Physics:

Motors & Generators1 Current Carrying Conductors1.1 Discuss the effect on the magnitude of the force on a current carrying conductor of variations in certain properties:

Formula:

F = BILsinθ

Strength of the Magnetic Field: o Force is proportional to the strength of the magnetic fieldo Stronger magnetic field, greater force on conductor

Magnitude of Current in Conductor: o Increasing current means increasing the velocity of the electronso Each moving charged particle experiences a force in proportion to its velocity

Length of Conductor: o The longer the section of conductor in a magnetic field, the more moving electrons

simultaneously experience a force o Force is proportional to the length within the magnetic fieldo Shorter length, smaller force on conductor

Angle between direction of magnetic field and conductor: o Force is strongest when particle is moving at right angles to the magnetic field (90°)o Force is zero when particle is moving parallel to the magnetic field (0°)o Movement of electrons is along a length of conductor, magnitude of force varies with

angle between conductor and magnetic fieldo As angle increases, force increases

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F = Force (N) B = Magnetic field strength (T) I = Current (A) L = Length of the conductor (m) θ = Angle of the conductor to the magnetic field

2 Parallel Conductors2.1 Describe qualitatively the force between long parallel current carrying conductors:

Force between parallel conductors exists because magnetic fields due to current flowing through the conductors interact with each other.

Direction of Force (Attraction or Repulsion): Depends on relative directions of the two currents Currents flowing in the same direction, attractive force, towards each other Currents flowing in opposite direction, repulsive force, away from each other

Magnitude of Force: Depends on magnitude of current within wire Increases or decreases with the product of the two currents Also depends on distance of separation between the conductors Increasing as the conductors are moved closer together

Relation to Length: Force between conductors depends on length of parallel conductors Larger for longer conductors "Force per unit length" - varies only with magnitude of the two currents and the distance

between them.Formula:

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F I1I2

l d

F = Force (N) l = Length of parallel conductors (m) I1 & I2 = Currents in the conductors (A) d = Distance between the conductors (m)k = constant (2.0x10-7)

k

3 Current Carrying Coils3.1 Define torque as the turning moment of a force:

Turning force or turning moment of a force Increased by increasing the applied force or perpendicular distance Formula:

τ = Fd

3.2 Describe the forces experienced by a current-carrying loop in a magnetic field and describe the net result of the forces:

Forces on the sides ab and cd: Experience maximum force since the current in them is perpendicular to the magnetic field Magnitude of the force does not change throughout its rotation Using the right hand palm rule, the direction of the force on sides ab and cd can be deduced The net result of these two forces is to produce a torque on the loop about the axis; in the

diagram above, the torque is acting in an anticlockwise directionForces on the sides bc and ad: The sides of the loop, ad and bc, experience no force because the current is parallel to the

magnetic field Magnitude of the force varies from zero to maximum

o Zero when the plane of the coil is parallel to the magnetic field (i.e. as above)o Maximum when the plane of the coil is perpendicular to the magnetic field

Net torque: Maximum when the plane of the coil is parallel to the magnetic field (i.e. as above) Direction alternates through a complete rotation Current-carrying loop orientated in a plane at right angles to a magnetic field will experience

no net force

Formula:

τ = nBIAcosθ

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τ = Torque (Nm) F = Applied force perpendicular to axis of rotation (N) d = Perpendicular distance between ‘line of action’ and pivot (m)

τ = Torque (Nm) n = number of turns/loops of the coilB = Magnetic field strength (T) I = Current flowing through the loop (A) A = Area of the loop (m2) θ = Angle between the plane of the loop and the field

3.3 Identify that the motor effect is due to the force acting on a current carrying conductor in a magnetic field:Force on a Current-Carrying Conductor – The Motor Effect:

Force on a current carrying conductor in a magnetic field causes it to move relative to the magnetic field

This movement caused by the forces is referred to as the Motor Effect

4 Motor Effect Applications4.1 Describe the application of the motor effect in the galvanometer and the loudspeaker:The Galvanometer:

