Generation of Electricity Notes
AREA OF STUDY 3: HOW ARE FIELDS USED IN ELECTRICITY GENERATION?
6. Generation of electricity
Key Knowledge:
Calculate magnetic flux when the magnetic field is perpendicular to the area, and describe the qualitative effect of differing angles between the area and the field:
Investigate and analyse theoretically and practically the generation of electromotive force (emf) including AC voltage and calculations using induced emf: , with reference to:
Rate of change of magnetic flux
Number of loops through which the flux passes
Direction of induced emf in a coil
Explain the production of DC voltage in DC generators and AC voltage in alternators, including the use of split ring commutators and slip rings respectively.
Describe the production of electricity using photovoltaic cells and the need for an inverter to convert power from DC to AC for use in the home (not including details of semiconductors action or inverter circuitry).
6.1 Overview
6.1.1 Introduction
Hans Christian Oersted discovered that a current-carrying wire induces a magnetic field.
Michael Faraday found that electricity could be produced from magnetism in 1831, enabling the generation of electricity on a massive scale.
This topic introduces magnetic flux and applies Faraday’s findings to create devices that generate electricity.
Learning Sequence:
6.1 Overview
6.2 Background Knowledge: Generating voltage and current with a magnetic field
6.3 Magnetic flux
6.4 Generating emf from a changing magnetic flux
6.5 Generators and alternators
6.6 Photovoltaic cells
6.7 Review
6.2 BACKGROUND KNOWLEDGE: Generating voltage and current with a magnetic field
Background Knowledge:
Explain how voltage and current is generated with a magnetic field.
Investigate and analyse the electromotive force (emf) induced in a moving conductor:
6.2.1 Generating voltage
When a metal rod moves through a magnetic field, the electrons and positively charged nuclei in the rod experience a magnetic force.
The magnitude of this force, , is equal to the charge, , multiplied by the velocity of the charge, , multiplied by the strength of the magnetic field, .
If the velocity is parallel to the magnetic field, the force will be zero.
The force on the electrons will be towards the far end of the rod, while the force on the nuclei will be to the near end of the rod.
The atomic structure of the metal prevents the movement of the positively charged nuclei.
The negatively charged electrons are free to move and move towards the far end of the rod, leaving the near end deficient in electrons and thus positively charged.
As the far end becomes more negative, there will be an increasingly repulsive force on any extra electrons at this end of the rod.
There will be an increasingly attractive force from the positively charged near end, attempting to keep the remaining electrons at that end.
The movement of the metal rod through the magnetic field has resulted in the separation of charge, causing a potential difference, or voltage drop, between the ends. This is called induced voltage.
As long as the rod keeps moving, the charges will remain separated.
As soon as the rod stops falling (at which point the velocity of the charges equals zero), the magnetic force on the charges is reduced to zero; electrons are then attracted back to the positive end and the electrons return to being distributed evenly in the rod.
A source of voltage, an emf (electromotive force), has been produced. It is like a DC battery with one end positive and the other negative.
The size of the induced emf depends on the number of electrons shifted to one end. The electrons are shifted by the magnetic force until their own repulsion balances this force.
The larger the magnetic force pushing the electrons, the more electrons are shifted to one end of the rod.
The pushing magnetic force depends on the size of the magnetic field and the velocity of the charge.
The faster the rod falls, the larger the induced emf.
When the rod is moving down with velocity , each electron experiences a force along the rod equal to .
This force pushes the electron along the length of the rod and so is doing work in separating charge.
The amount of work done, in joules, is equal to the force times the displacement:
The definition of emf (or the voltage drop across the rod) is energy supplied per unit of charge, measured in joules per coulomb, or volts.
The induced emf () is given by , which gives:
is the induced emf, in V
is the magnetic field strength, in T
is the length of the conductor, in m
is the velocity of the conductor perpendicular to the magnetic field, in m s–1
6.2.2 Generating a current
Emfs can be used to produce a current by attaching a wire to each end of the metal rod and connecting these wires outside the magnetic field, producing a closed circuit.
