9.3Motors and

Generator

1. Motors use the effect of forces on current-carrying conductors in magnetic fields

1.1 Discuss the effect on the magnitude of the force on a current-carrying conductor of variations in:- The strength of the magnetic field in which it is located

• The magnitude of the force is proportional to the magnetic field strength. Thus, an increase in magnetic field strength will cause an increase in the force on the wire and vice versa.- The magnitude of the current in the conductor

• Increasing the potential difference across a conductor increases the drift velocity of electrons within the conductor, thus increasing the magnitude of the current in proportion.

• Each moving charged particle experiences a force due to the magnetic field in proportion to its velocity. Hence, the magnitude of the current in the conductor varies in proportion to the magnitude of the of the force on the current-carrying conductor.- The length of the conductor in the external magnetic field

• The longer the length of the conductor in an external magnetic field, the more the moving electrons will simultaneously experience a force due to the field.- The angle between the direction of the external magnetic field and the direction of the length of the conductor

• The force on a moving particle in a magnetic field is a maximum when it is moving at a right angle to the direction of the magnetic field and at zero when it is moving parallel to the magnetic field.

• The direction of the drift velocity of electrons in a conductor is along the length of the conductor, and so the magnitude of the force on a current-carrying conductor in a magnetic field varies with the angle between the direction of the external magnetic field and the direction of the conductor.

• The force is at a maximum when the conductor and the external magnetic field are perpendicular, and is at a zero when the conductor and the magnetic field lie parallel to one another.

• The formula which represents the relationship between the force (F), the magnetic field strength (B), the current (I), the length of the conductor (l) and the angle (Ө) is defined by the following formula: F = BI lsinӨ

1.2 Describe qualitatively and quantitatively the force between long parallel curr ent-carrying conductors: F = k I1 I 2

l d • Qualitative (General idea: The force will vary based upon the magnitude between the two currents and the

distance between the two conductors):• When charges move within a conductor, they become magnets surrounded by magnetic fields. When two

conductors with current flowing through them are placed close enough, then they will both experience a force.

• The force between the conductors exist because the magnetic field due to the current in one conductor, interacts with the magnetic field of the other conductor. The direction of the force (attraction or repulsion) is depends upon the relative directions of the two currents. If the two currents are flowing in the same direction, each conductor undergoes a force of attraction towards the other conductor, however, if the current flows in the opposite direction each conductor will experience the force of repulsion driving it away from the other conductor.

• The magnitude of the force on each conductor is dependent on the magnitude of the current in each wire, increasing or decreasing with the product of two currents. The force also depends on the distance of separation between the two conductors, increasing as they are brought together or decreasing as they are driven apart.

• The force between the conductors is dependent on the length of the conductors, being stronger as the conductors are longer.

• The force between parallel conductors refers to the actual force between them, whilst the force per unit length between parallel conductors refers to the value of the force that would exist if the length of the conductors was 1m.

• Quantitative (formula):• Given that force is a vector, the direction is vital. • Force, F, and the Force per unit length between two long parallel current-carrying conductors is:

• proportional to the product of the two currents, I1 and I2

• inversely proportional to the distance, d, between the conductors• However, whilst the force is proportional to the length, l, of the conductors, the force per unit length is

independent of the length.• The magnetic field strength at a distance, d, from a long straight conductor carrying a current, I, can be found

using the formula: B= kL/d Where k= 2x10-7Na-2

1.3 Define torque as the turning moment of a force using τ = Fd • Torque is the turning effect of a force acting upon an object that causes it to rotate about its axis.• Torque is defined as the turning point of force, that is τ = Fd, where τ is torque, F is the component of applied

force perpendicular to the axis of rotation, and d is the perpendicular distance acting in a anti/ clockwise direction about an axis of rotation.

• This relationship shows that the rotational effect of force applied to a body that is allowed to rotate about the axis is dependent on two factors: the magnitude of the net applied force, F, and the perpendicular distance, d, from the axis of rotation to the line of action of the force.

• This means that the turning effect of a given force applied at a larger distance from the turning axis is greater than the effect of that same force applied closer to the turning axis. This rotational effect is called the turning moment of force, or torque.