Device used to measure magnitude and direction of small DC currentsThe Motor Effect: When current flows through the coil, the coil experiences a

force due to the presence of the external magnetic field The iron core of coil increases the magnitude of this force Needle rotated until magnetic force on the coil is equalled by

a counter-balancing ‘restraining spring’ Scale of galvanometer is linear, amount of deflection

proportional to current flowing through coil

The Loudspeaker: Device that transforms electrical energy into sound energy The Motor Effect: A current-carrying coil interacting with a permanent magnet

experiences a force as a result of the motor effect This force causes the coil to vibrate rapidly back-and-forth, in turn

making the speaker cone vibrate and send sound waves into the air 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

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5 DC Electric MotorsAn electric motor is a device which converts electrical energy to useful mechanical energy (usually rotation)

5.1 Describe the main features of a DC electric motor and the role of each feature & identify that the required magnetic fields can be produced either by current-carrying coils or permanent magnets:External Magnets:

1. Permanent Magnets: Made of ferromagnetic metals – two permanent magnets curved around the armature on

opposite sides of the motor, opposite poles face each other Role: Supplies the magnetic field producing the motor effect

2. Electromagnetic coils: A coil of current-carrying wire wound around a soft iron core – coils are shaped to fit around

the armature Role: Provides a stronger magnetic field which can be switched on and off when required

Armature: Cylinder of laminated iron mounted on an axle which coils are wound onto and placed inside

the magnetic field Role: Maximises the torque that can act on the coils, thus making the motor run more

efficiently – laminations reduce eddy currents which might otherwise overheat the armature

Rotor Coils: Turns of wire wound onto the armature – the ends of the coils are connected to bars on the

commutator Role: Provides the torque as the current passing through the coils interacts with the

magnetic field. Any torque acting on the coils is transferred to the rotor (which the coils are mounted on) and hence to the axle

Split-ring commutator: Cylindrical ring of metal mounted on the axle at one end of the armature – cut into an even

number of separate bars in which each opposite pair of bars is connected to one coil Role: Reverses the direction of current flow every half-revolution of the motor to ensure

that the torque on each coil is always in the same direction

Brushes: Compressed carbon blocks, connected to an external circuit, mounted on opposite sides of

the commutator – spring loaded to make close contact with the commutator bars Role: Provides the contact to conduct current into and out of the coils – they are also

responsible for maximising the torque on the axle

Axle: Cylindrical bar of hardened steel, through the centre of the armature and commutator Role: Provides a centre of rotation for the motor. Useful work extracted from the motor via

a pulley or cog mounted on the axle

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6 Michael Faraday6.1 Outline Michael Faraday's discovery of the generation of an electric current by a moving magnet:After discovering that an electric current produces a magnetic field, in 1820, Faraday’s ideas about conservation of energy led him to believe that since an electric current could cause a magnetic field, a moving magnetic field should be able to produce an electric current.In 1831, Faraday attached two wires through a sliding contact to touch a rotating copper disk located between the poles of a horseshoe magnet. This induced a direct current and was the basis to an electric generator.Faradays explanation was that the electric current was induced in the moving disk as it cut a number of lines of magnetic force coming from the magnet (the magnetic field). The wires allowed the current to flow in an external circuit where it could be detected.

7 Magnetic Flux 7.1 Define magnetic field strength (B) as magnetic flux density:Representing Magnetic Fields:

Magnetic flux lines 'flowing' out of the north pole and into the south pole Lines closer together near the poles where magnetic field is strongest Lines further apart at greater distances from the magnet Magnetic field of stronger magnet, larger number of magnetic flux lines Magnetic field of weaker magnet, smaller number of magnetic flux lines

Magnetic Flux Density: Measure of the number of magnetic flux lines passing through a unit area (1m2) Magnetic field strength at a point is the same as the magnetic flux density at that point

7.2 Describe the concept of magnetic flux in terms of magnetic flux density and area:Magnetic Flux:

Amount of magnetic field lines passing through a given area Product of strength of magnetic field (magnetic flux density) and area of coil perpendicular

to magnetic field Represented diagrammatically as number of flux lines passing through the area The relationship of the magnetic flux is given by (Note: This formula is not required):

Φ = BA

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where Φ = the total magnetic flux (Wb)B = magnetic field strength (T)A = perpendicular area through which the flux passes (m2)

ΔΦ Δt

ΔΦ Δt

7.3 Describe generated potential difference as the rate of change of magnetic flux through a circuit:Faraday's Law of Electromagnetic Induction:

