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INTRODUCTION:Modern society is geared to using electricity.
Electricity has characteristics that have made it uniquely suited for
powering a highly technological society. There
are many energy sources that can be readily converted into electricity.
In Australia, most power plants burn a fuel such as coal or use the
energy of falling water to generate electricity on a large scale.
Electricity is also relatively easy to distribute.
Electricity authorities use high voltage transmission lines and
transformers to distribute electricity to homes and industries around each
state. Voltages from power stations
can be as high as 500 000 volts but by the time this reaches homes, the
electricity has been transformed to 240 volts.
While it is relatively economical to generate electric power at a steady
rate, there are both financial and environmental issues that should be
considered when assessing the long-term impact of supplying commercial and
household power. The design of a motor for an electrical appliance requires
consideration of whether it will run at a set speed, how much power it must
supply, whether it will be powered by AC or DC and what reliability is required.
The essentials of an electric motor are the supply of electrical energy
to a coil in a magnetic field causing it to rotate. The generation of electrical power requires relative motion
between a magnetic field and a conductor. In
a generator, mechanical energy is converted into electrical energy while the
opposite occurs in the electric motor. The electricity produced by most generators is in the form
of alternating current. In general,
AC generators, motors and other electrical equipment are simpler, cheaper and
more reliable than their DC counterparts. AC
electricity can be easily transformed into higher or lower voltages making it
more versatile than DC electricity. This module increases students’ understanding of the applications and uses of Physics and the implications for society and the environment.
Magnetic Flux Density VectorOne measure of the strength of a magnetic field is the Magnetic Flux Density Vector, B. This is also called the Magnetic Induction Vector. The higher the value of B, the stronger the magnetic field. The direction of the B vector at a point in space is the direction of the magnetic field at that point. The SI Unit for B is called the tesla (T). Most magnetic fields are much smaller than 1T. A mathematical definition of B will be given later.
Moving Charges In A Magnetic FieldA moving electric charge carries with it an associated magnetic field. Thus, an electric charge moving through a magnetic field experiences a force, due to the interaction of the two magnetic fields present. The size of this force is given by: F = q v B Where q = size of charge, v = velocity of charge perpendicular to the field and B = magnetic flux density vector. If the charge enters the field at an angle q to the field direction, instead of perpendicular to it, we must use the component of v that is at right angles to the field direction. Thus the formula becomes: F = q v B sin q The direction of the force on a charge in a magnetic field may be determined by using Fleming’s Left Hand Rule. Hold the thumb, first finger and second finger of the LEFT hand mutually at right angles. Point the first finger in the direction of the magnetic field. Point the second finger in the direction of conventional current flow (ie in the direction of flow of positive charge). The thumb then points in the direction of the force on the charged particle. Although the theory above on "moving charges in magnetic fields" is not actually in the Syllabus for this topic - it appears in the "From Ideas To Implementation" topic - I have chosen to do it here since it makes good sense as an introduction to the following section on "forces on current-carrying conductors".
Magnetic Force On Current-Carrying ConductorsConsider a conductor of length L, sitting in a magnetic field of flux density B and carrying a current I, as shown below:
Clearly, a current is simply a flow of charge and since all moving charges experience a force when travelling through a magnetic field, a conductor carrying a current through a magnetic field will also experience a force. The size of this force can be shown mathematically to be: F = B I L sin q Where q is the angle made by the conductor with the magnetic field. See below.
Note that the magnitude of the force on a current-carrying
conductor depends on: u The strength of the magnetic field in which it is located (indicated by the size of the magnetic flux density vector); u The magnitude of the current in the conductor; u The length of the conductor sitting in the external magnetic field; and u The angle between the direction of the external magnetic field and the direction of the length of the conductor. The direction of the force on a current-carrying conductor sitting in a magnetic field is found by Fleming’s Left Hand Rule, as previously described. It should also be clear that neither a charge travelling parallel to a magnetic field nor a current-carrying conductor lying parallel to a magnetic field will experience any force due to the field, since for both, sinq = 0.
Try this java demonstration: http://www.walter-fendt.de/ph14e/lorentzforce.htm Use Fleming's LHR to predict the direction of the force on the conductor in the demo.