• If torque is applied to an object at an angle of less than 90º, than the formula τ = FdsinӨ is used.• The other formula to determine torque is τ = nBIAcosӨ

1.4 Identify that the motor effect is due to the force acting on a current-carrying conductor in a magnetic field• Charged particles moving in an external magnetic field will experience a force. If the moving particles are

flowing through, and confined within, a conductor that is also within the external magnetic field, the conductor will also experience a force. This effect was discovered by Faraday and is known as the Motor effect and causes that conductor to move relative to the magnetic field.

• Simply, a current-carrying conductor in a magnetic field will experience a force• The direction of the force on the current-carrying conductor can also be determined using the right-hand

push/palm/slap rule.

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

• The forces experienced by a current-carrying loop in a magnetic field depend upon the orientation of the loop relative to the magnetic field. When the axis of the rectangular coil is perpendicular to the magnetic field, and the long sides of the coil are parallel to the axis and are equidistant from it, then:• 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. The force on each long side can be shown, by the right-hand palm rule, 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.

• Each end of the coil will experience a force which varies from zero, when the plane of the coil is parallel to the field, to a maximum when the plane of the coil is perpendicular to the field. The forces on the two ends can be shown, by the right-hand palm rule, to be opposite in direction, always parallel to the axis, and alternating in direction through a full rotation of the coil. The right-hand palm rule shows that the left side (in below diagram) will experience a force down and the right-hand a force up. Together these forces will create a turning point, and so the coil will experience maximum torque at this point.

• When the coil has rotated to the position shown below, then the two forces for both sides of the motor will be acting in opposite directions along the same line of action and hence they will cancel each other out. However momentum pushes the coil past this point, along with the change in direction of the current due to the split ring commutator, the coil will start to experience a turning force again.

• 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,d, to the line of action is maximum, and reduces to zero as

the plane of the coil rotates to be perpendicular to the field, as the line of action of each force is then through the axis (d = zero). The direction of the torque alternates through a complete rotation of the coil: its direction is always to rotate the coil to be perpendicular to the field.

• As the force on the two ends are always opposite in direction and parallel to axis, the net effect is zero.• For any current-carrying loop in a magnetic field, free to rotate about any axis, the net effect of the forces

will be such as to rotate the loop to lie perpendicular to the magnetic field. A current-carrying loop orientated in a plane at right angles to a magnetic field will experience no net force.

1.6 Describe the main features of a DC electric motor and the role of each feature

Part Description Use

Stator: For the external magnets, one of the following arrangements are used:

(i) A pair of permanent magnets in a simple motor

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.

Magnets supply the magnetic field which interacts with the current in the armature to produce the motor effect. The shape of the pole faces makes the magnetic field almost uniformly radial where the coil passes.

(ii) Pairs of electro- magnetic coils in a more complex motor

Each stator coil (or “field” coil) is wound on a soft iron core attached to the casing of the motor. The coils are shaped to fit around the armature.

Each opposed pair of stator coils produces a magnetic field similar to that provided by a pair of permanent magnets. The iron core concentrates the field.

Other parts:

Armature Frame around which coil of wire is wound, that rotates in the motor magnetic field. The armature consists of a cylinder of laminated iron mounted on an axle, which is it free to rotate around. 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.

Rotor or coil/s 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. If the coil has n turns of wire on it, then these sides will experience a force n times greater, i.e. F = nBIlsinӨ (F = torque)

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.

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 (two in a simple motor).

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 opposite pair of bars is connected to one coil.

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.

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.

The axle provides a centre of rotation for the moving parts of the motor. Useful work can be extracted from the motor via a pulley or cog mounted on the axle.

1.7 Identify that the required magnetic fields in DC motors can be produced either by current-carrying coils or permanent magnets

• An electric motor uses magnets to create motion. In an electric motor, the magnets, depending on the poles, will either repel or attract, and the forces of attraction and repulsion are used to create rotational motion.

• There are two magnets within the motor: the armature is an electromagnet, while the field magnet is a permanent magnet.

