# HSC Physics – Motors and Generators notes – course summary

## HSC Physics – Motors and Generators notes

This is a set of HSC Physics dot-point summary notes for Motors and Generators. HSC Physics tutoring at Dux College provides students with the right support to achieve a band 6 result in HSC Physics.

## The Motor

### Conductors and Magnetic Fields

#### Magnetic field around a conductor

A circular magnetic field is generated around a current-carrying conductor. To work out the direction of this circular force, we use the right hand grip rule. Recall that dots represent a magnetic field out of the page, and crosses represent a magnetic field into the page.

#### Force on a conductor in an external magnetic field

Since a current-carrying conductor generates its own magnetic field, this magnetic field can interact with an external magnetic field to exert a force onto the conductor. To work out the direction of the force experienced, we used the right hand palm rule (F on palm, B on fingers, I thumb). This rule can also be used to determine the force on a beam of moving charges.

The magnitude of the force is dependent on several factors:

$Latex formula$

Where

• $Latex formula$ is the strength of the external magnetic field, in Teslas
• $Latex formula$ is the current in the conductor, in Amps
• $Latex formula$ is the length of the conductor in the magnetic field, in metres
• $Latex formula$ is the angle between the magnetic field lines and the current direction.

From the equation we can see that the force on the current-carrying conductor is directly proportional to the strength of the external magnetic field, the magnitude of the current, and the relevant length of the conductor.  A force will not exist upon the conductor if the conductor is parallel to the magnetic field (i.e. $Latex formula$). Otherwise, the greatest force on the conductor is when the angle between the current and the magnetic field is 90°.

### Force between current-carrying parallel conductors

The force between the conductors exists because the magnetic field due to the current in each conductor interacts with the magnetic field due to the current in the other conductor. The direction of the force (attraction or repulsion) depends on the relative directions of the two currents. Remember:

 Current directions Same Opposite Force Attraction Repulsion

In answering these types of exam questions, remember to specify the direction of the force (attractive or repulsive).

Quantitatively, the force between the two conductors is directly proportional to the currents in the conductors and the common length ($Latex formula$). It is inversely proportional to the distance between them. The proportionality constant is $Latex formula$, which is the magnetic force constant (given in the standard HSC formula sheet as $Latex formula$).

Mathematically, we can write:

$Latex formula$

### Torque

Torque is the turning moment of a force at a point of pivot. In other words, it is force in a twisting direction at the point of twisting. It is the product of the tangential component of the force ( ) and the distance the force is applied from the axis of rotation.

$Latex formula$

### The motor effect

Electric currents in conductors produce magnetic fields. If these conductors are inside an external magnetic field (e.g. produced by permanent magnets), they can actually start to move. This movement is caused by the interaction between the magnetic field induced by the conductor, and the external magnetic field. It is this movement of current-carrying conductors inside magnetic fields that is called the motor effect, and is the principle behind electric motors, hence the name.

A coil in a magnetic field

A coil in a magnetic field can be made to rotate by the motor effect.

Assume, for simplicity of discussion, that the axis of rotation of a rectangular coil is perpendicular to the magnetic field, and that the long sides of the coil are parallel to the axis and equidistant from it.

Each long side of the coil experiences a force whose magnitude does not change throughout a rotation of the coil, since the sides always remain perpendicular to the field. This force is given by $Latex formula$. The force on each long side can be shown to be always in the same direction throughout a rotation of the coil, opposite in direction to the force on the other long side, and always perpendicular to the axis.

The force on each long side produces a torque about the axis. As the forces are in opposite directions, and their lines of action are on opposite sides of the axis, they produce a torque in the same direction. Thus their effect is to rotate the coil about its axis. The net torque is at its maximum when the plane of the coil is parallel to the field, as the perpendicular distance, $Latex formula$, to the line of action is maximum, and reduces to zero as the plane of the coil rotates to be perpendicular to the field. The direction of the torque alternates through a complete rotation of the coil, so the coil will not complete a revolution (unless there is a switching device, such as a split-ring commutator).

For a rectangular coil with its axis of rotation perpendicular to the external magnetic field, the total torque is:

$Latex formula$

Where

• $Latex formula$ is the number of coils of wire
• $Latex formula$ is the angle between the plane of the coil and the magnetic field
• $Latex formula$ is the strength of the external magnetic field, in teslas
• $Latex formula$ is the current flowing through the coil, in amps
• $Latex formula$ is the area of the coil, in $Latex formula$

### The DC electric motor

An electric motor is a device that transforms electrical potential energy into rotational kinetic energy. Electric motors produce rotational motion by passing a current through a coil in a magnetic field. The DC motor is a common type of electric motor that is powered by direct current. It is an application of the motor effect.