Parallel Current-Carrying ConductorsConsider two very long, straight, parallel, current-carrying conductors as shown below:
The magnetic field produced by the current flowing through conductor 1 will pass through conductor 2. Thus, all of the charges flowing through conductor 2 will be flowing through a magnetic field and will thus experience a force. The same argument can be applied to deduce that conductor 1 will also experience a force. The size of the force F acting on each of the conductors is given by:
where k = m0/2p = 2 x 10-7 SI Units, I1 & I2 are the currents in conductors 1 & 2 respectively, d is the distance between the conductors and l is the common length of the conductors. (m0 is the permeability of free space and is a measure of the ability of free space to support a magnetic field.) Fleming’s LHR can be used to show that: u When the currents in the conductors are in the SAME direction, the force between the conductors is ATTRACTIVE. u When the currents in the conductors are in OPPOSITE directions, the force between the conductors is REPULSIVE.
Torque in Current Loops in a Magnetic FieldA torque is defined as the turning moment of a force. The torque about an axis of rotation is the product of the perpendicular distance of the axis from the line of action of the force and the component of the force in the plane perpendicular to the axis. See the diagram below.
For the situation above, the torque t on the bar about the pivot is: t = F d Consider a rectangular coil of wire carrying a current I and sitting in a magnetic field of flux density B, with its plane parallel to the field direction, as shown below:
For this coil: (a) force on AB is down into the page by Fleming’s LHR (b) force on CD is up out of the page by Fleming’s LHR Therefore, the coil turns
under the action of an applied net torque, with CD coming up out of
the page and AB going down into the page. Once the coil has passed through
the position where its plane is perpendicular to the field direction, the
direction of the net torque is reversed. (Use Fleming’s LHR to verify this
for yourself – remember the current direction in the coil stays the same
throughout.) Thus, the coil
will eventually stop and then turn in the opposite direction. And so the motion will
continue. The size of the torque on a coil of n turns of wire may be shown to be: t = B I A n cosq where B = magnetic flux density of the field, I = current flowing in coil, A = area of coil, n = number of turns of wire in coil and q = initial angle made by plane of coil and the B field direction.Note that when q = 90o (coil perpendicular to field direction), no torque exits since then F and d are both in the same plane.
The DC Electric MotorOne simple application of the motor effect is the DC electric motor. A simple electric motor consists of a current-carrying loop situated in a magnetic field, with its plane initially parallel to the field direction. Clearly, for the loop to continue to rotate in one direction, the current running through the loop must reverse direction just as the loop reaches the position where it is perpendicular to the field direction. A split ring commutator is used to achieve this reversal of the current direction. The split ring commutator is attached to the loop and conducts current into the loop by rubbing against the brushes. The brushes are usually carbon rods that carry current from the external power source to the commutator. See the diagram below (note that it has not been drawn to scale – commutator has been drawn larger than is actually the case):
The split ring is arranged so that each half of the commutator changes brushes just as the loop reaches the position where its plane is perpendicular to the field direction. Changing brushes reverses the current in the loop. As a result, the direction of the force on each side of the loop is reversed and the loop continues to rotate in the same direction. This process is repeated each half-turn. Thus, the loop spins in the magnetic field. In practice, electric motors have several rotating loops. Together they make up the armature (or rotor) of the motor. The magnetic field in which the armature sits is called the field structure (or stator) of the motor. This can be produced either by permanent magnets as in the simple case shown above or more usually by current-carrying coils called field coils wound around iron cores called pole pieces. These sit opposite one another inside the motor frame.
Try this java demonstration: http://www.walter-fendt.de/ph14e/electricmotor.htm The above demo gives a very good view of a split-ring commutator in action. It clearly shows how the commutator reverses the current in the coil every half cycle.
Also, have a look at this link on how to build a simple working DC electric motor.
