Ch 12 · 4.5.2 The a.c. Generator · O Level Physics 5054

Topic 12 of 17 in Electricity and Magnetism — O Level Physics 5054 — 49 lessons.

Introduction

A bicycle dynamo, a wind turbine and a giant power-station generator all work the same way: something spins, a coil and a magnet move relative to each other, and an alternating e.m.f. is induced. (Syllabus section 4.5.2.)

Key ideas — The rotating-coil generator

Slip rings and brushes. Each end of the coil is joined to its own metal slip ring, which turns with the coil. Carbon brushes press against the rings and connect them to the outside circuit. The rings let the coil turn freely without the wires twisting, and each brush always stays connected to the same end of the coil, so the output is a.c.

🧑‍🏫 Teacher's explanation

Imagine you are walking through a heavy rainstorm. If you hold a large rectangular hoop and spin it while walking, some parts of the hoop are moving 'with' the wind and some are moving 'against' it. In a generator, the 'wind' is the magnetic field. As the coil rotates, one side of the wire is always moving across the magnetic field lines in one direction, while the opposite side is moving in the opposite direction. This creates a push (e.m.f.) in one direction, then a push in the other direction half a turn later.

📖 Definitions

🔍 Worked example — Easy

A simple a.c. generator consists of a coil rotating in a uniform magnetic field. If the coil completes 50 full rotations in 1 second, how many times does the direction of the induced e.m.f. reverse in that second?

🔍 Worked example — Standard

A generator produces an e.m.f. e that follows a sinusoidal pattern. At t = 0 s, the coil is perpendicular to the magnetic field lines. At t = 0.005 s, the coil has rotated 90^° (one quarter turn). What is the state of the induced e.m.f. at t = 0.005 s?

🔍 Worked example — Exam-style

A generator's e.m.f. is given by e = 12 sin(100π t) where e is in Volts and t is in seconds. Calculate the maximum e.m.f. produced by this generator.

⚠️ Common errors

🧠 Quick check 1

🧠 Quick check 2

🎯 Exam question

Key ideas — The rotating-magnet generator

Instead, a magnet can spin inside a fixed coil (as in a bicycle dynamo and in power-station generators, where the "magnet" is an electromagnet). The changing field through the coil induces an alternating e.m.f. Because the coil does not move, no slip rings or brushes are needed for the output.

🧑‍🏫 Teacher's explanation

Imagine you are holding a flashlight and spinning it rapidly in front of a sensor. As the beam sweeps across the sensor, the light intensity isn't constant; it pulses. An a.c. generator works on a similar principle of 'changing' something to create an effect. Instead of light, we use a magnetic field.

📖 Definitions

🔍 Worked example — Easy

A simple a.c. generator produces a peak e.m.f. of 0.5 V. What is the e.m.f. when the coil is at a position where the magnetic flux linkage is exactly half of its maximum value?

🔍 Worked example — Standard

A generator coil rotates at a constant speed. At t = 0 s, the e.m.f. is 0 V. At t = 0.01 s, the e.m.f. reaches its maximum positive value. What is the period T of the rotation?

🔍 Worked example — Exam-style

A generator produces an e.m.f. described by e = 12sin(100π t). Calculate the maximum e.m.f. produced.

⚠️ Common errors

🧠 Quick check 1

🧠 Quick check 2

🎯 Exam question

Key ideas — The e.m.f.–time graph

The output is a wave (a sine-shaped curve) above and below zero. Relating it to the coil's position:

🧑‍🏫 Teacher's explanation

Imagine a rectangular wire loop spinning inside a magnetic field. To generate electricity, the wire must 'cut' through the magnetic field lines. The amount of electricity (e.m.f.) produced depends on how many field lines the wire cuts per second. Think of it like a person running through a series of vertical poles; if you run directly through them, you hit them frequently (maximum effect), but if you run parallel to them, you never actually hit them (zero effect).\n\nWhen the coil is vertical (perpendicular to the field lines), the sides of the loop are moving parallel to the field lines. They aren't 'cutting' anything, so the e.m.f. is zero. When the coil is horizontal (parallel to the field lines), the sides are moving at right angles to the field lines, cutting them at the maximum rate. This creates the peak of the wave. As the coil continues to rotate, the direction of the wire's motion relative to the field flips, which is why the graph goes from a positive peak to a negative trough.

📖 Definitions

🔍 Worked example — Easy

A simple a.c. generator rotates at a constant speed. If the coil is in the vertical position (perpendicular to the field lines), what is the value of the e.m.f. produced?

🔍 Worked example — Standard

A generator produces a peak e.m.f. of 5.0 V when the coil is horizontal. What is the e.m.f. when the coil has rotated through an additional 90^° from the horizontal position?

🔍 Worked example — Exam-style

An a.c. generator completes 50 full rotations in 1 second. Calculate the frequency of the e.m.f. produced.

⚠️ Common errors

🧠 Quick check 1

🧠 Quick check 2

🎯 Exam question

Key ideas — Changing the output

🧑‍🏫 Teacher's explanation

Imagine you are standing by a river and you are swinging a stick through the water. If you swing the stick very fast, you feel more resistance because you are cutting through more water molecules every second. This is exactly what happens in an a.c. generator. The 'resistance' you feel is the electromotive force (e.m.f.) being generated.

📖 Definitions

🔍 Worked example — Easy

A simple a.c. generator produces a peak e.m.f. of 2.0 V when rotating at a frequency of 50 Hz. If the rotation speed is doubled, what is the new peak e.m.f. and the new frequency?

🔍 Worked example — Standard

A coil with N = 200 turns produces a peak e.m.f. of 12 V. If the number of turns is increased to 500 turns while keeping the rotation speed constant, calculate the new peak e.m.f.

🔍 Worked example — Exam-style

An a.c. generator's e.m.f. graph shows a peak of 5.0 V at t = 0.005 s and the next zero-crossing (where the signal goes from positive to negative) occurs at t = 0.010 s. Calculate the frequency of the generator.

⚠️ Common errors

🧠 Quick check 1

🧠 Quick check 2

🎯 Exam question

(a) State what happens to the peak e.m.f. if the number of turns is doubled. (b) State what happens to the frequency of the output if the rotation speed is doubled. (c) Sketch a graph of e.m.f. against time for one full cycle, labeling the peak e.m.f. value. [4 marks]

Worked example

A generator coil turns 50 times every second. (a) What is the frequency of the a.c.? (b) How many times per second is the e.m.f. zero? (c) Sketch what happens to the graph if the coil turns at 100 times per second.

🔍 Worked example — Easy

A simple a.c. generator coil rotates at a constant rate of 25 Hz. Calculate the frequency of the induced e.m.f.

🔍 Worked example — Standard

A generator coil completes 60 revolutions per second. How many times per second does the induced e.m.f. reach a value of zero?

🔍 Worked example — Exam-style

A generator produces an e.m.f. graph with a peak voltage of 4.0 V at a frequency of 50 Hz. If the speed of rotation is doubled to 100 Hz, what is the new frequency and what happens to the peak voltage (assuming the magnetic field and coil area remain constant)?

⚠️ Common errors

Common mistakes

Practice

Answers: (1) They connect the rotating coil to the external circuit without the wires twisting; each brush stays connected to the same end of the coil. (2) When the plane of the coil is parallel to the field lines; the sides of the coil are then cutting field lines at the fastest rate. (3) Any two: turn the coil faster; use more turns; use a stronger magnet. (4) The output coil is fixed; only the magnet moves, so the coil's wires can be connected directly.

Ch 12 · 4.5.2 The a.c. Generator · O Level Physics 5054

All chapters in Electricity and Magnetism