• Commutators are mechanical switches that automatically change the direction of the current flowing through the coil when the torque fall to zero. It consists of a split metal ring, each part of which is connected to either end of the coil. As the coil rotates, first one ring and then the other will make contact with the brush, that connects the commutator to the DC source. The contact between the rings and the brushes will reverse the direction of the current through the coil.

• The electromagnet makes its half turn, at the moment of completion the field of the electromagnet flips due to the change in direction of the electrons flowing through the coils as it is reversed. The flip causes the electromagnet to make another half-turn. If the direction of the current through the coil is reversed at the exact moment that each half-turn of motion is complete, the electric motor will spin freely.

• The required magnetic fields in DC motors can be produced by permanent magnets shaped to fit around the armature, or electromagnets.

• electromagnets can be produced by winding coils around iron cores attached to the case of the motor and passing current through these coils at the same time as through the rotor coils. These stator coils are wound so that pairs of coils facing the rotor coils have magnetic fields the same as would be produced by pairs of permanent magnets with their north and south poles facing each other.

1.8 Identify data sources, gather and process information to qualitatively describe the application of the motor effect in: - the galvanometer

• A current flowing in the coil produces a magnetic field around the coil. The field interacts with the permanent field due to the magnets. The interaction produces forces on opposite sides of the coil (the motor effect). The forces produce a torque which turns the coil. The pointer attached to the coil turns with the coil. As the coil turns it tightens the spring. The coil stops turning when the restoring force in the spring equals he torque. The scale is calibrated so that the pointer reads the current through the coil. When the current is turned off, the torque on the coil is zero, so the restoring force in the spring returns the pointer to the zero position.

• Radial magnets are used as they produce a uniform field regardless of the angle of rotation of the coil and therefore allow the use of a linear scale.

A galvanometer- the loudspeaker

• A current through a coil wrapped around the frame of the speaker cone produces a changing magnetic field according to the right hand rule. This magnetic field interacts with the south pole of the permanent magnetic field causing the speaker cone to move (the motor effect). This interaction attracts or repels the speaker cone. As the alternating current in the coil changes direction and magnitude (due to the input sound levels), the speaker cone moves back and forth. This vibration of the speaker cone causes vibrations in the air which our ears interpret as the sounds we hear.

• The intensity of the sound is proportional to the current in the voice coil (larger oscillations of the cone). The pitch of the sound is determined by the frequency of the AC input. The higher the frequency, the higher the pitch. Different pitches are produced when the speaker cone vibrates with different frequencies- this occurs when the input current to the coil changes frequency.

• Increased current flow through the voice coil causes a stronger electromagnetic attractions and repulsions and this results in larger scale movements of the voice coil and attached cone. The amplitude of the vibrations increases, so the volume increases.

1.9 Solve problems and analyse information about the force on current-carrying conductors inmagnetic fields using: F = nBIlsinӨ

• Question 1: A conductor carrying 2.5A experiences a force of 0.6N when 0.4m of its length is placed in a magnetic field of intensity 2.0T.(a) Calculate the angle the conductor makes with the field

I = 2.5A F = nBIlsinӨ (Assume n = 1, simple motor)F = 0.6N 0.6 = 2(2.5)(0.4)sinӨL = 0.4m Ө = sin-1 (0.6/(2 x 2.4 x 0.4)B = 2.0T = 17o 27' 27.37''

(b) Predict the angle where the conductor will experience maximum force Maximum when sinӨ = 1, hence Ө = 90o, therefore the conductor will be perpendicular to the magnetic field(c) Predict the angle where the conductor will experience zero force. Justify your answer.

Zero when sinӨ = 0, hence Ө = 0o, therefore the conductor is parallel to the magnetic field(d) Predict the force on a new conductor with half the electrical resistance of the initial conductor placed in an identical position in the same field. Justify your answer.

R = V/I, hence when resistance decreases by half, the current will double. Given that the force is directly proportional to the current, it will also double.