Magnetic FluxThe entire group of field lines that flow out of the N pole of a magnet constitute the flux of the magnet, represented by f (phi). The SI Unit of magnetic flux is the weber (Wb). Most magnets have flux values in the microweber range (mWb). Two magnets are of equal strength if they have the same flux (the same total number of lines emerging from their N poles). But if the area of the pole face of one magnet is half that of the other, then the concentration of lines of force must be twice as great in the magnet with the smaller pole face. This degree of concentration of flux is what we called earlier the flux density, B. So clearly B = f /A. Thus, if a uniform magnetic flux density B, extends over an area A, the magnetic flux is given by: f = B A
The Discovery of Electromagnetic InductionThe term “electromagnetic induction” refers to the creation of an electromotive force (voltage) in a conductor moving relative to a magnetic field. The effect was discovered by the British scientist Michael Faraday (1791-1867). In 1831, Faraday discovered that moving a magnet near a wire induces an electric current in that wire. In one experiment he showed that when a permanent magnet moved towards a coil of wire connected to a sensitive galvanometer, a current was induced in one direction in the coil. When the magnet was stationary or inside the coil, no current flowed through the coil. When the magnet was removed from the coil, another current was induced in the coil, this time in the opposite direction to the original induced current. Faraday reasoned that the presence of an induced current implied the presence of an induced electromotive force (emf) that caused the current. In
further experiments Faraday showed that an induced emf and a corresponding
induced current was produced whenever there was relative motion between
the magnet and the coil. He also showed that this induced
emf & current were proportional to: (a)
The relative velocity of the magnet and
coil; (b)
The strength of the magnet; (c) The number of turns of wire per unit length. In the same year Faraday demonstrated the induction of one electric current by another.
Faraday’s Law of Electromagnetic InductionFaraday eventually deduced from his experiments that an emf was induced in the coil, only when magnetic field lines were being cut by the coil. Faraday’s Law of Electromagnetic Induction states that: An emf is induced whenever a coil or circuit experiences a change of magnetic flux with time and the magnitude of the emf depends on the rate of change of the magnetic flux through the coil or circuit. Mathematically, for a conductor of N turns of wire, cutting through a magnetic flux of Df in a time of Dt, the emf e, induced across the ends of the conductor is:
(Although this equation is not required by the syllabus, it is useful in understanding Faraday’s Law and its implications.)
Origin of Induced emfLet us now consider how an induced emf originates. The
diagram below shows a magnetic field directed down into the plane of the page.
A copper wire is being moved to the right through this magnetic field at
a constant velocity v.
Since the copper wire contains many free electrons, these electrons are literally moving to the right through the magnetic field. Therefore we have a situation where charged particles, electrons, are moving through a magnetic field. We know from our earlier work that whenever this happens the charged particles experience a force. The size of this force is F = qvB. Fleming’s Left Hand Rule gives the direction of this force. Applying this rule to the motion of the electrons we have: field direction (index finger) down into the page, conventional current direction (2nd finger) to the left of the page (since the electrons are moving to the right) and therefore the direction of the force on the electrons (indicated by the thumb) is down towards the bottom of the page, as indicated by the arrow inside the copper wire in the above diagram. Thus, in the above situation, electrons will move down to
the bottom end of the wire making that end negatively charged and leaving the
top end of the wire positively charged. It
is this charge separation between the ends of the wire that creates the emf or
potential difference between the ends of the wire.
If the wire were moved through the field whilst being attached to an
external circuit, it would act as a battery for the circuit, supplying current
that would flow around the circuit.
Direction of Induced emf – Lenz’s LawLenz’s Law states that the direction of an induced current is always such that the changes causing the induction are opposed. In other words, an induced emf always opposes the changes that caused it. To remind us of this fact, a minus sign is included in the equation for induced emf:
Lenz’s Law is really a consequence of the conservation of energy law, since if the induced emf did not oppose the changes that caused it, then it would be possible to create a self-perpetuating energy supply. The Second Law of Thermodynamics proves that such an energy supply is impossible. Back emf in MotorsLenz’s Law can be used to explain an interesting effect in electric motors. In an electric motor, a current supplied to a coil sitting in a magnetic field causes it to turn. However, while the coil of the motor is rotating, it experiences a change in magnetic flux with time and by Faraday’s Law an emf is induced in the coil. By Lenz’s Law this induced emf must oppose the supplied emf driving the coil. Thus, the induced emf is called a back emf. As the coil rotates faster, the back emf increases and the difference between the constant supplied emf and the back emf gets smaller. Clearly, this difference between the two emf’s is equal to the potential difference across the motor coil and hence determines the actual current in the coil. It is interesting to note that when the motor is first turned on and the coil begins to rotate, the back-emf is very small, since the rate of cutting flux is small. This means that the current passing through the coil in the forward direction is very large and could possibly burn out the motor. To ensure that this does not happen, adjustable starting resistors in series with the motor are often used, especially with large motors. Once the motor has reached its normal operating speed, these starting resistors can be switched out, since by then the back emf has reached a maximum and has thereby minimised the current in the coil. Note also that if the load on the motor is increased at some time, the motor will slow down, reducing the back-emf and allowing a larger current to flow in the coil. Since torque is proportional to current, an automatic increase in torque will follow an increase in load on the motor.
