F. Electricity and Magnetism · Electricity and MagnetismGenerators, Alternating Current and Direct Current
F3.6 F3.7 F3.4 F2.1About 70 minutes
Learning goals- I can explain how an AC generator and a DC generator work, including the job of slip rings and a split-ring commutator.
- I can sketch the output of AC and DC generators and relate it to the position of the coil.
- I can distinguish alternating current from direct current and use frequency, period and peak values.
- I can use Lenz's law to explain why a generator under load is harder to turn.
Words to know
generator
A device that changes kinetic (mechanical) energy into electrical energy by electromagnetic induction.
alternating current (AC)
Current that reverses direction many times a second. In Canada the grid's frequency is 60 Hz.
direct current (DC)
Current that flows in one direction only.
slip rings
Two complete rings on the axle of an AC generator, each connected to one end of the coil, which let the alternating current out through brushes.
frequency (f)
The number of complete cycles per second, in hertz (Hz). Period T = 1 ÷ f.
peak and effective values
The peak is the largest value an AC voltage reaches. The effective (rms) value is the DC value that would deliver the same power; for a sine wave, peak = √2 × effective.
turbine
A machine with blades that is turned by moving water, steam or wind and in turn spins a generator.
Spinning makes power
Turn the crank on an emergency radio or flashlight and it lights up. Inside, you are spinning a small generator. Ontario's power stations do the same thing on a giant scale: falling water at Niagara, steam from nuclear reactors or burning natural gas, or wind turns a turbine, and the turbine spins a generator. The physics is the electromagnetic induction you learned in the last lesson.
The AC generator
A coil (the armature) is turned in a magnetic field. As it turns, the field through the coil keeps changing, so a potential difference is induced (Faraday's law).
- Each end of the coil is connected to its own slip ring. Brushes press on the rings and carry the current to the external circuit.
- During one half-turn, one side of the coil moves up through the field while the other moves down. During the next half-turn, the sides swap. So the induced current reverses every half-turn: alternating current.
- The output is greatest when the coil's sides are moving straight across the field lines (the plane of the coil is parallel to the field). It is zero at the instant the sides move along the field lines (the plane of the coil is perpendicular to the field).
- Plotted against time, the output is a sine wave. For a simple two-pole generator, one turn of the coil gives one cycle.
Large power-station generators usually do it the other way round: a powerful rotating electromagnet (the rotor) spins inside stationary coils (the stator). It is still a changing field through a coil, and it avoids sending huge currents through sliding contacts.
A simple AC generator. A turbine turns the coil between the magnet's poles. Each end of the coil connects to its own slip ring, and the brushes carry the alternating current to the lamp.The DC generator
Replace the slip rings with a split-ring commutator, just like the one in a DC motor. Every half-turn, just as the induced current in the coil reverses, the commutator swaps the connections. The current in the external circuit always flows the same way, but it rises and falls: pulsating DC.
Notice the symmetry: a DC motor and a DC generator have the same parts. Supply current and it turns (motor); turn it and it supplies current (generator).
Output of a simple generator over two turns. With slip rings the voltage reverses every half-turn (AC). With a split-ring commutator every half-cycle is flipped to the same side (pulsating DC).Lenz's law in a generator
When a generator supplies current, that current flows through the coil, which sits in a magnetic field. By the motor principle there is a force on it, and by Lenz's law that force opposes the rotation. So:
- With no load (open circuit), no current flows and the generator turns easily.
- With a bigger load (more current drawn), the opposing force is bigger, and the turbine must push harder.
That is why a power station must burn more fuel, or let more water through its turbines, when Ontario's demand rises on a hot summer afternoon. The electrical energy comes from the work done turning the generator.
AC versus DC
- DC flows one way. Sources: batteries, solar cells, DC generators, phone chargers' outputs.
- AC reverses direction regularly. In Canada and the rest of North America the grid alternates at 60 Hz, so each cycle lasts T = 1 ÷ 60 ≈ 0.0167 s, and the current reverses 120 times a second.
- A household outlet is rated 120 V. That is an effective value. For a sine wave, the peak is √2 × 120 ≈ 170 V. (Stoves and dryers use 240 V.)