• Question 2: Calculate the force on the conductor in a magnetic field of strength 0.2T shown in the diagram. It carries a current of 3.0A and the length of the conductor in the magnetic field is 0.25m. The conductor makes an angle of 30o

with the field as shownF = ? Therefore, F = BIlsinӨI = 3.0A = 0.2(3)(0.25)(sin60)l = 0.25m = 0.1299038106NB = 0.2T = 0.13N into the pagesinӨ = 90o – 30o (NB> Force is a vector, must give a direction!) = 60o

1.10 Solve problems and analyse information about simple motors using: τ = nBIAcosӨ • A 5cm square coil with 150 turns of wire is in a magnetic field of intensity 0.25T. The plane of the coil makes an

angle of 30o with the magnetic field. The coil carriers a current of 3A.(a) Calculate the magnitude of the force acting on each side of the coilF = nBIlsinӨ F = nBIlsinӨ = 150(0.25)(3)(0.05)sin30 = 150(0.25)(5)(0.05)sin1 = 2.8125N into the page for two sides as 30o = 5.625N into the page (?) for two sides perpendicular(b) Calculate the torque on the coilτ = nBIAcosӨ = 150(0.25)(3)(0.052)cos30 = 0.243569448Nd-1

= 0.24 Nm (approx.)(c) Predict the position of the coil relative to the magnetic field when the torque is a maximum cosӨ = 1 Ө = 0, Hence, when the conductor is parallel the torque is a maximum(d) Predict the position of the coil relative to the magnetic field when the torque on it is a minimum cosӨ → 0

Ө → 90o, hence, as the conductor becomes closer to being perpendicular to the magnetic field, the torque becomes a minimum.

1.11 Solve problems using: F = k I1 I2

l d • Question 1: Two parallel conductors are 0.3m long and 0.15m apart. They each carry a 2.5A current in the same

direction.(a) Calculate the Force between them: F = ? F = 2 x 10 -7 (2.5)(2.5)(0.3)

I1 = I2 = 2.5A 0.15d = 0.15m = 2.5 x 10-6N, attraction l = 0.3mk = 2.0 x 10-7 (b) Calculate the force per unit length between them

F = 2.5 x 10 -6 l 0.3

= 8.3 x 10-6 N, attraction (approx.)(c) Predict the force between the wires if each current was doubled, the distance between them doubled and one of the current direction was reversed

The force would be negative i.e. repulsion, and the force would be double, i.e. F = 5 x 10-6N, repulsion • Question 2: Three current-carrying conductors are set up as shown. Calculate the force per unit length on wire P

and Q due to the currents in the other two wires.P: F = kI1I2 l d F = (2 x 10 -7 )(2)(3) + (2 x 10 -7 )(2)(4) 0.1 0.3 F = 1.73333... x 10-5 Nm ≈ 1.73 x 10-5 Nm, up the page

Q: F = kI1I2 l dF = (2 x 10 -7 )(3)(2) + (2 x 10 -7 )(3)(4) 0.1 0.2F = 2.4 x 10-5 Nm, down the page

2. The relative motion between a conductor and magnetic field is used to generate electrical voltage

2.1 Outline Michael Faraday's discovery of the generation of an electric current by a moving magnet• In 1820, Hans Christian Oersted and Andre Marie Ampere discovered that an electric current produces a

magnetic field. 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. Faraday demonstrated this in 1831.

• Faraday conducted numerous other experiments that showed that when he moved a magnet into or out of a coil of wire, an electric current flowed within the wire. In his first experiment he simply moved a magnet in and out of a coil and noticed that the ammeter in the circuit registered a current whose direction depended on the movement of the magnet. He also noted that the size of the induced current depended on how fast the magnet (or coil) was moved and the strength of the magnet.

• Faraday also experimented with two coils of wire wound around opposite sides of a soft iron ring. He noticed that when he switched on the current in the first loop nothing happened, but when he switched the current on and off continuously, a current was induced in the second coil. He concluded that it was the changing current in the first coil that caused the induced current in the second coil.

• Faraday attached two wires through a sliding contact to touch a rotating copper disc located between the poles of a horseshoe magnet. This was the same as moving a magnetic field near an electric circuit. This induced a continuous direct current. Faraday had invented the first electric generator. Prior to this, continuous electricity could only be produced by batteries or galvanic cells.

