11 min readPathway sheetSection B short answer (3 marks) or long answer (5 marks): principle, parts and working of an AC generator with a diagram; very short answer (2 marks): AC and DC generators compared; Section A objective (2 marks, two parts) on stabilisers and inverters

AC and DC generators, and coping with low voltage and load shedding

A generator turns a coil in a magnetic field, giving ε = NABω sin ωt. Slip rings give AC; a split-ring commutator gives DC.

PrincipleElectromagnetic induction: a coil turning in a magnetic field has a changing flux, so an emf is induced

emf of an AC generatorε = NABω sin ωt, with peak ε₀ = NABω, where ω = 2πν

AC and DC generatorsAC: slip rings and brushes. DC (dynamo): a split-ring commutator, so the output never reverses

InverterChanges DC from a battery into AC at the mains voltage and 50 Hz

Principle and parts of an AC generator

A generator changes mechanical energy into electrical energy using a magnetic field. It works on electromagnetic induction. It has four main parts. (i) The armature is a coil of many turns of insulated copper wire, wound on a soft iron drum that turns on a shaft. (ii) The field magnet gives a strong magnetic field. (iii) Two slip rings are metal rings fixed to the shaft, each joined to one end of the coil. (iv) Two brushes, carbon or metal strips, press on the rings and carry the current to the outside circuit. The soft iron drum supports the coil and makes the field through it stronger. Falling water, steam from coal or nuclear fuel, wind or a diesel engine can supply the turning.

Working, and deriving ε = NABω sin ωt

1
The coil, of N turns and area A, turns at a steady angular speed ω in a uniform field B.
2
At time t, the angle between B and the normal to the coil is θ = ωt. The flux through each turn is φ = AB cos ωt.
3★
Induced emf: ε = −N dφ/dt = NABω sin ωt = ε₀ sin ωt, with peak ε₀ = NABω.
4
The emf is zero when the plane of the coil is at right angles to B, and largest when the plane lies along B.
5
During one half turn, each side of the coil moves up through the field; during the next, it moves down. So the current reverses every half turn: it is alternating.
6
Fleming's right-hand rule gives the direction of the current in each side at any moment.
7
In large power-station generators, the coils stay still and the magnet turns. This avoids sparking at slip rings when huge currents flow.

★ key step

AC generator vs DC generator (dynamo)

AC generator (alternator)Each end of the coil is joined to its own slip ring. The connection to the outside circuit never changes, so the output reverses every half turn: a sine-shaped AC.

DC generator (dynamo)The coil ends are joined to the two halves of one split ring, the commutator. Just as the emf reverses, the halves swap brushes. So one brush always stays positive, and the output flows one way, though it rises and falls to zero twice each turn.

Many coils set at angles to each other, with a commutator of many segments, make a dynamo's output nearly steady. Older cars used a dynamo to charge the battery; a bicycle 'dynamo' that lights a lamp is usually a small AC generator.

How to draw the AC generator

Draw the curved pole pieces of the field magnet, N on the left and S on the right.
Between them, draw a rectangular coil ABCD on a shaft, with a curved arrow showing its rotation.
At the end of the shaft, draw two separate rings, the slip rings R₁ and R₂, each joined to one end of the coil.
Draw two brushes B₁ and B₂ pressing on the rings. Join the brushes to a load, such as a bulb or a resistor.
Beside it, sketch the output: a sine curve of ε against t, with the peak ε₀ marked.
For a dynamo, draw one ring split into two halves instead, and sketch the output as humps that stay above the time axis.

Low voltage and stabilisers; load shedding and inverters

Low voltage, and the stabiliserWhen the supply voltage falls below its proper value, appliances such as fridges and air conditioners do not work properly. Low voltage is less harmful than high voltage, but it still causes trouble. A voltage stabiliser, or a constant voltage transformer (CVT), gives a steady output voltage as long as the input stays within its range.

Load shedding, and the inverterA local transformer must not carry more load than its rating, or it may burn out. When demand is too high, the supply company cuts power to some areas for a time. This is load shedding. An inverter then changes DC from a battery into AC at the mains voltage and 50 Hz, so lights and fans keep running.

A stabiliser corrects a supply that is present but low; an inverter makes AC when the supply is cut.

Worked example: peak and rms emf of a generator

Problem

A generator coil has 500 turns, each of area 0.020 m². It turns at 50 revolutions per second in a uniform field of 0.050 T. Find (a) the peak emf, (b) the rms emf and (c) the peak emf if the speed is doubled. (π = 3.14, √2 = 1.414)

Working

ω = 2πν = 2 × 3.14 × 50 rad s⁻¹ = 314 rad s⁻¹.
(a) ε₀ = NABω = 500 × 0.020 m² × 0.050 T × 314 rad s⁻¹.
500 × 0.020 × 0.050 = 0.50, so ε₀ = 0.50 × 314 V = 157 V.
(b) ε_rms = ε₀/√2 = 157 V ÷ 1.414 ≈ 111 V.
(c) Doubling the speed doubles ω, so ε₀ doubles to 314 V. The frequency also doubles, to 100 Hz.

Answer

(a) 157 V; (b) about 111 V; (c) 314 V, at 100 Hz

In real life

Most of India's electricity comes from huge AC generators turned by steam or water. Diesel generator sets in shops and hospitals work the same way. During load shedding, a home inverter turns battery DC into 50 Hz AC.

Exam angle

5 marks: “Explain the principle, construction and working of an AC generator with a labelled diagram. Show that the emf it produces is ε = NABω sin ωt.” Principle: electromagnetic induction; parts: armature, field magnet, slip rings, brushes; diagram; φ = AB cos ωt per turn, ε = NABω sin ωt; reverses every half turn; output is a sine curve.

2 marks: “Distinguish between an AC generator and a DC generator.” AC: slip rings, so the output reverses every half turn. DC: a split-ring commutator, so the output flows in one direction (though it fluctuates).

2 marks: “What is load shedding? How does an inverter help during it?” Cutting the supply to some areas for a time when the load is too high for the transformers or the system. An inverter changes battery DC into AC at the mains voltage and 50 Hz.

Remember it

Slip rings for AC, split ring for DC. Peak emf ε₀ = NABω: more turns, more area, a stronger field or faster turning give more volts.