Now the electrons have the path of a low-resistance conductor to move to the positively charged end of the rod.
Once the electrons reach the positive end, they will be back in the magnetic field, falling down through the magnetic field with the metal rod, and will again experience a magnetic force pushing them to the far end of the rod.
The electrons will then move around the circuit for a second time.
The electrons will continue to flow around the circuit as long as the wire is moving through the magnetic field.
An electric current has been generated.
6.2.3 The source of a current’s electrical energy
Electric current has electrical energy.
Before the rod was released, it had gravitational potential energy.
If it is dropped outside the magnetic field, this gravitational potential energy is transformed into kinetic energy.
If it is dropped inside the magnetic field, the potential energy is transformed into kinetic energy and electrical energy.
Since energy is conserved, there must be less kinetic energy in the rod falling in the magnetic field than the rod falling outside of the magnetic field.
The rod in the magnetic field is falling at a slower speed.
The induced current in the falling rod means that, when the electrons are in the rod, they are moving in two directions — downwards with the rod and along the rod.
The downward movement of the rod through the magnetic field produces the sideways force along the rod that keeps the current flowing.
The movement of electrons along the rod means there is a current- carrying conductor in the magnetic field, causing the field to exert a second force on the rod.
The direction of this force is once again given by the hand rule; the magnetic field is directed to the right, the conventional current directed to the near end of the rod (out of the page), and so the force is directed upwards.
This magnetic force opposes the downward force due to gravity on the rod.
The size of the upward magnetic force depends on the size of the current.
This current will depend, in turn, on the size of the voltage drop between the ends of the rod.
Voltage will increase as the rod moves faster.
When the rod first starts falling, the magnetic force opposing the force due to gravity is small but, as the rod falls faster, the opposing magnetic force increases until it equals the force due to gravity on the rod.
At this point the rod has reached a maximum steady speed.
This situation is identical to the terminal velocity experienced by objects falling through the air.
As the metal rod falls through the magnetic field at constant speed, its kinetic energy remains constant, so the loss in gravitational potential energy is converted to electrical energy as the generated emf drives the current through the circuit.
This effect is difficult to demonstrate in practice; a magnetic field large enough for the rod to achieve terminal velocity is too difficult to construct.
However, it is possible to drop a magnet through a cylindrical conductor.
With a sufficiently strong magnet, a measurable decrease in speed against the acceleration due to gravity can be observed.
Therefore, the magnet falls with an acceleration less than 9.8 m s–2 because it experiences a retarding magnetic force.
6.3 Magnetic flux
Key Knowledge
Calculate magnetic flux when the magnetic field is perpendicular to the area and describe the qualitative effect of differing angles between the area and the field:
6.3.1 What is magnetic flux?
Magnetic flux is the amount of magnetic field passing through an area, such as a coil.
The stronger the magnetic field going through an area, the larger the magnetic flux.
Similarly, the larger the area that the magnetic field is going through, the larger the magnetic flux.
Due to this definition, the magnetic field strength is sometimes referred to as the magnetic flux density.
Magnetic flux can be calculated as the product of the strength of the magnetic field and the area that is perpendicular to the field lines.
is the magnetic flux, in Wb
is the strength of the magnetic field, in T
is the area perpendicular to the magnetic field, in m2
indicates that the area referred to in the formula is the area perpendicular to the magnetic field.
Magnetic flux is measured in webers (Wb).
One weber (Wb) is the amount of magnetic flux from a uniform magnetic field with a strength of 1.0 tesla passing through an area of 1.0 square metre.
The magnetic flux can also take on positive and negative values, depending on which side of the area the magnetic field is coming from.
This description has assumed that the area is at right angles to the magnetic field.
This leads to a maximum value for .
If the magnetic field went through the area at an angle less than 90°, the amount of magnetic flux passing through the area would be less.
If the magnetic field is parallel to the area, the amount of magnetic flux will be zero.
None of the magnetic field lines pass through the area from one side to the other.