The size of an induced EMF is directly proportional to the rate of change in magnetic flux In order to induce an EMF, a changing magnetic flux is essential

Factors that determine the size of the induced EMF: The size of the change in the magnetic field The speed of the relative motion between the magnetic field and the conductor The number of turns of coil or conductors The change in area that the magnetic field passes through Formula (Note: This formula is not required):

ɛ = n

8 Lenz’s Law8.1 Account for Lenz's Law in terms of conservation of energy and relate it to the production of back EMF in motors & explain that in electric motors, back EMF opposes the supply EMF:Lenz’s Law:

“The direction of any induced EMF will always be such that it opposes the change that caused it”

To find the direction of an induced emf (or induced current) we apply the RHPR to the given situation and then reverse the direction of the current flow

Conservation of Energy: The law of conservation of energy states: Energy cannot be created or destroyed, it can only

be transformed or transferredConsider a magnet moving into a coil: By Lenz's law, work must be done to move magnet into coil providing energy to induce EMF If Lenz's Law did not hold true, the magnet would be accelerated into the coil – i.e. creating

mechanical energy with no input energy Thus, to obey the law of conservation of energy, the induced current must flow to oppose

the cause

Back EMF: When an electric motor is first switched on, the applied voltage produces a large current in

the coils. When the coils begin to rotate, changing flux within coils induces an emf; by Lenz's law, the induced emf is opposite to the emf applied to the motor and this is known as the back emf

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where ɛ = Potential difference (V)n = Number of turns in the coilΦ = Magnetic flux (Wb) t = Time (seconds)

= Rate of change in magnetic flux

8.2 Explain the production of eddy currents in terms of Lenz's Law: Eddy currents - current loops induced in a conductor by a changing magnetic field By Lenz's Law, eddy currents oppose the changing magnetic field producing them Eddy currents produce its own magnetic field which opposes the relative motion of the

magnetic field which created it

9 Applications of Induction9.1 Identify how eddy currents have been utilised in electromagnetic braking:

Eddy current braking works when a rotating metal disc is placed within a magnetic field, causing the motion to slow down

This occurs because eddy currents are induced in the metal disc as a result of the presence of a magnetic field, thus changing magnetic flux

The eddy currents circulate to create a magnetic field which opposes the motion of the disc, hence slowing it down

As the motion of the metal disc decreases, so does the effect of the braking due to weaker eddy currents being induced, resulting in a smooth stopping motion

Eddy current braking has been used for train braking and also some roller-coasters where the cart needs to stop at the end of the track

o Very strong magnets are lowered down next to the metal wheels, inducing eddy currents. The eddy currents oppose the motion of the wheels, therefore the slowing down the motion of the train

9.2 Explain how induction is used in cook tops in electric ranges: In order for induction to occur there needs to be a change in magnetic flux, therefore

induction cook tops work on AC current, to create a fluctuating magnetic field When an iron-rich (ferromagnetic) cookware item is placed on the induction cooktop's

cooking element, eddy currents are induced within the cookware at its base With the high frequency, it causes the eddy currents to move around the cookware very

fast, and since iron is a relatively poor conductor of electricity, the resistance in the cookware causes heat to be produced within the cookware, effectively heating/cooking its contents.

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10 GeneratorsAn electric generator is one that converts mechanical energy to electrical energy using the principle of electromagnetic induction.

10.1 Describe the main components of a generator: Rotor: Usually consists of several coils wound on an armature which is made to rotate

within a magnetic field. Armature: Cylinder of laminated iron mounted on an axle which is carried in bearings

mounted in the external structure. Torque applied to axle to make the rotor spin. Coil: Each coil consists of many turns of copper wire wound on the armature. The two ends

of each coil are connected either to two slip rings (AC Generator) or two opposite bars of a split-ring commutator (DC Generator).

Brushes: The brushes are carbon blocks that maintain contact with the ends of the coils via the slip rings (AC) or the split-ring commutator (DC), and conduct electric current from the coils to the external circuit.

Stator: Fixed part of the generator which supplies the magnetic field in which the coils rotate.

Magnetic field: The magnetic field can be provided by permanent magnets or electromagnets which are mounted and shaped in such a way that opposite poles face each other and wrap around the rotor.