Why AC for the grid? AC can be stepped up and down easily with transformers, which need a changing current. Sending electricity at very high voltage means a small current, which wastes far less energy in the lines. In the 1880s and 1890s, Thomas Edison promoted DC systems while George Westinghouse and Nikola Tesla promoted AC; AC won mainly because of the transformer. You will see the details in the lessons Transformers and Transmitting Electrical Energy.
DC is still used inside every electronic device, and some very long-distance lines use high-voltage DC, which needs special converter stations at each end.
From energy source to the grid. Almost every type of power station ends with a turbine spinning a generator; solar photovoltaic panels are the main exception.Worked exampleExample 1: Frequency and rotation
A simple two-pole AC generator produces 60 Hz. (a) What is the period? (b) How many turns does the coil make per second and per minute? (c) How many times per second does the current change direction?
- (a) T = 1 ÷ f = 1 ÷ 60 Hz ≈ 0.0167 s (16.7 ms).
- (b) One turn makes one cycle, so it turns 60 times per second, or 60 × 60 = 3600 rpm.
- (c) The current reverses twice per cycle: 2 × 60 = 120 times per second.
0.0167 s; 60 rev/s (3600 rpm); 120 reversals per second.
Worked exampleExample 2: Peak voltage
A Canadian outlet supplies 120 V (effective). A stove outlet supplies 240 V (effective). Find the peak voltage of each.
- Peak = √2 × effective.
- 120 V outlet: √2 × 120 ≈ 1.414 × 120 ≈ 170 V.
- 240 V outlet: √2 × 240 ≈ 339 V.
- The effective value is the one used with P = VI to find average power.
Worked exampleExample 3: Where is the output biggest?
A coil turns in a horizontal magnetic field (N on the left, S on the right). At which positions is the induced voltage (a) greatest and (b) zero?
- The induced voltage depends on how quickly the coil's sides cut across field lines.
- (a) Greatest when the plane of the coil is horizontal (parallel to the field): the sides are moving straight up and down, perpendicular to the field lines.
- (b) Zero when the plane of the coil is vertical (perpendicular to the field): the sides are moving horizontally, along the field lines, for an instant, so they are not cutting across them.
Greatest with the coil's plane parallel to the field; zero with it perpendicular.
Just for funThe current in your wall outlets changes direction 120 times every second. Your toaster never complains, and it never gets dizzy.
Hands-on activityFeel Lenz's law in a generator
Option A (with a crank device): if your home has a hand-crank emergency radio or flashlight, turn the crank with the light or radio off, then on at full volume or brightness. Compare how hard it is to turn.
Option B (with a small motor): use a small DC toy motor (from an old toy, batteries removed; ask a grown-up to help take it out), an LED, and a multimeter if you have one. Wind a string around the motor's shaft and pull it quickly to spin the motor. Connect the motor to the meter (mV DC) or to the LED. Try pulling slowly and quickly, and spinning one way, then the other.
Option C (computer): in the PhET "Faraday's Law" or "Generator" simulation, run the water wheel at different speeds with the bulb or voltmeter.
What to look for: the crank is harder to turn when it is supplying energy (Lenz's law: the induced current makes an opposing force). A spun motor works as a generator: faster spinning gives a larger reading. Reversing the direction of spin reverses the sign of the reading, and an LED lights only for one direction, because it lets current through only one way.
Your turn
1What energy change happens in a generator?
Kinetic (mechanical) energy → electrical energy.
2What is the difference between the slip rings of an AC generator and the split ring of a DC generator?
Slip rings are two complete rings, each always connected to the same end of the coil, so the alternating current passes straight out. A split ring swaps the connections every half-turn, so the output current always flows the same way (pulsating DC).
3A two-pole AC generator turns 50 times per second. What is the frequency and period of its output?
f = 50 Hz; T = 1 ÷ 50 = 0.020 s.
4Find the peak voltage of an AC supply with an effective voltage of 230 V.
5Why is a generator harder to turn when it is connected to a lamp than when the circuit is open?
With the lamp connected, a current flows in the coil. By the motor principle and Lenz's law, the force on this current opposes the rotation, so more work is needed. With an open circuit, no current flows and there is no opposing force.
6Give one reason AC is used to transmit electrical energy.