In general, the magnetic flux can be expressed in terms of the magnetic field strength, the area and the angle () between the magnetic field and a normal to the area:
For example, if the plane of the loop is parallel to the magnetic field, the angle between the field and the normal to the area is 90°.
As , using the formula will determine the flux to be 0 Wb.
6.4 Generating emf from a changing magnetic flux
Key Knowledge
Investigate and analyse theoretically and practically the generation of electromotive force (emf) including AC voltage and calculations using induced emf, , with reference to:
rate of change of magnetic flux
number of loops through which the flux passes
direction of induced emf in a coil.
6.4.1 Faraday’s discovery of electromagnetic induction
Michael Faraday was aware of the magnetic effect of a current and he spent six years searching for the reverse effect — that is, the electrical effect of magnetism.
Faraday observed that the galvanometer needle gave a little kick as the battery switch was opened and a little kick the opposite way as the switch was closed.
The rest of the time, when the switch was either open or closed, the needle was stationary, reading zero.
The current was momentary, not the constant current he was looking for.
What Faraday had observed came to be called electromagnetic induction.
Investigating further, Faraday found that using an iron ring instead of a wooden ring increased the size of the current.
He concluded that when the magnetic field of the battery coil was changing, there was a current induced in the other coil.
He therefore replaced the battery coil with a magnet.
Moving the magnet through the other coil changed the magnetic field and produced a current.
The faster the magnet moved, the larger the current.
When the magnet was moved back away from the coil, current flowed in the opposite direction.
If there was an induced current, there must have been an induced emf.
An emf, , gives energy to a charge to move it through the wire, and the resistance of the wire limits the size of the current.
So it is more correct to say that the changing magnetic field induced an emf.
Changing magnetic flux and induced emf
Whenever the magnetic flux passing through a coil changes, an emf is induced in the coil.
A change in magnetic flux occurs when one of the following happens:
the angle between the magnetic field and the coil changes
the magnetic field strength changes
the area of the coil changes
6.4.2 Factors that affect induced emf
Rate of change of magnetic flux
The concept of magnetic flux can be used to explain the induced emf.
The two principles are described here.
An emf is induced in a coil when the amount of magnetic flux passing through the coil changes.
The size of the emf depends on how quickly the amount of magnetic flux changes.
These two statements can be written formally as follows:
This statement is known as Faraday’s Law.
The word ‘average’ is included because the change in magnetic flux takes place over a finite interval of time.
Direction of induced emf in a coil
To determine the direction of the induced current in a coil according to Lenz’s Law, the problem needs to be broken down into several steps:
Determine the change in flux: is it increasing or decreasing (and in which direction)?
Determine the direction of the induced magnetic field such that it compensates for the increase or decrease in flux.
Determine the direction that the induced current must flow in order to produce the induced magnetic field in step 2.
Lenz’s Law states: The direction of the induced current is such that its magnetic field is in the opposite direction to the change in magnetic flux.
In other words, a coil responds to a change in magnetic flux in such a way as to keep its magnetic environment constant.
If the coil experiences an increase in flux, it will compensate by inducing a magnetic field in the opposite direction to the flux.
If the coil experiences a decrease in flux, it will compensate for the loss by inducing a magnetic field in the same direction as the flux.
This can be incorporated in the equation as a minus sign:
Number of loops
Examples concerning emf have been previously discussed when there is a single coil of wire.
When there are multiple turns (or loops) in the coil, the emf produced will be the sum of all the individual turns.
Therefore, if the coil consists of several turns of wire, the equation can be generalised further:
is the induced emf, in V
is the number of turns (or loops) in the coil
is the change in magnetic flux, in Wb
is the time interval, in s
6.5 Generators and alternators
Key Knowledge
Explain the production of DC voltage in DC generators and AC voltage in alternators, including the use of split ring commutators and slip rings respectively.
6.5.1 Induced emf in a rotating loop
A magnet moving in and out of a coil to generate a current is not a very efficient means of converting the mechanical energy of the moving magnet into the electrical energy of a current in the coil.
A generator is a device that transforms mechanical kinetic energy into electrical energy.