 Part Description Role in the motor Coils There may be only one, in a very simple motor, or several coils, usually of several turns of insulated wire, wound onto the armature. The ends of the coils are connected to bars on the commutator. The coils provide torque, as the current passing through the coils interacts with the magnetic field. As the coils are mounted firmly on the rotor, any torque acting on the coils is transferred to the rotor and thence to the axle. Permanent magnets Two permanent magnets on opposite sides of the motor, with opposite poles facing each other, the pole faces are curved to fit around the armature and to provide a radial magnetic field. The magnets supply the magnetic field which interacts with the current in the armature to produce the motor effect. A pair of electromagnets can be used instead of permanent magnets. Split-ring Commutator The commutator is a broad ring of metal mounted on the axle at one end of the armature, and cut into an even number of separate bars (2 in a simple motor). Each opposite pairs of bars is connected to one set of coils. The commutator provides points of contact between the rotor coils and the external electric circuit. It serves to reverse the direction of current flow in each coil every half-revolution of the motor. This ensures that the torque on each coil is always in the same direction. Brushes Compressed carbon blocks, connected to the external circuit, mounted on opposite sides of the commutator and spring loaded to make close contact with the commutator bars. Graphite, which is used in the brushes, is a form of carbon which conducts electricity and is also used as a lubricant. The brushes are the fixed position electrical contacts between the external circuit and the rotor coils. Their position brings them into contact with both ends of each coil simultaneously, as each coil is positioned at right angles to the field, to maximise torque. Axle A cylindrical bar of hardened steel passing through the centre of the armature and the commutator This provides a centre of rotation for the moving parts. Useful work can be extracted from the motor via the axle. Armature The armature consists of a cylinder of laminated iron mounted on an axle. Often there are longitudinal grooves into which the coils are wound. The armature carries the rotor coils. The iron core greatly concentrates the external magnetic field, increasing the torque on the armature. The laminations reduce eddy currents which might otherwise overheat the armature. Stator The stator describes everything connected to the casing. It is the part that houses all the other parts of the motor, and does not move. The stator includes the magnets, casing and brushes of a DC motor. The stator houses the DC motor, preventing dust or foreign objects from interfering the rotation of the motor. Rotor The rotor describes everything connected to the axle that spins with it. The rotor includes the main coils, commutator and armature of a DC motor. The rotor spins with everything connected to it, producing kinetic energy from electrical energy.

### Applications of the motor effect

#### The Galvanometer

A galvanometer is a device used to measure the magnitude and direction of small DC currents.

The coil consists of many loops of wire and it is connected in series with the rest of the circuit so that the current in the circuit flows through the coil. When the current flows, the coil experiences a force due to the presence of the external magnetic field (the motor effect).

The needle is rotated until the magnetic force acting on the coil is balanced by a counter-balancing spring. As force is proportional to the current flowing through the coil ($Latex formula$), the position of the needle is an accurate measure of how much current is flowing through the coils.

Note that the magnets around the core are curved. This results in a radial magnetic field; the plane of the coil will always be parallel to the magnetic field and the torque will be constant no matter how far the coil is deflected. This also means that the scale of the galvanometer is linear, with the amount of deflection being proportional to the current flowing through the coil, making measurements accurate.

#### The Loudspeaker

Loudspeakers are devices which transform electrical energy into sound energy. A loudspeaker consists of a circular magnet that has one pole on the outside and the other on the inside. For example, the diagram below shows the central magnet has South and the side magnets as North.

A coil of wire (known as the voice coil) sits in the space between the poles. The voice coil is connected to the output of an amplifier. The amplifier provides a current that changes direction at the same frequency as the sound that is to be produced. The current also changes magnitude in proportion to the amplitude of the sound. The voice coil is caused to vibrate about the magnets by the motor effect.

The voice coil is connected to a paper speaker cone that creates sound waves in the air as it vibrates. When the magnitude of the current increases, so too does the force on the coil. When the force on the coil increases, it moves more and the produced sound is louder.

## Generation of electrical voltage

In 1831, Michael Faraday discovered that a current can be induced within a conductor if the conductor is subject to a moving magnetic field. Alternatively, the same effect is also produced when a conductor moves relative to a magnetic field.