• Faraday's explanation was that the electric current was induced in the moving disc as it cut a number of lines of magnetic force emanating from the magnet (the magnetic field). The wires allowed the current to flow in an external circuit where it could be detected.

• Faraday summarised his experiments as: When there is a relative movement between a conductor and a magnetic (either physical movement or a change in magnitude), a potential difference is generated. If the conductor is part of an electric circuit, a current is induced in the circuit. The magnitude of the induced potential difference is directly proportional to the rate at which the conductor 'cuts through' the magnetic field.

2.2 Define magnetic field strength B as magnetic flux density • Magnetic flux density is a measure of the number of magnetic flux lines passing through a unit area, 1m2, and is

represented diagrammatically by the number of magnetic flux lines drawn in a particular area. Magnetic field strength, B, at a point is defined to be the same as magnetic flux density.

• Visualising a magnetic field involves imagining a large number of invisible magnetic flux lines“flowing” out of the north pole and into the south pole of a magnet. The magnetic flux lines are shown close together near the poles where the magnetic field is strongest but further apart at greater distances from the magnet. The magnetic field of a strong magnet is represented by showing a larger number of magnetic flux lines than for the field of a weaker magnet.

2.3 Describe the concept of magnetic flux in terms of magnetic flux density and surface area• Magnetic flux, Ф, is the amount of magnetic field threading or “flowing through” a certain area, A, such as the

area inside a flat coil of wire. This is represented diagrammatically by the total number of magnetic flux lines that pass through area A.

• In the SI system, Ф is measured in Weber (Wb), and the strength of magnetic field, B, is also known as the magnetic flux density. In the SI system, B is measured in telsa (T) or weber per square metre, (Wb m -2).

• The stronger the magnetic field at a point, the higher the magnetic flux density B is at that point and the more magnetic flux lines there are cutting or threading a given area. B is a measure of magnetic flux per unit area perpendicular to the direction of the field at a point in the field.

• If the particular area, A, is perpendicular to uniform magnetic field of strength B, then the magnetic flux, Ф, is the product of the magnetic flux density B by the number of square metres in area A. The formula being: flux = flux density x area, or Ф = BA.

• The magnetic flux, Ф, passing through an area is reduced if the magnetic field is not perpendicular to the area, and Ф is zero if the magnetic field is parallel to the area. The above relationship between magnetic flux density and area is written as: Ф = B┴ A, where B┴ is the component of magnetic flux density that is perpendicular to the Area, A.

2.4 Describe generated potential difference as rate of change of magnetic flux through a circuit• Induced potential difference is the potential difference whenever there is relative movement between a

conductor and a magnetic field. The rate of the relative movement between the conductor and the magnetic field affects the magnitude of an induced potential difference. The relative direction of the movement between the conductor and the magnetic field will affect the direction of an induced potential difference

• In Faraday's experiment, for the current to flow through the galvanometer there must be an electromagnetic force (emf, symbol ε). The magnitude of the current through the galvanometer depends on the resistance of the circuit and the magnitude of the emf generated in the circuit.

• Faraday noted that there had to be a change occurring in the apparatus for an emf to be created. The quantity that was changing in each case was the amount of magnetic flux threading (passing through) the coil in the galvanometer circuit. The rate of change of magnetic flux through a circuit is the generated potential difference (voltage).

• Faraday's law of induction is expressed as follows: The induced emf in a circuit is equal in magnitude to the rate at which the magnetic flux through the circuit in changing with time.Mathematically, this can be written as: ε = -ΔФ ( The negative sign indicates the direction of the

Δt induced emf)• When calculating quantities using Faraday's law of induction, ΔФ = Фfinal – Фinitial

• Since Ф = B┴ A, then a change in Ф can be caused by a change in the magnitude field strength, B, or in the area of that coil that is perpendicular to the magnetic field, or both.

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

2.5 Account for Lenz's law in terms of conservation of energy and relate it to the production of backemf in motors

• Lenz discovered a away to predict the direction of induced current, the method called 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.

• It basically means that the direction of any induced potential difference will be such that it opposes the change that caused it.