10.2 Compare the structure and function of a generator to an electric motor:Structure:

Similarities: Both have a stator providing the magnetic field, both have a rotor which rotates in this field In both, the magnetic field is supplied by either permanent magnets or electromagnets In both, rotor consists of coils wound on armature connected to brushesDifferences: DC Generators and electric motors – use a split-ring commutator to connect external circuit AC Generators – use slip rings to connect external circuit

Function: The function of an electric motor is the reverse function of a generatorElectric motors: Converts electrical energy into mechanical energy Rotates when current is suppliedGenerators: Converts mechanical energy into electrical energy Supplies current when rotor rotates

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11 AC vs. DC Generators11.1 Describe the differences between AC and DC generators & discuss advantages / disadvantages of AC and DC generators related to their use:AC Generators:

Brushes run on slip rings, constant connection between coil and external circuit

Induced EMF changes polarity with every half-turn of the coil

Voltage in the external circuit varies like a sine wave Current alternates direction

Advantages: Brushes in AC generator last longer because they don't wear as quickly Less maintenance and more reliable, better suited to high current demands Uses slip rings which cost less to manufacture and requires less maintenance AC voltage can be easily increased/decreased using transformers Can be used for power distribution AC output loses less energy during transmission than DC output Disadvantages: Cannot be used to power some devices which rely solely on DC current to function AC output in different regions around the country must be synchronised for correct

integration of electricity – i.e. have the same frequency and are in-phase AC output is much more dangerous than the equivalent DC output

DC Generators: Brushes run on split-ring commutator, which work by

reversing the connection between the coil and the external circuit each half-turn

Induced emf does not change polarity Voltage in external circuit fluctuates between zero

and maximum Current flows in one constant direction

Advantages: DC output can be used for devices which rely solely on DC current to function DC current is generally more powerful than AC (for a given voltage)Disadvantages: Brushes in DC generator do not last as long because they wear quicker Chance of creating electrical short circuit between segments due to pieces of metal worn

from commutator bars Cannot supply power over long distance

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EMF Output of a DC Generator

EMF Output of an AC Generator

12 Edison vs. Westinghouse12.1 Analyse the competition between Westinghouse and Edison to supply electricity to cities:Westinghouse was the overall winner, as the AC system was more efficient.Thomas Edison:

Direct Current System DC Generators use commutators, which were a problem – i.e. maintenance, cost, performs

poorly at high speed rotations Could only supply power to areas a few kilometres away Relied on thick copper cables to carry electric current

George Westinghouse: Alternating Current System Westinghouse saw the advantages of AC, and so he purchased the rights to Tesla's AC

motors and generators AC transmissions through the action of transformers were much more energy efficient Electricity could be transmitted over longer distances with only a small energy loss

13 Transmission Lines13.1 Identify how transmission lines are insulated from supporting structures and protected from lightning strikes:Insulation from Supporting Structures:

Large insulators that consist of stacks of disks made from porcelain are used to separate transmission lines from metal support towers

Prevents sparks jumping across the gap between the wires and tower The insulators (commonly porcelain) are strong and retains its high insulating properties

even under a very high voltage

Protection from Lightning Strikes: A non-current carrying wire runs over and parallel to the transmission wires. If lightning strikes it will hit the overhead wire first and the wire will conduct the huge

current of the lightning into the earth, leaving the transmission wires untouched The transmission lines do not suffer a sudden surge of voltage

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14 Energy Losses14.1 Discuss the energy losses that occur as energy is fed through transmission lines from the generator to the consumer:Energy loss due to resistance:

As current flows through the transmission lines that has a resistance, heat will be dissipated The heat lost during transmission can be quantitatively described by using the formula: Formula:

P = I2R

Minimisation: Transmission at highest possible voltage, lowest possible current Careful choice of materials – i.e. using good conductors (e.g. copper), thicker wires = less resistance

Energy loss due to induction of eddy currents: Induction of eddy currents in iron core of transformers Circulation of eddy currents generates heat representing energy loss to the system

Minimisation: Transformer core made of laminated iron - thin layers of iron, separated by thin insulating layers Limiting eddy currents and reducing corresponding heat loss by utilising cooling fins on the outside of

the transformer and cooling oil circulating on the inside

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where P = heat lost during transmission (J)I = the current flow through the wire (A)R = the total resistance of the wire (Ω)