In his first successful experiment, Faraday set out to produce and detect a current in a coil of wire by the presence of a magnetic field set up by another coil. The coils were separated with twine. One coil was connected to a galvanometer and the other to a battery. When the battery circuit was closed, Faraday observed ‘there was a sudden and very slight effect at the galvanometer’. Faraday had observed a small brief current that was created in the galvanometer circuit. A similar effect was also produced when the current in the battery circuit was stopped, but the momentary deflection of the galvanometer needle was in the opposite direction.

In a further experiment, Faraday used a ring made of soft iron. He wound the primary coil on one side and connected it to a battery and switch, He wound the secondary coil on the other side and connected it to a galvanometer.

When the current was set up in the primary coil, the galvanometer needle immediately responded, as Faraday stated, ‘to a degree far beyond what has been described when the helices without an iron core were used, but although the current in the primary was continued, the effect was not permanent’.

When the current in the primary coil was stopped, the galvanometer needle moved in the opposite direction. He concluded that when the magnetic field of the primary coil was changing, a current was induced in the secondary coil.

### Magnetic flux

Magnetic flux is the name given to the amount of magnetic field passing through a given area. It is given the symbol ФB. In SI units, ФB is measured in weber (Wb). If the particular area, A, is perpendicular to uniform magnetic field of strength B then the magnetic flux is the product of B and A.

$Latex formula$

The strength of magnetic field, B, is also known as the magnetic flux density. It is the amount of magnetic flux passing through a unit area. In SI units, B is measured in tesla (T) or weber per square meter ($Latex formula$).

Electromagnetic induction is the production of an EMF in a conductor when it is in relative motion to a magnetic field, or it is situated in a changing magnetic field. Such an EMF is known as an induced EMF. In a closed conducting circuit, the EMF gives rise to a current known as an induced current.

For current to flow through the galvanometer in Faraday’s experiments, there must be an EMF.  Faraday noted that there had to be a changing magnetic field in order for EMF to be produced. The quantity that was changing in each case was the amount of magnetic flux threading the secondary coil which is connected to the galvanometer. The rate at which the magnetic flux changes determines the magnitude of the generated EMF. This gives Faraday’s Law of Induction:

The induced EMF in a circuit is equal in magnitude to the rate at which the magnetic flux through the circuit is changing with time.

Mathematically, Faraday’s law is expressed as:

$Latex formula$

If a coil has  turns of wire on it, the EMF induced by a change in the magnetic flux threading the coil would be  times greater than that produced if the coil had only one turn of wire.

### Lenz’s Law, back EMF and eddy currents

#### Lenz’s Law

An induced EMF always gives rise to a current that creates a magnetic field that opposes the original change in flux through the circuit.

This is a consequence of the principle of conservation of energy. The minus sign in Faraday’s law of induction is placed there to remind us of the direction of the induced EMF.

#### Back EMF

Back EMF is an electromotive force that opposes the main current flow in a circuit. When the coil of a motor rotates, a back EMF is induced in the coil due to its motion in the external magnetic field. Electric motors use an input voltage (the primary EMF) to produce a current in a coil to make the coil rotate in an external magnetic field.

However, an opposing EMF is induced in a coil that is rotating in an external magnetic field. The EMF is produced because the amount of the magnetic flux that is threading the coil is constantly changing as the coil rotates. The EMF induced in the motor’s coil, as it rotates in the external magnetic field, is in the opposite direction to the input voltage or supply EMF. If this was not the case, the current would increase and the motor coil would go faster and faster forever, violating the conservation of energy.

The induced EMF produced by the rotation of a motor coil is known as the back EMF because it is in the opposite direction to the supply current. When the motor is stationary, back EMF is 0. As the motor spins up, back EMF increases until it is approximately equal to the input EMF from the input voltage.

#### Eddy currents

An eddy current is a circular current induced in a conductor in a changing magnetic field.

Induced currents occur in wires, coils, iron cores of transformers, and all other conductors subject to changing magnetic fields. In general:

• When there is a magnetic field acting on part of a metal object and there is relative movement between the magnetic field and the object
• When a conductor is moving in an external magnetic field
• When a metal object is subjected to a changing magnetic field

Eddy currents are an application of Lenz’s law. The magnetic fields set up by the eddy currents oppose the changes in the magnetic field acting in the regions of the metal objects.

### Applications of EM induction

#### Induction cooktops

Eddy currents can cause an increase in the temperature of the metal. This is due to the collisions between moving charge carriers and the atoms of the metal, as well as the direct agitation of atoms by a magnetic field changing direction at a high frequency.