• Consider the example where a current is produced by inserting a magnet into a coil connected into a circuit with a galvanometer to show current flow direction. If the south pole of a bar magnet is inserted into the coil the current induced in the coil will flow in a direction such that it produces a south pole opposing the insertion of the bar magnet. Pushing the bar magnet against that field means that work must be done.

• If the same magnet is pulled out of the coil from the same end the current induced in the coil will be in the opposite direction so that it produces a north pole that attracts the south pole of the magnet being withdrawn. This attraction means work must be done to pull the magnet out of the coil.

• Lenz's law follows from the Law of Conservation of Energy. That law says energy cannot be created nor destroyed but can simply change form. In the case of the magnet and coil, energy must be transferred to the coil to produce the induced current flow (electrical energy). That energy is the work done in inserting the coil or withdrawing it. Work must be done against the magnet moving relative to the coil if it is to generate the emf in the coil. If it were not so, the induced magnetic field would accelerate the magnet, thus increasing the induced emf which, in turn would increase the strength of the induced field, further accelerating the magnet, and so on, contravening the Law of Conservation of Energy.

• Electric motors use an external emf applied to the coils to produce an electric current in the coils positioned in an external magnetic field. This current produces a magnetic field that interacts with the external magnetic field. As the coils rotate in the external magnetic field, an emf is induced in the coils due to the constantly changing magnetic flux threading the coils. By Lenz's Law, this induced emf is in the opposite direction to the external supply emf causing the rotation, and it has the effect of reducing the net emf applied to the coils. Because the induced emf is in the opposite direction to the supply emf, it is known as the back emf.

2.6 Explain that, in electric motors, back emf opposes that supply emf• Back emf is the electromagnetic force that opposes the main current flow in the circuit. When the coil of a motor

rotates, a back emf in the coil is induced due to its motion in external magnetic field. Back emf is the induced potential difference which opposes any supply potential difference (as in electric motors). Because a motor

involves relative movement between a conductor (the coil) and a magnetic field, an induced emf will be produced which opposes the direction of rotation of the motor coil.

• By Lenz's law the direction of that induced emf opposes the emf causing the motion of the armature. The current generated in the motor is an eddy current. The direction of the motor eddy current is such that it opposes the supply emf that produces the motion in the motor. The net emf applied to the coils equals the supply emf minus the back emf.

• The back emf increases as the speed of the motor increases, until the net emf is just sufficient to provide the energy for the work the motor is doing, against its own internal friction and any load that is applied to it. If there were no back emf, the motor would continue to spin faster and faster indefinitely which effectively means it is 'creating' energy, which directly goes against the Law of Conservation of Energy.

• When a greater load is applied to the motor, the armature rotates more slowly and the back emf is reduced. This allows a greater current to flow through the coils, resulting in an increased torque to match the extra load.

• At low speeds, when the back emf is small, the motor coils are protected by a series resistor from the large currents that could flow and burn out the motor. This resistor is switched out at higher speeds when the back emf replaces the role played by the resistor at low speed.

• Explanation of the consequences of back emf for the design of an electric motor and the supply of voltage: The back emf will reduce the effective supply emf, so to get maximum efficiency from the motor, the supply emf will need to be larger than the emf needed by the amount of back emf. This means that until the motor reaches maximum speed, the current flowing through the coil may be too large, so a variable resistor needs to be built into the circuit. This resistor automatically reduces zero as running speed (and maximum back emf) is reached.

2.7 Explain the production of eddy currents in terms of Lenz's Law• An eddy current is a circular or whirling current induced in a conductor that is stationary in a changing magnetic

field, or that is moving through a magnetic field,i.e. An eddy current is a current produced by an induced potential difference.

• Induced currents do not only occur in coils and wires. They also occur 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• a conductor is moving in an external magnetic field• a metal object is subjected to a changing magnetic field; such currents are known as eddy currents.

• The magnetic fields set up by the currents oppose the changes in the magnetic field acting in the regions of metal objects.

• One method of producing an eddy current is when a rectangular sheet of metal is being removed from an external magnetic field that is directed into the page (x). One the left of the edge of the magnetic field charged particles in the metal sheet experience a force because they are moving relative to the magnetic field.