In its simplest form, a generator consists of a coil of wire that is forced to rotate about an axis in a magnetic field.
As the coil rotates, the magnitude of the magnetic flux threading (or passing through) the area of the coil changes.
This changing magnetic flux produces a changing emf across the ends of the wire that makes up the coil.
This is in accordance with Faraday’s Law of Induction, which can be stated as follows: The induced emf in a coil is proportional in magnitude to the rate at which the magnetic flux through the coil is changing with time.
Rotating a coil in a magnetic field continually changes the rate at which the magnetic flux changes through the coil and therefore induces a changing voltage.
When the loop is ‘face on’ to the magnetic field, the maximum amount of magnetic flux is passing through the loop: .
As the loop turns, the amount of flux decreases.
When it has turned 90° and is parallel to the field, there is no flux passing through it at all: .
As the loop continues to turn between 90° and 180°, the magnetic field passes through the loop from the other side: a negative amount of flux, from the point of view of the loop.
The magnitude of the magnetic flux passing through the loop increases to a maximum again, but in the opposite direction: .
Then it decreases back to zero when the loop has rotated 270°, and finally passes through the original face of the loop.
The amount of magnetic flux passing through the loop varies in the form of a sine wave.
The induced emf across the ends of the loop is proportional to the change of magnetic flux with time.
Since , the induced emf is shown on the graph as the negative gradient function of the magnetic flux–time graph, and hence is also a sine wave.
The emf graph is the same shape as the flux graph but shifted sideways, so that when the flux is a maximum, the emf is zero.
When the flux is at a maximum (or minimum) the flux–time graph is flat, so the gradient is zero and hence the emf is zero.
Similarly, when the flux is zero, the flux–time graph is steepest, so the gradient is a maximum (or minimum) and hence the emf is a minimum (or maximum).
6.5.2 AC alternators
Which way does the current travel when a rotating loop is placed in a magnetic field?
As the loop rotates, the magnetic flux changes from passing through one side to passing through the other.
At this point in the rotation, the current will enter the external circuit from the slip ring at and return to the loop by the slip ring at .
So, for the time being, the current flows through the external circuit from to , with being the positive terminal and the negative.
In the diagrams, the wire from is attached to the front metal ring, the one connected to , and the wire from is attached to the back ring, the one connected to .
These connections are fixed.
When the loop rotates about its axis, the two slip rings also rotate about the same axis.
The blocks are made of graphite.
They are being held in place against the spinning slip rings by the springs.
Graphite is used because it not only conducts electricity but is also a lubricant.
The spinning slip rings easily slide past the fixed block.
The blocks are also called ‘brushes’ because early designs used thin metal strips that brushed against the slip rings.
Consider the loop as it continues to rotate clockwise through the vertical position.
The flux is increasing from left to right through the loop as it moves to the vertical position.
The induced current flows through in order to induce a magnetic field from right to left through the loop to counteract the increasing flux.
When the loop rotates past the vertical position and begins to move again towards the horizontal position, the flux from left to right decreases, inducing a magnetic field from left to right through the loop, below the edge .
For this to be possible, the induced current must now move in the direction .
The current in the external circuit will now flow from to , that is, in the opposite direction!
The direction of the induced current will reverse every time the loop passes through the vertical position (when the plane of the loop is perpendicular to the field), or every half-turn.
The sinusoidal emf drives current through the external circuit first one way, then the opposite way, and is thus called alternating current (AC).
This design of a rotating coil in a magnetic field is called a generator.
If the ends of the coil are connected to slip rings, then the voltage across the external connections is alternating in direction, producing an alternating current.
The device can also be called an alternator.
Slip rings
Slip rings maintain a continuous electrical connection with the spinning loop and are used when an AC output is required.
Using magnetic force on the charges in the wire
As the loop rotates through the horizontal plane, the left side of the loop, , is moving up, and the right side, , is moving down.
Using the right-hand-slap rule, the force of the magnetic field on the positive charges in will be towards , while the force on the electrons in will be towards .