Induction cooktops use induction coils connected to a source of AC, producing a rapidly changing magnetic field. These coils sits beneath an insulating ceramic plate, upon which a metal saucepan or piece of cookware sits.

The rapidly changing magnetic field induces strong eddy currents in the metal cookware, which act to heat up the cookware through joule heating.

This heating up of the cookware will then heat the food inside it by conduction and convection currents, more efficiently than normal electric or gas ranges, which lose energy from escaped heat. Because induction cooktops work by inducing eddy currents in a conducting piece of cookware, they cannot be used to heat glass or other non-conducting substances. Induction cooktops are much more energy efficient and clean, but can be dangerous, since any metal object held near the cooktop can rapidly heat up, causing burns if it is held by someone.

#### Electromagnetic braking

Consider a metal disk that has a part of it influenced by an external magnetic field. As the disk is made of metal, the movement of the metal through the region of magnetic field causes eddy currents to flow. The eddy currents within the magnetic field will flow in a direction such that the associated magnetic field gives rise to a force through its interaction that opposes the original motion causing the eddy currents. Such is a consequence of Lenz’s law and the principle behind EM braking.

Electromagnetic braking is used to produce smooth, even braking for a rotating or sliding metal disc or rail, for example in fun park rides, trams and trains. The principle is the same for both sliding and rotating objects.

## Generators and Power production

### Components of a generator

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.

The main structural difference between a simple AC generator and a DC motor is the split-ring commutator in the DC motor is replaced with slip-ring commutators. If a generator used split-ring commutators, the generator would generate DC current.

#### How it works

As the coil rotates, the magnitude of the magnetic flux threading the area of the coil changes. This changing magnetic flux induces a changing EMF across the ends of the wire that makes up the coil. This is in accordance with Faraday’s Law of Induction. When the coil of a generator is forced to rotate at a constant rate, the flux threading the coil and the EMF produced across the ends of the wire vary with time. The EMF is the greatest when the plane of the coil is perpendicular to the magnetic flux lines and the least when the plane is perpendicular to the flux.

#### To determine the direction of current

To determine the direction of the produced current, apply Lenz’s law to the coil. To do this, determine the way in which the flux threading the coil is changing at the instant in question (i.e. is the coil effective area getting bigger or smaller? If the coil area is getting bigger at that instant, the induced current would oppose the magnetic flux. If the coil area is getting smaller, the induced current will support the magnetic flux). The current induced in the coil will produce a magnetic field that opposes the change in flux through the coil.

 Part Description Role in the motor Coils Same as DC motor. Instead of having an external current flow through the coil, an AC generator induces a current in its coils by Lenz’s Law, as the rotor is forced to spin by an external kinetic energy source. This induced current is what the generator outputs. Permanent magnets Same as DC motor. Same as DC motor. Slip-ring commutator The slip-ring commutator consists of two parallel rings, each attached to one end of the coil. These commutators provide electrical contact to an external circuit via the carbon brushes. An AC generator generates EMF and provides this EMF into the external circuit via its slip-ring commutators. Unlike split-ring commutators, slip-ring commutators do not achieve switching of current direction. Brushes Same as DC motor. Same as DC motor. Axle Same as DC motor. Instead of outputting kinetic energy, external kinetic energy is input via turning the axle of an AC generator. Armature Same as DC motor. Same as DC motor. Stator Same as DC motor. Same as DC motor. Rotor Same as DC motor. Rotor is turned by external kinetic energy.

### AC versus DC Generators

In an AC generator, the brushes run on slip rings which maintain a constant connection between the rotating coil and the external circuit. This means that the produced voltage in the external circuit varies like a sine wave.

In a DC generator, the brushes run on a split-ring commutator which reverses the connection between the coil and the external circuit for every half-turn of the coil. This means that as the induced EMF changes polarity with every half-turn of the coil, the voltage in the external circuit fluctuates between zero and a maximum while the current flows in one constant direction.

AC and DC generators produce electricity that is very different, and so each has its own advantages and disadvantages.