(This equation can be derived by combining the power equation P = IV and Ohm’s law V = IR)

15 Impact of AC Generators15.1 Assess the effects of the development of AC generators on society and the environment:Effects on society:

Positive Effects: Development of a wide range of machines, processes and appliances – improving the

standard of living Many tasks once performed by hand now can be accomplished with electrical appliances Most domestic and industrial work requires less labour Influencing technology development - tasks such as electronic communication now achievedNegative Effects: Reduction in demand for unskilled labour, thus increasing long-term unemployment Disruption to supply compromises safety, causes widespread inconvenience and loss of

production Injuries and deaths from electric shocks with the widespread use of AC power A major electricity failure could cause economic crisis

Effects on Environment:Negative Effects: Transmission lines criss-cross the country, strip through environmentally sensitive areas Remote wilderness areas tapped for energy resources such as hydroelectricity Air pollution from burning fossil fuels, cause of acid rain Global increase of atmospheric C02, long-term global climate change Radioactive waste from nuclear power stations

16 Impact of Transformers16.1 Discuss the impact of the development of transformers on society:

More efficient transmission of electricity – power loss during transmission is dramatically reduced

Allows the development of devices which run at different voltages Access to high-voltage electricity in remote areas, stepped-down by transformers in order

for use in devices Raised living standards in rural communities (e.g. electrical lighting, refrigeration, air-con.) Industry no longer clustered around power stations and can be developed away from

residential areas Power stations in remote locations, relocated pollution away from homes

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16.2 Discuss the need for transformers in the transfer of electrical energy from a power station to its point of use & explain the role of transformers in electricity sub-stations:

Without transformers electricity would be generated at voltage typically used, resulting in very large energy losses and costly transmission losses

In large cities, many power stations would be required every few kilometres and each different voltages require separate power stations and distribution systems

Transformers: More efficient to use very high voltages for long distance transmission Transformers step-up voltage for transmission, progressively step-down voltage along

transmission lines until it reaches consumer

The voltage change during the transmission from the power plant to consumers:

17 Transformers17.1 Describe the purpose of transformers in electric circuits:

Transformers are devices that increase or decrease the size of the AC voltage as it passes through them via electromagnetic induction

Step-down transformers are used for appliances containing components requiring lower voltages – e.g. clock radios, hair dryers, CD players, etc.

Step-up transformers are used for appliances which require higher voltages to function – e.g. televisions, air conditioners, etc.

Many appliances contain both step-up and step-down transformers supplying different voltages for different components

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Electricity is usually generated by a three-phase AC generator; generally the voltage generated is as big as 23000V and current output from each set of the coil is almost 10000A

For long distance transmissions, the electricity is then fed into a step-up transformer that increases the voltage to 330000V and correspondingly decreases the size of the current (P=VI)

After this electricity has been transmitted over a long distance, the voltage is stepped down at different regional sub-stations, mainly for safety reasons. Correspondingly, the current increases.

Eventually, the voltage is stepped-down to 240V at the local telegraph pole transformers for domestic uses; industries may use slightly higher voltages

VpnpVsns

17.2 Compare step-up and step-down transformers:Step-up transformers:

Two inductively coupled coils on laminated iron core The secondary coil has more turns than the primary coil Voltage output from the secondary coil is larger than the voltage input into the primary coil Lower output current than input current Used for:

o Increasing voltage at power stations for transmissiono Devices: televisions, air conditioners, etc.

Step-down transformers: Two inductively coupled coils on laminated iron core The secondary coil has less turns than the primary coil Lower output voltage than input voltage Higher output current than input current Used for:

o Decreasing voltage at sub-stations for domestic and commercial useo Devices: clock radios, hair dryers, CD players, etc.