Similarly, the positive charges in will be pushed to , while the electrons will be pushed towards .
This means that conventional current will flow in the direction , while the electrons will travel around the loop in the order .
The conventional current will enter the external circuit from the slip ring at and return to the loop by the slip ring at .
Once the loop passes through the vertical plane, will move downwards and will move upwards.
The force of the magnetic field on the positive charges in will be towards , while the force on the electrons in will be towards , and the conventional current will now flow in the opposite direction: , entering the external circuit at and returning to the loop at .
This is the same result obtained as with the previous method.
6.5.3 DC generators
What happens if the slip rings are replaced with split rings like those used in a DC motor?
When the current in the loop reverses every half-cycle as the loop rotates through the vertical position, the ends of the coil swap to the other side of the split ring so that the direction of the current flowing through the external circuit remains the same.
Essentially, the direction of the output to the external circuit is changed by the split ring commutator, and so the alternating current in the loop is converted into pulsating direct current (DC) in the external circuit.
The device is now called a DC generator.
A split ring commutator is a device used in a DC motor to reverse the direction of the coil’s current every half revolution of the loop so that the direction of the current flowing through the external circuit remains the same.
The alternating current in the loop is thus converted into direct current.
6.5.4 Comparison of motors and generators
Recall from topic 5 that a motor consists of a coil connected to a power supply in the presence of a magnetic field.
The magnetic field induces a force on the electrons moving through the coil, causing the coil to turn.
A motor converts electrical energy into mechanical energy.
A generator consists of a coil in the presence of a magnetic field.
By manually rotating the coil, the magnetic flux through the coil changes, inducing an emf in the coil, which subsequently induces a current through the coil.
If connected to an external circuit, the current through the coil can provide electricity to the circuit.
A generator converts mechanical energy into electrical energy.
Motors convert electrical energy into mechanical energy.
Generators convert mechanical energy into electrical energy.
When the coil of a motor rotates, a back emf is induced in the coil due to its motion in the external magnetic field.
Lenz’s Law informs us that this emf opposes the emf powering the motor.
This self-generated emf is known as back emf.
This results in the net emf in the motor being less than the supplied emf when the motor is rotating.
6.5.5 Producing a greater emf
The AC voltage produced by a generator has a substantial technological application because it is easy to make things spin.
Hydroelectricity is produced when water falls under gravity through pipes and hits the vanes of a propeller connected to a generator.
In coal and gas-fired turbines, the burning fuel heats up water to a high temperature, producing steam at high pressure.
The steam is directed against the vanes of the turbine.
The emf that is produced by a generator has a frequency that is the same as the frequency of the rotation of a coil in a magnetic field.
Using the Faraday equation for average emf: and ignoring the \,-\ sign (which relates to direction), the ways to produce a larger emf can be deduced, as follows:
increase the number of turns or coils
increase the strength of the magnetic field
increase the area of each coil
decrease the time for one turn (that is, increase the frequency of rotation).
(Note that turning the coil twice as fast doubles both the induced emf and the frequency — that is, it halves the period.)
Other technological strategies can also increase the emf
The pole ends of the magnet can be curved so that the coils are close to the magnets for more time during the rotation.
An iron core can be placed inside the coils to strengthen the magnetic field.
The coils can be wound onto the iron core in grooves cut into the outer surface so that the iron core is as close as possible to the magnetic poles to increase the magnetic field.
6.6 Photovoltaic cells
Key Knowledge
Describe the production of electricity using photovoltaic cells and the need for an inverter to convert power from DC to AC for use in the home (not including details of semiconductors action or inverter circuitry)
6.6.1 The production of electricity using photovoltaic cells
Visible light is a part of the electromagnetic spectrum.
Light behaves like waves, and it is often described in terms of its wavelength.
The wavelength of light depends on the energy of the light: high energy light has a short wavelength, and low energy light has a long wavelength.
Red light is low energy and has wavelengths greater than 700 nm (nanometres).
Violet light is high energy and has wavelengths less than 400 nm.
Light also behaves like particles or discrete packets of energy.