 Advantage of AC Disadvantage of AC The ability for the output voltage to be stepped up for efficient transmission and stepped down for domestic use. The high voltage transmission for AC electricity minimises energy loss by heating effects. AC generators have fewer moving parts and are easier and cheaper to maintain. They produce less friction, heat and noise and are lighter and more efficient than DC generators. They are more compact than DC generators of equivalent output because their design is more efficient and there is less likelihood of overheating occurring. Slip ring commutators offer better electrical contact, and hence much higher currents can be drawn from an AC generator than from a DC generator. The output from an AC generator needs to be constantly shielded so that energy is not lost to the environment by induction as AC current is always fluctuating and therefore cause changing flux that may induce eddy currents in metals nearby. High voltage AC produces radiowaves which can interfere with other radiowave communications media (e.g. mobile phones, radio stations). This is also another source of energy loss. AC is more dangerous than DC. AC shocks are more likely to cause death or serious injury due to its effect on the heart and lung diaphragm. AC needs to be rectified first before it can be used with many home appliances that run on DC. For example, computers, electric toothbrushes, mobile phone chargers etc.

 Advantages of DC Disadvantages of DC DC generators are the same as DC motors , but used in reverse. Therefore, they are versatile, and can be used as a motor or a generator, without needing modification. DC electricity is less likely to cause death or serious injury, unlike AC, which can cause heart attacks. DC electricity does not need to be rectified before being used by many household appliances, such as computers, battery chargers and electric toothbrushes. The commutator in a DC generator is subject to wear and tear and is more prone to breakage. DC generators are also not as reliable due to sparking and wear across split ring commutators. Sparking caused by the split-ring commutator produces strong radiowave interference, and also ozone, which is an irritant gas. Because DC voltages cannot be stepped up using transformers, electricity produced by DC generators will be subject to large energy losses during long-distance transmission.

The main disadvantage of DC over AC is DC’s inability to have its voltage stepped up for long-distance transmission. As a result, powerplants produce AC, as AC electricity can be transmitted over long distances with minimal power loss.

### Energy losses during transmission

Energy losses from $Latex formula$

Recall from the preliminary course that $Latex formula$. From this equation, ther are two factors determining energy loss in the transmission of electricity:

• Resistance in wires
• Current in wires

Resistance in the wires is limited to the materials chosen to be used to manufacture transmission wires. Long distance transmission lines are usually made of aluminium, which is a good balance between electrical conductivity, light weight of Al, and relative low cost.

Current in wires can be controlled through the use of step-up transformers. From the equation $Latex formula$, it is evident that by minimising the current flowing through the wires, we minimise power loss.

Typically, electricity is transmitted at high voltages of up to 500kV. Since $Latex formula$, maximising voltage minimises current (due to the conservation of power). Step-up transformers are used to maximise transmission voltage, and is why electricity is transmitted as AC.

#### Energy losses in transformers

There are additional losses in the transformer, largely due to EM induction, producing eddy currents in the iron cores inside transformers. Not only is the induction of eddy currents inefficient because EMF has been used to produce them, but the resulting eddy currents heat the iron core and therefore the transformer coils, increasing their resistance.

Energy losses in transformers can be minimised by laminating the iron core, and by using cooling fans to keep the transformer cool.

#### Energy losses due to emission of radiowaves

The rapid switching of current direction in AC causes transmission lines to act as a huge radio antenna, emitting radiowaves with the same frequency as the AC. In Australia, AC is transmitted at a frequency of 50 Hz, causing transmission lines to emit radiowaves at 50 Hz. This is another source of energy loss during transmission of electricity, and can disrupt certain radio communications.

### Societal and Environmental Impacts of AC generators

#### Impact on society

AC generation and its ability to have its voltage changed by transformers has had a positive impact on society.

AC power can be transmitted long distances with minimal power loss, as its voltage can be stepped up and down using transformers. This means that electricity generation can occur away from urban areas, limiting pollution near population centres. Power generation can also be located close to natural resources, such as coal mines, which lowers the cost of electricity. AC generation can also be carried out on a large scale and then distributed over long distances to many people. This leads to economies of scale, resulting in cheaper electricity. Lowering the cost of electricity has raised the standard of living for the entire population, by making it accessible to more people.

The versatility of AC electricity to be stepped up or down and rectified to produce DC led to the development of household appliances that increased our convenience in everyday life. For example, washing machines reduce the need for manual labour in domestic washing, fridges keep our foods fresh for longer, and airconditioners and heaters keep us in comfort. Industry is able to use electricity delivered over long distances on a large scale to power heavy machinery.

