peak emf · slip rings.
Q1 — Term–definition match
1.1 AC generator (alternator) • 1.2 slip rings • 1.3 brushes • 1.4 peak emf (ε0) • 1.5 angular frequency (ω) • 1.6 magnetic flux (Φ) • 1.7 Faraday’s Law • 1.8 coil area (A) • 1.9 period (T) • 1.10 commutator.
Q2 — True / false with correction
2.1 False. When the coil is perpendicular to the field (ωt = 0), flux IS at a maximum BUT the emf is ZERO (not maximum), because the rate of change of flux is zero at that instant.
2.2 True.
2.3 False. Slip rings do NOT reverse the current direction. They maintain continuous contact with the rotating coil without reversing current, which is why the output remains alternating (AC). It is the split-ring commutator that reverses current to produce DC output.
2.4 True. Doubling ω (= 2πf) doubles the peak emf via ε0 = NBAω, and also doubles the output frequency f, so both effects are correct.
2.5 False. When the coil starts perpendicular to the field at t = 0, flux is at its maximum and follows Φ = NBA cos(ωt), not sin(ωt). The sin function describes the emf: ε = NBAω sin(ωt).
2.6 True.
Q3 — Cloze paragraph
In order: flux / cosine / NBAω / maximum / parallel / alternating / slip rings / sine.
Q4.1 — Why emf is zero when coil is perpendicular
When the coil is perpendicular to the magnetic field, the coil sides are moving parallel to the field lines and are not cutting through them. The rate of change of flux (dΦ/dt) is zero at this instant, so by Faraday’s Law (ε = −dΦ/dt) the induced emf is also zero. This is the point of maximum flux, but minimum rate of change of flux.
Q4.2 — Slip rings vs commutator
Slip rings are continuous conducting rings that maintain electrical contact with the rotating coil without reversing the current direction; they pass the alternating voltage unchanged to the external circuit, preserving the AC output. A split-ring commutator, by contrast, is split into two halves that swap the connection to the external circuit every half-turn, reversing the current at the output to produce a pulsating DC. AC generators need slip rings precisely because the AC output must not be rectified.
Q4.3 — Peak emf and four variables
ε0 = NBAω: peak emf is directly proportional to each of N (turns), B (field strength), A (coil area), and ω (angular frequency). If coil area A were halved, peak emf would also halve (direct proportion), assuming all other quantities remain constant.
Q4.4 — Phase relationship between flux and emf
Flux and emf are 90° (one quarter-cycle) out of phase. Flux is maximum (Φ = NBA) when the coil is perpendicular to the field (ωt = 0°), but emf is zero at this instant. The emf is maximum (ε = NBAω) when the coil is parallel to the field (ωt = 90°), at which point flux is zero but changing at its fastest rate.
Q5 — Formula recall table
Φ = NBA cos(ωt): Calculates magnetic flux through the rotating coil at time t. SI unit: weber (Wb). One factor that doubles the result: doubling N (number of turns) OR doubling B OR doubling A.
ε = NBAω sin(ωt): Calculates instantaneous induced emf at time t. SI unit: volt (V). One factor that doubles the result: doubling N, B, A, or ω.
5.1: N = number of turns (dimensionless); B = magnetic flux density / field strength (tesla, T); A = coil area (metres squared, m²); ω = angular frequency (radians per second, rad s−1).
Q6 — Sample concept map
Valid arrows include:
- magnetic flux — is 90° out of phase with → induced emf
- coil orientation — determines the magnitude of → magnetic flux
- angular frequency — directly determines → peak emf
- induced emf — is limited by → peak emf
- slip rings — transfer to external circuit → induced emf
- peak emf — equals NBAω, so depends on → angular frequency
Award 1 mark per valid labelled arrow (minimum 6 required, maximum 6 marked).