18 Voltages and Coils18.1 Identify the relationship between the ratio of the number of coils in the primary and secondary coils and the ratio of primary to secondary voltage:

Ratio of primary to secondary voltage = ratio of number of turns in the coils Step-up transformers - more turns and higher voltage in secondary coil Step-down transformers - less turns and lower voltage in secondary coilFormula:

18.2 Explain why voltage transformations are related to conservation of energy:Conservation of Energy:

Amount of electrical energy entering must equal total energy in all forms leaving Power in = power out

Ideal transformers: Pp = IpVp = IsVs = Ps

where subscript ‘p’ indicates primary coil and subscript ‘s’ indicates secondary coil No power loss – if voltage increases, current correspondingly decreases, and vice versa

Real transformers: Heat due to eddy currents acting in the resistance of iron core Energy is lost from the system in the form of heat – escaping into the air Power output cannot exceed power input, power output is less than power input;

Pinitial > Pfinal due to loss of heat energy

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where Vp = voltage input into primary coil (V)Vs = voltage output from secondary coil (V)np = number of turns of the primary coilns = number of turns of the secondary coil

19 Electrical appliances in the home19.1 Discuss why some electrical appliances in the home that are connected to the mains domestic power supply use a transformer:

Many household appliances function at voltages other than the standard domestic voltage of 240V

Appliances that run on 240V AC: Electricity supplied to homes typically 240 V AC Many domestic appliances designed to run at this voltage Connected directly to the mains supply without a transformer

Running on Lower Voltages: Some appliances contain components operating at lower voltages than supplied For these appliances, a step-down transformer can be used to decrease the voltage to

required – e.g. phone chargers use a transformer to step-down the voltage from 240V to the required voltage (commonly <10V)

Running on Higher Voltages: Appliances such as television receivers and computer monitors contain cathode ray tubes

requiring voltages above supply voltage These appliances have a built-in step-up transformer to provide the necessary voltage

20 Heat Reduction20.1 Discuss how difficulties of heating caused by eddy currents in transformers may be overcome:Reducing Eddy Currents:

To minimise the heat dissipation by the soft iron core, the core is laminated – stacks of thin iron sheets, each coated with insulation materials

Lamination effectively increases the resistance of the core to the flow of eddy currents, therefore restricting the circulation of large eddy currents – thus, less heat dissipation

Keeping Transformers Cool: Ventilated cases to allow air to remove heat by convection Internal fan to assist air circulation to remove excess heat faster Transformer case filled with a non-conducting oil which circulates inside the case; transports

heat produced in core to outside where heat can be dissipated to environment Heat-sink fins added to metal transformer case, heat dissipation can occur more quickly over

larger surface area Large transformers such as at sub-stations located in well-ventilated areas to maximise air

flow around them for cooling

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21 AC Electric Motors21.1 Describe the main features of an AC electric motor:Standard AC Electric Motors:

Same features as DC electric motor, except slip rings used instead of split-ring commutator Slip rings – conducts electricity from the power source without interfering with the rotation

of the coil The motor spins at 50 revolutions per second, as it is the same frequency as the oscillation of

AC current (50Hz)

AC Induction Motors: Stator:

The stationary component of the motor, it contains the electromagnet coils which create the magnetic field and it surrounds the rotor.

o Electromagnet coils: When current flows through the coils, it produces a magnetic field. There are 3 pairs of coils in the stator, which when turned on one after the other, creates a rotating magnetic field.

Rotor: The rotating component of the motor. Induced eddy currents flow in the rotor in such a way that it will rotate in the same direction as the rotating magnetic field created by the stator.

o Squirrel cage: The squirrel cage is made up of parallel aluminium bars that have their ends embedded in a metal ring at each terminal. It is covered by laminated soft iron and embedded in the stator.

22 Energy Transformations22.1 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

In the home: o Ovens and kettles create heat energy from electrical energyo Stereo systems create sound energy from electrical energyo Light globes and TVs create light energy from electrical energyo Washing machines create kinetic energy from electrical energy

In the industry:o Mainly turning electrical energy into kinetic energy for drills and other machineryo Light energy in large industrial lights from electrical energy

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Practicals to cover:(1.) Perform a first-hand investigation to demonstrate the motor effect

(2.) Perform an investigation to model the generation of an electric current by moving a magnet in a coil or a coil near a magnet

(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 the distance between the coil and magnet is varied, the strength of the magnet is varied, the relative motion between the coil and the magnet is varied

(3.) Plan, choose equipment or resources for, and perform a first-hand investigation to demonstrate the production of an alternating current

(4.) Perform an investigation to model the structure of a transformer to demonstrate how secondary voltage is produced

(5.) Perform an investigation to demonstrate the principle of an AC induction motor

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