Eddy CurrentsWhen a solid conductor is placed in a region of changing magnetic flux, circular eddy currents are induced in the conductor. Lenz’s Law can be used to explain the direction of flow of eddy currents in particular cases. Consider the case below. A uniform magnetic field is set up by placing a magnetic north pole above the plane of this page and a south pole below the plane of the page. The magnetic field direction is therefore down into the page as shown. Next a copper sheet originally sitting stationary in the magnetic field is pulled out of the field in the plane of the page as shown below. By Faraday’s Law, eddy currents will form where there is a change of flux with time, that is along the right hand edge of the field where the metal sheet is leaving the field.
By Lenz’s Law, the induced eddy currents must oppose the change that caused them. That is they must oppose the relative motion between the conductor and the magnetic field. The easiest way to determine the direction of the currents is to ask which direction of the current around the loop would produce a magnetic field that will oppose the motion of the conductor. Clearly, the clockwise direction of the eddy currents as shown in the diagram would produce a south pole inside the loop on this side of the metal sheet and a north pole inside the loop on the other side. The south pole on this side of the metal sheet would be attracted to the north pole of the magnet (on this side of the sheet) producing the original field. Likewise the north pole created by the eddy currents on the other side of the sheet will be attracted towards the south pole of the magnet on the other side of the sheet. The net effect is that there is an attractive force that acts on the copper sheet and opposes the motion of the sheet to the right. As usual in Physics there are many different ways to reach the same conclusion. A variation on the above is to realize that as the conductor is pulled out of the field, the magnetic flux passing through the conductor at the right hand edge of the field changes from a particular value to zero. Ultimately then, the change at work here is the disappearance of field lines along the right hand edge of the field as the conductor is pulled out of the field. So, the eddy currents will be in such a direction as to create a magnetic field that strengthens the original field by putting new field lines in to replace those that are disappearing. Thus, the direction of the eddy currents must be clockwise as shown above. We can easily verify the direction of the
eddy currents in the above example by using Fleming’s LHR.
Clearly, if the eddy current in the magnetic field is moving up towards
the top of the page and the field direction is down into the page, by
Fleming’s LHR, the force on the metal sheet is towards the left, opposing its
motion to the right. Thus, the
eddy currents are in a direction such that the changes causing
them are opposed. The current Syllabus asks you to “explain
the production of eddy currents in terms of Lenz’s Law”.
Please
note that to explain the production of eddy currents you need both Faraday’s
Law and Lenz’s Law. Note
also that while the methods used in the example above can be applied to solve
most cases, there are several other ways to determine the direction of eddy
currents. Another one using
Lenz’s Law as a starting point is as follows. Pick a point on the metal surface in the magnetic field but close to where the field ends. Since the eddy current must oppose the motion of the metal sheet (by Lenz’s Law), the eddy current will cause a force on the sheet in the opposite direction to the motion of the sheet. So, the force is back towards the left, the field is down into the page & therefore by Fleming’s LHR, the eddy current must move up towards the top of the page. Since the eddy current forms at the boundary of the magnetic field (ie where the magnetic flux changes from a particular value to zero), the eddy current will form in a clockwise direction in this case, as shown. In other words, the circle must come out of the field, not go further back into the field. Note that since eddy currents oppose the motion of the conductor in which they flow, they can be used for electromagnetic braking purposes. Examples include the EM braking used in the manufacture of electronic balances and in Theme Park rides such as The Giant Drop at Dreamworld on the Gold Coast. Eddy currents can also be used to produce heat in induction cooktops and induction heaters.