• By applying the right-hand push rule, it can be seen that positive charges experience a force up the page in this region.

• To the right of the edge of the magnetic field charged particles will experience no force. Therefore the charged particles that are free to move at the edge of the field contribute to an upward current that is able to flow downward in the metal that is outside the field. This forms a current loop known as eddy current.

• The side of the eddy current loop that is inside the magnetic field experiences a force due to the magnetic field. The direction of the force on the eddy current can be determined using the right-hand push rule and it is always opposite to the direction of the motion of the sheet.

2.8 Gather, analyse and present information to explain how induction is used in cook-tops in electric ranges• When an alternating current passes through coils under the cooktop, which do not have to get hot, a constantly

changing magnetic field is set up. If an iron/steel saucepan is place on the glass cooktop over the coil a similar alternating current will be induced in it.

• The resistance of the metal changes the induced electricity into heat energy and this cooks the food.

2.9 Gather secondary information to identify how eddy currents have been utilised in electromagnetic braking• If a conducting wheel passes between magnetic poles, eddy currents are set up in them.• The eddy currents set up a magnetic field which opposes the field producing it. The two fields attract and slow

down the wheels.

3. Generators are used to provide large-scale power production

3.1 Describe the main components of a generator

Component of Generator Description

Rotor In its simplest form, the rotor consists of a single loop of wire made to rotate within a magnetic field. In practice, the rotor usually consists of several coils of wire wound on an armature

Armature The armature is a cylinder of laminated iron mounted on an axle. The axle is carried on bearings mounted in the external structure of the generator. Torque is applied to the axle to make the rotor spin.

Coil Each coil usually consists of many turns of copper wire wound on the armature. The two ends of the coil are connected to either two slip rings (AC) or two opposite bars of slip ring commutator (DC).

Stator The stator is the fixed part of the generator that supplies the magnetic field in which the coil rotates. It may consist of two permanent magnets with opposite poles facing and shaped to fit around the rotor. Alternatively, the magnetic field may be supplied by two electromagnets.

Field electromagnets Each electromagnet consists of a coil of many turns of copper wire wound on a soft iron core. The electromagnets are wound, mounted and shaped in such a way that opposite poles face each other and wrap around the rotor.

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

3.2 Compare the structure and function of a generator to an electric motor• Electric motors and generators share parts of their structures that are common. Each consists of a stator that

provides a magnetic field and a rotor that rotates within the magnetic field. In both, the magnetic field may be supplied by either two permanent magnets or by electromagnets. The rotor in both consists of coils wound on a laminated iron armature and connected through brushes to an external circuit.

• An electric motor and a DC generator are similar in that their rotor coils are connected to the external circuit through a split-ring commutator. An AC generator differs as it used two split-rings to connect the rotor coils to the external circuit. An AC induction motor is different from a generator as its rotor coils are not connected to an external circuit and its field is always supplied by electromagnets.

• The function of an electric motor is the reverse of the function of a generator. An electric motor converts electricity into mechanical (usually rotational) energy and rotates when current is supplied. A generator performs the reverse function and supplies current when the rotor is made to rotate.

• It is possible for a DC motor to act as a generator by providing the energy to rotate the armature containing the coils.

3.3 Gather secondary information to discuss the advantages/disadvantages of AC and DC generators and relate it to their uses

• The advantages of AC and DC generators relates to the advantages of AC and DC current. Generally, AC current, compared to DC current is easy to transform and so can be transmitted at high voltage, low current to minimise energy loss by heating effects and then transformed to low voltage, higher current for consumer use.

• The generators themselves have fewer moving parts and are easier and cheaper to maintain. Their disadvantages include the protection of back emf due to eddy currents which lowers power output, and wires carrying AC require thicker insulation to minimise interference from emitted electromagnetic radiation by other electronic equipment.

• DC does not need as much insulation as it has no high frequency electromagnetic radiation output and therefore does not cause interference in other equipment o signals, it has significantly lower back emf, and transmission has no energy loss due to induction in adjacent lines and metal structures. However, it cannot be transformed and is therefore more difficult to supply to houses by line distribution. The generators themselves are not reliable due to sparking and wear across split-ring commutators. This sparking also causes interference in other equipment.