On the negative side, atmospheric pollution due to by-products of the burning of coal in power stations has increased enormously as more demand or electrical power has been met over the years. Pollution is adverse to our health, and can enter the foodchain through crops, aquatic or farm livestock. Widespread use of AC has increased our reliance on crude oil products, which puts us at risk of political events, like war in the middle east, or other economic factors that may affect the price of crude oil. As we move into the future, crude oil prices will increase, leading to an increase in the cost of electricity that is derived from crude oil.

#### Impact on the environment

The impact on the environment, stemming from the development of AC generators and the widespread use of electricity, has been negative overall.

By placing power generation away from population centres, pollution levels near cities have been reduced. Large scale production of electricity is more efficient than small-scale generators dispersed throughout urban areas. Increased efficiency reduces pollution released per unit of electricity generated. Lastly, the cheap and widespread availability of electricity has allowed scientists and engineers to develop technologies that can lead to renewable sources of energy (e.g. solar, wind power), environmentally friendly cars (e.g. hybrid cars, electric cars), and ways to deal with climate change.

However, carbion dioxide emissions resulting from large-scale electricity generation is a significant contributor to global warming. A current issue of today’s world politics is the issue of how to fight climate change, due to decades of pollution from vehicles, industry and electricity generation.

In addition to atmospheric pollution, power stations release thermal pollution in the form of warm water into natural waterways. This negatively affects aquatic organisms, by reducing dissolved oxygen in water, or giving false cues to fish species, or killing off organisms in a food chain, affecting higher organisms in the chain.

There are concerns about health risks to people living near high voltage transmission lines. The development of hydroelectricity schemes to generate AC electricity impacted severely on specific areas of the environment, requiring huge dams, flooding of forests, valleys and even towns.

### Westinghouse versus Edison

Westinghouse and Edison were in direct competition to supply electricity to cities. Edison, who had developed early appliances for DC power (e.g. light bulbs, and DC motors), planned out a DC power grid and advocated DC as a solution for powering cities. Westinghouse was working with Tesla, who developed a system of AC distribution that had the advantage of being able to manipulate voltage of current along the way.

 Advantages of DC Advantages of AC DC was safer. A DC electric shock is less likely to be fatal since it did not have any special effect on the heart. In contrast, an electric shock from AC can disrupt the heart’s coordination, and can cause fibrillation (a heart attack), leading to death in minutes. DC did not need to be rectified for many appliances that used DC. In the late 1800s, the only electrical appliances used by consumers were the incandescent lamp (light bulb), and the DC motor, both of which worked well with DC. DC did not suffer from the skin-effect, which AC experiences as it moves through conductors. The skin-effect describes the tendency for AC to flow near the surface of conductors, increasing the apparent resistance of conductors for AC. DC transmission does not emit radiowaves, unlike AC. (However the last two points were not understood at the time of the currents debate.) DC generators required a split-ring commutator, which wore out quickly, caused sparking and was inefficient in delivering high currents. AC voltages could be manipulated using transformers. This was the main advantage of Westinghouse’s distribution system over Edison’s, as AC generation could be conducted on a large scale, away from population centres. In contrast, DC generators needed to be located within 1-2km from the consumers. Beyond this distance, the voltage drop due in transmission became too high. Large scale generation of AC away from population centres leads to: Increased efficiency Lower pollution in population centres No need to coordinate / deliver fuels into the cities for local DC generators

In the end, the superior efficiency of AC distribution systems, and the resultant ability to build AC power plants away from population centre outweighed the dangers and other arguments against AC. Westinghouse’s AC system thus became the precursor to the way electricity is distributed today.

### Safety devices in transmission lines

#### Insulation from supporting structure

In dry air, high voltage electricity can jump a distance of 1cm for every 10,000V of potential difference. Therefore, a 330kV transmission line can spark to the pylon holding it, if it is within 33cm of the conductor.

In high humidity conditions (e.g. during rain), the maximum sparking distance is larger. To prevent sparks jumping from transmission lines to the pylons, large ceramic disk-shaped insulators separate the conductors from the pylons holding them. The disks are stacked on top of each other, so that even during rain, water cannot form a continuous trickle, forming a conductive gap between the pylon and conductor. Also the disk shape means that current has a longer distance to traverse, increasing safety.

#### Protection from lightning strikes

On each pylon, there is a pair of conductors (or one conductor) that sits at the very top of the pylon. This is called the shield conductor.

In the event of a lightning strike, lightning hits the highest point on the pylon, and so the shield conductor at the top will be hit instead of the lower conducting lines.

The shield conductor is earthed by being connected to a wire that runs from the top of a tower pole right down to the ground (known as the earth wire), so that lightning can travel from the sky to the ground via shield conductors rather than power lines.