GeneratorsAn important application of electromagnetic induction is in the generation of electric current. AC generators produce an electric current via the motion of coils in a magnetic field or by rotating a magnet within a stationary coil. The term alternator is also often used interchangeably with the term electric generator. Strictly speaking, an alternator refers to an electromagnet rotating inside a fixed coil, such as is the case in most power stations. Consider the diagram of a simple AC generator shown below.
Clearly, the main
components of a generator are:
u The armature – a coil wound around a metal core and mounted between the poles of an electromagnet. u The electromagnet consisting of an iron core surrounded by a set of coils called the field windings. A steady current flows through these coils to produce the required magnetic field. u The slip rings – each end of the armature coil is connected to a metal ring. These rings are mounted on the armature shaft but are insulated from it and from each other. u The graphite brushes – these connect the slip rings to an external circuit and conduct the current induced in the armature coil to the external circuit. The armature is mechanically driven by a steam turbine or a belt & pulley system or by hydroelectric means. As the armature turns, one side moves up through the magnetic field and the other side moves downwards. The coil thus experiences a change of magnetic flux with time. The result is that an emf is induced in one direction in one side of the coil and in the other direction in the other side of the coil. Thus, these emf’s act in the same sense around the coil. The ends of the coil are connected to slip rings against which rest graphite brushes. When these brushes are connected across an external circuit, the induced emf produces an electric current. Each time the coil passes through the position where its plane is perpendicular to the magnetic field lines, the direction of the emf in the coil is reversed. Hence an alternating current is produced at a frequency equal to the number of revolutions per second of the armature. An alternating current generator may be
converted to a direct current generator in a couple of
ways: u
By using a split ring commutator instead of slip rings.
The split ring commutator is mounted on the armature shaft but is
insulated from it. The commutator
reverses the connections of the coil to the external circuit each time the
current in the coil reverses. Thus, a DC output is achieved from the AC generator. u
By using a bridge rectifier circuit.
This is an arrangement of electronic components (diodes) that
converts the AC output from the generator to a DC output. Note that in an electric current generator, mechanical energy is transformed into electrical energy. In an electric current motor, electrical energy is transformed into mechanical energy.
Try these java demonstrations: http://www.walter-fendt.de/ph14e/generator_e.htm http://micro.magnet.fsu.edu/electromag/java/generator/ac.html http://micro.magnet.fsu.edu/electromag/java/generator/dc.html
Effects of AC GeneratorsThe development of AC generators has had both positive and negative effects on society and the environment. Firstly, from a social point of view, electricity generation has allowed the development of the highly mechanized and electronic lifestyles to which people in the developed world have become accustomed. Our lives are made easier every day by the use of vast numbers of electrical gadgets. Electricity runs our lighting, our heaters & air conditioners, our computers and communications equipment, our refrigerators, toasters, electric fry pans & stoves, washing machines, vacuum cleaners, stereos, TV’s, garden equipment, industrial equipment and so on – the list is almost endless. Unfortunately, because electricity has greatly reduced the amount of physical labour necessary to live our everyday lives, it has also resulted in negative social effects such as a reduction in unskilled jobs and a reduction in the size of work-forces needed to perform certain jobs, which have led to increased unemployment. Secondly, in terms of the environment, the development of AC generators has had mainly negative effects. Most power generation stations around the world still use fossil fuels as their energy source. Fossil fuel power stations produce thermal pollution, acid rain and air pollution due to the release of particulate matter and oxides of nitrogen and sulfur. Fossil fuel power stations release huge amounts of carbon dioxide into the atmosphere, which adds to the Greenhouse Effect, which is believed to be raising Earth’s temperature. Fossil fuel power stations also indirectly cause the land desecration and pollution associated with the coal mining, necessary to maintain supply of fossil fuel.
Physiological Effects of HV Power Lines - Not ExaminableSome epidemiological studies have suggested that a link may exist between exposure to power-frequency electric and magnetic fields (EMFs) and certain types of cancer, primarily leukaemia and brain cancer. Other studies have found no such link. Laboratory researchers are studying how such an association is biologically possible. At this point, there is no conclusive scientific evidence of a link between the electromagnetic radiation produced by high voltage power lines and physiological conditions such as leukaemia or cancer. Scientists agree that better information is needed. In the USA, a national EMF research effort is under way, and major study results are expected in the next few years.