AC can be stepped up and down with transformers, so it can be transmitted at very high voltage and low current, which greatly reduces energy losses in the lines.
More practice: warm-up
1What is the frequency of the electrical grid in Canada?
2Name the two main parts of a large power-station generator.
The rotating rotor (an electromagnet) and the stationary stator (coils).
Any two: batteries, solar cells, DC generators, the output of a phone charger.
It is turned by moving water, steam or wind and spins the generator.
5Which Ontario electricity source does NOT use a spinning generator?
Solar photovoltaic panels.
More practice: on your own
1Sketch or describe the output of a simple AC generator over two turns, and mark when the coil's plane is parallel to the field.
A sine wave with two full cycles. The peaks (positive and negative) occur when the coil's plane is parallel to the field; the output crosses zero when the plane is perpendicular to the field.
2A DC motor is unplugged and its shaft is spun by hand. What happens and why?
It acts as a DC generator: its coil turns in the magnet's field, so a potential difference is induced, and the commutator makes the output pulsating DC. The same parts work as a motor or a generator.
3Large hydroelectric generators turn slowly, yet still produce 60 Hz. How is this possible?
They have many pairs of poles on the rotor. Each pole pair passing a stator coil produces one cycle, so many cycles are produced per turn. (For example, a rotor with 40 pole pairs needs only 60 ÷ 40 = 1.5 turns per second, or 90 rpm.)
4On a hot summer day, demand for electricity rises. Use Lenz's law to explain why generating stations must increase their energy input.
More demand means more current from each generator. A larger current in the coils makes a larger opposing force (torque) (Lenz's law), so the turbines must do more work each second, which needs more water, fuel or steam.
5Explain why AC from a wall outlet can be rated at 120 V even though the voltage swings up to about 170 V.
120 V is the effective (rms) value: the DC voltage that would deliver the same average power. A sine wave spends only an instant at its peak of √2 × 120 ≈ 170 V, and much of the time below 120 V.
Challenge
1An electric car slows down using regenerative braking. Explain the energy changes and why the car slows.
The wheels turn the motor, which now acts as a generator: the car's kinetic energy becomes electrical energy that charges the battery. The induced current in the motor's coils experiences a force that opposes the rotation (Lenz's law), which provides the braking.
2When a large electric motor first starts, it draws a very large current, which drops as it speeds up. Use induction to explain this. (Hint: a spinning motor is also a generator.)
A spinning motor's coil also acts as a generator, inducing a potential difference that, by Lenz's law, opposes the supply voltage (called a back emf). At start-up the coil is not spinning, so there is no back emf and only the coil's small resistance limits the current: the current is large. As the motor speeds up, the back emf grows, the net voltage across the coil falls, and so does the current.
3A generator delivers 2.0 A at an effective 120 V to a lamp. The generator is 80% efficient. How much mechanical power must the turbine supply?
Electrical output: P = VI = (120)(2.0) = 240 W. Input: 240 ÷ 0.80 = 300 W.
Check your understandingQuiz
1. What makes an AC generator's output alternate?
2. Which part turns the output of a simple generator into DC?
3. What is the period of 60 Hz AC?
4. Why is it harder to turn a generator when it supplies a large current?
5. The main reason AC is used to transmit electricity is that…
6. When is the induced voltage in a rotating coil zero?
For parents and teachersBig idea: Generators use electromagnetic induction to turn kinetic energy into electrical energy (F3.6). This lesson also covers the difference between AC and DC and why AC is used to transmit electricity (F3.7).
How to help: If you have a hand-crank flashlight or radio, let your teen feel how much harder it turns when the light or radio is on. That is Lenz's law and energy conservation in their hands. Talking about where your household electricity comes from (Ontario's mix of nuclear, hydro, gas, wind and solar) is a good link to the last lessons of this unit.
Common difficulties:
- Mixing up slip rings (AC out) and the split-ring commutator (DC out).
- Thinking the output is greatest when the coil faces the magnet squarely. It is greatest when the sides cut across the field fastest, with the coil's plane parallel to the field.
- Confusing 120 V (effective) with the peak voltage of about 170 V.
- Forgetting that electrical energy must come from somewhere: a generator under load needs more input work.