## Transformers

### Purpose of transformers

A transformer is a device that can manipulate current and voltage in a circuit. It consists of two coils, one called the primary coil, and one called the secondary coil. These coils can be wound together onto the same soft iron core, or linked by a soft iron core. The latter is shown on the left.

When AC is fed through the primary coil, it induces rapidly switching magnetic flux lines through the iron core, threading the secondary coil. This changing flux induces a secondary AC into the secondary coil, at a different voltage and current.

The voltage and current of the induced AC in the secondary coil relative to the original AC can be controlled by the ratio of how many turns between the primary and secondary coil.

### The common ratio

The secondary voltage can be greater or less than the primary voltage, depending on the design of the transformer. The magnitude of the secondary voltage depends on the number of turns of wire in the primary coil, np, relative to the number of turns in the secondary coil, ns.

If the transformer is ‘ideal’, it is:

• 100% efficient and the energy input at the primary coil is equal to the energy output of the secondary coil (conservation of energy is followed)
• The rate of change of flux through both coils is the same

Faraday’s law can be used to show that the secondary voltage is found using the formula:

$Latex formula$

Similarly, the input primary voltage, Vp, is related to the change in flux by the equation:

$Latex formula$

Dividing these equations produces the transformer equation:

$Latex formula$

### Step-up versus Step-down transformers

If ns is greater than np, The output voltage will be greater than the input voltage. Such a transformer is known as a step-up transformer.

If ns is less than np, the output voltage will be less than the input voltage. Such a transformer is known as a step-down transformer.

 Step-up transformers Step-down transformers Consists of two inductively coupled coils wound on a laminated iron core More turns in secondary coil than primary coil Output voltage is more than input voltage Output current is less than input current Used at power stations to increase voltage and reduce current for long-distance transmission. Also used inside CRT televisions, microwave ovens and other appliances requiring high voltage Consists of two inductively coupled coils wound on a laminated iron core. More turns in primary coil than in secondary coil Output voltage is less than input voltage Output current is more than input current Used at substations and in towns to reduce transmission line voltage for domestic and industry use. Also used in battery chargers for electronics equipment (e.g. mobile phone chargers, ipod chargers) to conver 240V AC into lower DC voltages

### Transformers and The conservation of energy

The law of conservation of energy states that energy cannot be created nor destroyed but energy can be transformed from one form to another. Transformers  are no exception to this law, so the power supplied to the primary coil must equal to the power generated at the secondary coil (for an ideal transformer).

Therefore:

$Latex formula$ $Latex formula$

Combining this equation with the transformer equation we get another relationship:

$Latex formula$

So combining both relationships, we get:

$Latex formula$

### Eddy currents in transformers

#### Managing eddy currents

For non-ideal transformers, some energy is usually transformed into thermal energy in the transformer due to the occurrence of eddy currents in the iron core. In other words, eddy currents in the iron core cause the transformer to heat up. There is a decrease in usable energy whenever energy is transformed from one form to another.

Eddy currents are caused because as the changing magnetic flux threads the iron core, electrical current is also induced in the iron core, heating it up. This causes transformers to be inefficient, as not all the electrical power supplied to the primary coil is recovered in the secondary coil.

• Instead of iron, ferrites, complex oxides of iron and other metals can be used. Ferrites are good at transmitting flux but poor at conducting electricity, so eddy currents and heating are minimised.
• The iron core can be sliced into thin layers and then put back together with insulation between each layer. This process, known as lamination, breaks up large eddy currents and minimises them because currents can only form in each of the lamina. This means smaller eddy currents and therefore less heating. The laminations must be perpendicular to the plane of coils to minimise eddy current formation.

#### Problems stemming from hot transformers

If the transformer gets hot, the resistance of the wiring in the coils increases. If the electrical resistance of the coils increases then the passage of electricity produces more heat and the transformer gets even hotter. To keep the transformer cool, we can:

• Add heat sinks to the transformer to increase the rate of heat dissipation to the environment through a larger surface area.
• Make the transformer case out of a black material on the inside, so that the heat produced internally is efficiently absorbed by the case and re-radiated to the environment quicker.
• Add fans to vent hot air out of the inside of a transformer.
• Fill the transformer with oil that has a high thermal conductivity, taking heat away from the coils quickly.
• Keep the transformer in the open, in well ventilated areas to maximise air flow around them.