The AC Electric MotorAn AC electric motor consists of two main parts: u The armature or rotor – usually cylindrical that rotates about the axis of the motor’s shaft. The rotor usually completes one revolution for each cycle of the AC electricity supply. u The field structure or stator – this is the stationary part of the motor usually connected to the frame of the machine. It supplies the external magnetic field in which the rotor sits and which produces the torque on the rotor. Both the rotor and stator have a core of ferromagnetic material to enhance the magnetic field. This core usually consists of thin laminations of steel separated by thin insulating layers to reduce the size of induced eddy currents that would reduce the efficiency of the motor. In some AC motors slip rings are used to conduct electricity to and from the motor. Note that AC motors (with a few exceptions) do not use split ring commutators. AC motors can be classified as either single-phase or polyphase motors. Single-phase motors run on only one of the three phases of current produced by power stations and can therefore operate on the domestic electricity supply. Polyphase motors run on two or three of the phases of current produced by power stations and are mainly used for high power applications including heavy industry. We will now consider single-phase AC induction motors as an example of AC motors.
The Single-Phase AC Induction MotorThe single-phase AC induction motor is the most common AC motor in use today. A changing magnetic field in the stator induces an AC current in the rotor. The current in the rotor produces its own magnetic field, which then interacts with the magnetic field of the stator, causing the rotor to turn. Clearly, the name induction motor comes from the fact that no current is fed directly to the rotor from the mains supply. Current is induced in the rotor by the changing magnetic field of the stator. The rotor of an induction motor consists of a cylindrical arrangement of copper or aluminium conducting bars attached to two end rings at either end of the bars. These end rings short circuit the bars and allow current to flow from one side of the cylinder to the other. This type of rotor is usually referred to as a squirrel cage, owing to its resemblance to the cage or wheel that people use to exercise pet squirrels or mice. See diagram below.
The squirrel cage fits into a laminated iron core or armature, which is mounted on the shaft of the motor.
The stator consists of a number of coils of wire wrapped on laminated iron cores. The stator surrounds the rotor. Single-phase alternating current flowing through the stator coils produces a changing magnetic field that threads through the rotor. This changing magnetic field induces an alternating current in the rotor, which in turn sets up its own changing magnetic field. Various special techniques beyond the scope of this course are used to ensure that the changing magnetic field produced by the stator actually rotates and drags the magnetic field of the rotor around with it. Thus, the rotor rotates in the same direction as the rotating field of the stator.
The remaining notes on AC Induction motors are not required by the current Syllabus. They have been left on this site as interesting extension material. Single-phase AC induction motors tend to be low power motors. There are a couple of reasons for this. Firstly, as with all induction motors, current is not fed directly to the rotor from the mains supply, it is induced by the changing magnetic field of the stator. Less energy reaches the rotor than would be the case if the mains supply was connected directly to the rotor. Secondly, the rotating stator field in a single-phase induction motor is irregular and is not of constant strength as in a polyphase induction motor. Therefore the torque developed by a single-phase induction motor is irregular or pulsating, which results in more energy being wasted as vibration and sound than occurs in a polyphase induction motor. Due to their inherent low power, AC induction motors are used in applications such as power tools (drills, saws, sanders etc), electric kitchen implements (beaters, food processors etc) and other household appliances (hair dryers, fan heaters etc). Though not in the syllabus, it is worth noting that not all induction motors are low power motors. Polyphase induction motors can be much more powerful than their single-phase counterparts and are often used in high power applications including heavy industry. Part of their power advantage comes from the fact that it is much easier to establish stable, constant-strength, rotating stator fields in polyphase (especially three-phase) induction motors than it is in single-phase motors.