These particles are called photons.
Solar energy is the energy we receive from the Sun.
The Sun emits the full range of radiation of the electromagnetic spectrum.
When photons strike a photovoltaic cell, they are either absorbed by the cell or reflected from the surface.
If photons have enough energy, they cause electrons to be removed from atoms in the cell.
If the photons do not have enough energy, their energy is transformed into thermal energy and the solar cell heats up.
Solar cells are not very efficient because most of the photons in light from the Sun do not have enough energy to release electrons in the cells.
Released electrons are collected and travel around an electrical circuit.
The resulting electrical current is a direct current (DC).
It flows in one direction.
As the intensity of the light increases, it has more photons that release more electrons, creating a bigger electric current.
The voltage produced by a solar cell depends on the materials used to manufacture the cell.
The voltage produced by the cell is not affected by the intensity of the light.
Silicon-based solar cells
Most household solar cells are silicon-based.
Silicon-based solar cells are p-n junction diodes.
A silicon-based solar cell has two thin layers of silicon sandwiched together.
The two silicon layers are both made from highly purified silicon.
In the silicon layer on the right, phosphorus atoms are inserted among the silicon atoms, in a process called ‘doping’.
A phosphorus atom has one more electron in the outer shell than does a silicon atom.
This extra electron is held quite loosely, which is why a phosphorus atom releases an electron when it absorbs energy from a photon that has enough energy.
This layer is called an n-type layer because it is a source of negatively charged electrons.
The silicon layer on the left side has been ‘doped’ with boron atoms.
A boron atom has one less negatively charged electron in the outer shell than does a silicon atom.
The presence of boron atoms in the silicon lattice therefore creates ‘positive holes’, and is thus called a p-type layer.
Where the two layers meet is termed a p-n junction.
Electrons from the n-type material drift across the junction to fill holes, forming a ‘depletion layer’.
Semiconductors (generally silicon) in photovoltaic cells exposed to light will absorb the light’s energy.
Electrons in the silicon valence band are promoted to the conduction band, and holes are formed in the valence band.
The charge carriers can travel in the form of an electrical current through the semiconductor material and an external circuit.
They can also recombine, with their energy being dissipated as heat.
When the n-type semiconductor and the p-type semiconductor are put together in a p-n junction, an electric field is formed at the p-n junction, moving the flow of electrons and holes in opposite directions, which reduces electron-hole recombination.
Thus, when light is shone on the top layer of a photovoltaic cell, the top layer is covered with a grid of silver to collect the released electrons.
The result is the generation of an electric current when it is connected to a closed electric circuit.
Silicon-based solar cells produce a maximum voltage of about 0.65 V (DC).
The top is a thin layer of n-type material.
This allows photons to reach the junction.
6.6.2 Solar panels and solar arrays
A solar panel consists of a set of solar cells connected in series and/or in parallel to produce a desired voltage and current.
The solar cells are set into a watertight frame.
A single solar cell has a maximum output voltage of about 0.65 V DC.
The solar panel in the illustration has 60 solar cells connected in series.
This gives a nominal output voltage of 24 V DC.
The maximum voltage can be greater than 36 V.
A solar array is a set of solar panels connected in a grid.
Solar arrays are often used on the rooftops of buildings.
If the solar array generates more electricity than is required in the building, the excess electrical energy is fed back into the electricity grid or stored in a battery.
6.6.3 Solar electricity for buildings
A rooftop solar system is the name given to the solar panels together with the electrical circuit that must be set up to link the solar array to the electrical circuitry in the building.
The electrical current produced by a solar cell is a direct current (DC).
In Victoria, household electrical appliances operate on a 230 V 50 Hz AC supply.
For this reason, a device known as an inverter must be inserted into a rooftop solar system to convert the direct current into an alternating current and change the voltage to 230 Vrms.
The electrical energy generated that is not needed at the time can be stored in batteries and/or fed back into the power grid.
When electrical energy is fed back into power grid, a meter measures the electrical energy that has been supplied and the owners are paid for the power they supply.