### Transformers in power transmission

Power losses in the transmission of electricity are largely caused by heating in transmission wires. The power lost in transmission is given by the equation: $Latex formula$, so it is evident that power loss is dependent on the current flowing through the wire, as well as the wire’s resistance.

To minimise power lost in transmission, we use step-up transformers to raise the voltage of electricity and thereby reduce current (recall that $Latex formula$). This significantly reduces the power consumed by transmission wires, and thereby reduces energy wasted.

Using transformers in the transfer of electrical energy from a power station to its point of use provides massive efficiency gains, reducing the fuel consumed by a power plant and reducing the price of electricity. From the equation $Latex formula$, it is evident that P decreases quadratically with I. For example, the transmission voltage is doubled, the current is halved and the power loss is reduced by a factor of four. If the current is reduced by a factor of 10, the power loss is reduced by a factor of 100!

Electricity is generated at around 10kV to 25kV, which is then stepped up to high voltages before being transmitted. In Australia, electricity is most commonly transmitted at 500kV to minimise energy loss. When electricity reaches population centres, it is sequentially stepped down, until it reaches the household at 240V AC for safety.

Also, different devices require different voltages –computers and incandescent lights require much lower voltages than TVs and fluorescent lamps which can require up to 10,000V. Transformers are required to ensure each device is supplied with an appropriate voltage.

However, high voltage power lines are subject to arcing and so need to be separated, as do substations which can be extremely dangerous for people nearby. Although transformers have significantly increased the efficiency of electricity transmission, they have also produced safety concerns and have required specialised infrastructure to keep people safe.

### AC electric motors

There are two types of AC motors in the HSC course:

• Universal motors
• Induction motors

#### Universal motors

A universal motor is similar to a DC motor, but instead of permanent magnets, electromagnets are used, and instead of a split-ring commutator, slip ring commutators are used. It can operate on an AC or DC supply (but the DC version must use a split-ring commutator, instead of a slip-ring commutator).

The reason a universal motor can use AC is because as the AC switches direction, the magnetic field produced by the electromagnets also switch in direction at the same time. This dual switching at the same time causes the direction of torque on the coil to remain the same.

The universal motor is commonly used for small machines such as portable drills and food mixers.

#### Induction motors

An induction motor is an AC machine in which torque is produced by the interaction of a rotating magnetic field produced by the stator and currents induced in the rotor. Induction motors have rotors that are not connected to a power source. Instead, the rotor is threaded with the flux of a spinning magnetic field, and rotation is achieved by the rotor acting on Lenz’s Law in ‘chasing’ the spinning magnetic field to counter the relative motion.

 Advantages Disadvantages Since rotor is not attached to anything, it spins with low friction. Therefore, induction motors experience less wear and tear over normal usage No need for a commutator means there is no sparking or efficiency losses due to friction, and also high currents can be delivered to the motor Speed of rotation is predictable, as rotation will be the same frequency as the AC frequency Relatively low starting torque Requires 3 phases of AC instead of just 1 for universal motors or DC motors Relatively complex, requiring multiple coil pairs Speed is limited and cannot exceed the AC frequency. For example, in Australia, our AC is at a frequency of 50 Hz, therefore all induction motors cannot exceed a rotation speed of 50 revolutions per second (or 3,000 rpm)

### Energy tranformations in industry and the home

Electricity is simply an easy way to transmit energy from point to point. The advantage of electricity is not only that it is relatively easy to transport, but also that it is easy to convert it into other forms.

In the home, electricity is converted into kinetic energy (e.g. hair dryers, washing machines) or electromagnetic radiation (e.g. light bulbs, microwave ovens, computer screens) or thermal energy (electric cooktops, electric heaters, electric blankets). In industry, the same conversions also occur.

 Home Industry Electrical energy in the home is transformed into the following energy types:Electromagnetic radiation Light from light bulbs Microwave radiation, inside microwave ovens Light, from televisions and computer screens Heat Electric cooktops Electric ovens Electric blankets Electric heaters Kinetic energy Hair dryers Washing machines Fans Sound Speakers inside radios and TVs Alarms Chemical potential energy Recharging batteries inside mobile phones, ipods etc Electrical energy in industry is transformed into the following energy types:Electromagnetic radiation General lighting Lasers in integrated circuit manufacture X-rays for crack detection Radiowaves for communications Heat Induction furnaces to melt metals Electrical arc welding Kinetic energy Industrial motors Chemical potential energy Electroplating Electrolytic processes Manufacturing batteries