AC induction motors have several advantages over other types of motor. These include:
AC induction motors have some disadvantages as well. These include:
AC induction motors form one of three general classes of single-phase AC motor. For the sake of completeness, the other two classes of single-phase AC motors are:
TRANSFORMERSA transformer is a device in which an input alternating current produces an output alternating current of different voltage. A step-up transformer results in an increased voltage. A step-down transformer results in a decreased voltage. The transformer itself consists of two separate coils, a primary and a secondary, usually wound around a soft iron core, to intensify the magnetic field in the primary. The transformer works on the principle of mutual induction. An alternating current flows in the primary, thus creating a changing magnetic field that threads through the secondary. Thus, there is a changing magnetic flux in the secondary coil, which produces a current in that coil. Since the magnetic field is changing at a given frequency, the current induced in the secondary coil is also an alternating one. If the secondary coil contains more turns of wire than the primary, the transformer will be a step-up one. If the secondary coil contains less turns of wire than the primary, the transformer will be a step-down one. A step-up transformer is shown below.
Mathematically:
where VP = primary voltage, VS = secondary voltage, NP = number of turns of wire in primary coil and NS = number of turns of wire in secondary coil.
EXERCISE: Derive this last formula. Hint: By the principle of self-induction, the changing B field in the primary also gives rise to a back-emf and a back current in the primary that by Lenz’s Law opposes the original voltage. The induced current in the secondary coil has an alternating magnetic field associated with it, which strengthens the back-emf in the primary coil.
In an ideal transformer no energy is lost and so the energy input is the same as the energy output per unit time. We can write this as: Power in = Power out VP IP = VS IS From which we have:
This formula implies that in a step-up transformer, although the output voltage is higher than the input voltage, the output current is lower than the input current. This is a direct consequence of the conservation of energy law. Clearly, if the output current did not decrease compared to the input current, VS IS would be greater than VP IP and energy would have been created from nothing. Similarly for step-down transformers, the output voltage is lower than the input voltage but the output current is higher than the input current. From a practical point of view, transformers need to be designed carefully. There are many sources of potential energy losses in transformers, heat losses in the coils, heat losses in the core due to eddy currents and possible magnetic leakage. The eddy currents in the core are induced by the changing magnetic fields threading through the transformer. To reduce the effect of eddy currents, the core is made of layers called laminations separated by thin insulating layers, rather than being one solid block of metal. Modern transformers operate with around 99% efficiency and have many practical applications. Perhaps the most important application is in the transfer of electrical energy from a power station to its point of use. Energy losses in power transmission lines can be shown to be proportional to I2R. Clearly, the lower the current, the lower the energy loss in the line. For this reason, the 240 V power produced by the generators at a power station is stepped up by transformers to very high voltages (220 kV to 500 kV) before being transmitted from the power station. In this way the current flowing in the transmission lines is very low and energy loss in the lines is minimised. (Also, lower currents mean that smaller diameter transmission lines can be used, which leads to savings in materials and construction costs.) In order to be used by the various consumers, the voltage needs to be stepped down to the required value. This happens at electricity sub-stations, where transformers step the high voltage down to 240 V for domestic use or other particular values for industry and public transport (eg electric trains). Transformers are also used in certain electrical appliances in the home that are connected to the mains domestic power supply. For example, transformers in the 1 to 100 watt power level are often used as step-down transformers to couple electronic circuits to loudspeakers in radios, television sets, and Hi-Fi equipment. In many electronic devices a number of different voltages are required for normal operation. Transformers are used to convert the 240 V mains supply voltage to the required voltage. This can be achieved by having several secondary coils wrapped around the primary or by having one secondary coil and tapping into it after the appropriate number of turns of wire.
IMPACT OF TRANSFORMERSTransformers have had a major positive impact on society. Transference of electrical energy with low levels of loss, over huge distances between power stations and consumers is only possible due to the existence of transformers. If electrical energy could not be transmitted efficiently over large distances many more power stations with their associated pollution would be necessary to supply power to their local areas. Transformers enable power from the one power station to be used in many different applications. Sub-stations can step the power down in stages to the various levels required by households, industry, public transport and so on. Without transformers, different industries requiring different voltages would have to build generators to produce those specific voltages. The existence of transformers has enabled the construction of many of the electronic labour-saving and entertainment devices we take for granted. TV’s, computers, mobile phones, stereos, radios, electronic clocks, many kitchen appliances and countless other electronic devices require transformers for their operation.
WORKSHEET No.1
1.
Perform a first-hand investigation to demonstrate the motor effect.
(In class) 2.
Identify data sources, gather and process information to qualitatively
describe the application of the motor effect in both the galvanometer and the
loudspeaker. (Homework - see my Useful
Links page for several references.) 3.
In the diagram below, a conductor of length 0.6 m is lying perpendicular
to a magnetic field of flux density 4.5 x 10-4 T while carrying a
current of 0.5 A towards the bottom of the page.
Determine the magnitude and direction of the force on the conductor. 4.
Determine the size and direction of the force experienced by the
conductor in question (3) above, if it was lying at an angle of X = 35o
to the field lines as shown below. 5.
A piece of copper wire is bent into the shape of a square with sides 6 cm
long. The loop is placed into a
magnetic field of 3 x 10-3 T so that the plane of the square coil is
lying parallel with the plane of the magnetic field.
If a current of 2 A flows in the wire loop, what is the torque on the
loop? (2.16 x 10-5 Nm) 6.
If the coil in question (5) was placed so that its plane was
perpendicular to the plane of the magnetic field, what would be the new value of
the torque on the coil. (0 Nm) 7.
A rectangular coil with sides 0.1 m and 0.2m consists of 2000 turns of
wire. The coil lies in a magnetic
field of 2.5 x 10-3T so that the plane of the coil makes an angle of
63o with the plane of the magnetic field.
If the torque on the coil is 0.23 Nm, find the size of the current
flowing in the coil. (5.1 A) 8.
Two parallel copper wires 13 m long are 0.004 m apart.
They are horizontal, one being fixed to a bench top, the other hanging
above the first from a spring balance calibrated in newtons.
When no current flows in the wires, the spring balance reads 3.600 N. a.
The current has the same direction in each wire; and b. The current in one wire is in the opposite direction to that in the other. (Force per metre on wire = 0.005 N, so total force on 13 m length of wire is 0.065 N. So, in (a) force will be attractive & therefore reading on spring balance will increase by 0.065 N to 3.665 N and in (b) force is repulsive & therefore reading on spring balance will be 0.065 N less, that is 3.535 N.)
WORKSHEET No.2
1.
Perform an investigation to model the generation of an electric current
by moving a magnet in a coil or a coil near a magnet.
(In class) 2.
Plan, choose equipment or resources for, and perform a first-hand
investigation to predict and verify the effect on a generated electric current
when: a.
The distance between the coil and magnet is varied; b.
The strength of the magnet is varied; and c.
The relative motion between the coil and the magnet is varied. (This will be done in class.) 3.
Gather, analyse and present information to explain how induction is used
in cooktops in electric ranges. (Homework - see my Useful Links
page for some references.) 4.
Gather secondary information to identify how eddy currents have been
utilised in electromagnetic braking. (Homework
- see my Useful Links page.)
WORKSHEET No.3
1.
Plan, chose equipment or resources for and perform a first-hand
investigation to demonstrate the production of an alternating
current.
(In class) 2.
Gather secondary information to compare advantages and disadvantages of
AC and DC generators and relate these to their use.
(Homework) 3.
Analyse secondary information on the competition between Westinghouse and
Edison to supply electricity to cities. (Homework
- see my Useful Links page for several
references.) 4.
Gather and analyse information to identify how transmission lines are: a.
Insulated from supporting structures; and b.
Protected from lightning strikes.
WORKSHEET No.4
1.
Perform an investigation to model the structure of a transformer to
demonstrate how secondary voltage is produced.
(In class) 2.
Gather, analyse and use available evidence to discuss how difficulties of
heating caused by eddy currents in transformers may be overcome.
(Homework) 3.
Gather and analyse secondary information to discuss the need for
transformers in the transfer of electrical energy from a power station to its
point of use. (Homework) 4.
Perform an investigation to demonstrate the principle of an AC induction
motor. (In class) 5.
Gather, process and analyse information to identify some of the energy
transfers and transformations involving the conversion of electrical energy into
more useful forms in the home and industry.
(Homework) 6.
A step up transformer has a primary coil of 600 turns and a secondary
coil of 1200 turns. If the voltage
across the primary coil is 12 V, determine the voltage across the secondary.
(24 V) 7.
An electrician uses a transformer to convert the 240 V mains supply to 12
V. State the ratio of the number of
turns in the primary to the number of turns in the secondary of the transformer
that will do the job. (20:1)
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