3.4 Describe the differences between AC and DC generators• The essential difference between an AC and DC generator is the connection between the rotor coils and the

external circuit.• 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 induced emf changes polarity with every half-turn of the coil, the

voltage in the external circuit varies like a sine wave and the current alternates direction.• In a DC generator, the brushes operate on a split-ring commutator which reverses the connection between coil

and the external circuit every half-turn of the coil. This means as the induced emf changes polarity with every half-turn of coil, he voltage in the external circuit fluctuates between zero and maximum while the current flows

in one constant direction.

3.5 Discuss the energy losses that occur as energy is fed through transmission lines from the generator to theconsumer

• There are two main types of energy losses that occur: those resulting from the resistance of the lines, and those resulting from the induction of the eddy currents3.5.1 Resistive energy loss

• Heat is generated in transmission lines due to the resistance of the wire. The resistance per/km is small, but the resistance of a long transmission line is quite significant. Distances are often great, up to hundreds of kilometres, because power stations are often located in remote places, close to the primary energy source such as a major coal field or a system of dams for a hydroelectric scheme, rarely close to consumers in the city.

• The power loss in transmission lines is given by the relationship: P= V I or P = I2 R. Power loss is proportional

to the square of the current. As the resistance of the conductor is relatively constant, power loss is affected most by the size of the current. Increasing the current by a factor of two increases the power loss by a factor of four.

• Energy losses are kept to a minimum by transmitting the electricity at the highest practicable voltage, with the lowest practicable current. Generally, the greater the distance, the higher the voltage. Closer to the consumer, voltages are lower but energy losses are not substantial since distances are shorter and the current is shared by many separate distribution lines.

• The type of electricity transmitted over long distances is predominantly AC, since AC can be changed easily to

high voltages and correspondingly low currents by the use of a step-up transformer. With advances in solid state technology it is becoming easier to step DC voltages up and down, and DC is increasingly being used for long distance power transmission.

• Energy losses can also be minimised through careful choice of materials and design of conductors. Transmission lines are typically made of either copper or aluminium, as these metals have low resistivity, that is, they are good conductors. Resistance is inversely proportional to the area of cross-section of the conductor, so the thicker a conductor, the lower the heat losses. However, heavier conductors require more expensive support structures. Aluminium has higher resistivity than copper but it is much lighter than copper, and less susceptible to corrosion. The smaller weight and lower maintenance costs more than compensate for the larger diameter of aluminium needed to carry a certain current. Recent experiments with superconducting materials show some promise for reducing energy losses from high voltage transmission lines even further in the future.

• For energy losses to be minimised, the transmission voltage must be very high. This requires high poles or towers and large insulators. These are expensive to build and maintain and have an adverse effect on the visual environment. Trees must be kept well clear of high voltage transmission lines to avoid damage to the lines during storms and to reduce the possibility of a short to earth. This often requires a wide corridor to be cleared, sometimes through environmentally sensitive areas.3.5.2 Induction of eddy currents

• Energy is also lost through the induction of eddy currents in the iron core of transformers. This applies both to step-up transformers at the power station and to step-down transformers at the sub-station and on power poles on suburban streets. The circulation of eddy currents in the transformer core generates heat because of the resistance of the iron. The heat represents an energy loss from the electrical system.

• Transformer cores are usually made of laminated iron, consisting of many thin layers of iron sandwiched together, with thin insulating layers separating them. This limits eddy currents to the thickness of one lamina and reduces the corresponding heat loss. Eddy currents may be further limited in transformer cores made of granular ferrites, as used in some recent experiments. The ferrites allow the magnetic flux to change freely but have high resistance to the eddy currents.

• Heat loss inevitably occurs in the core of a transformer. As overheating can damage the transformer, various cooling techniques are used to dissipate the heat. These include cooling fins on the outside of the transformer, radiator pipes to allow cooling oil to circulate by convection and transfer heat to the air, and electric fans to force cooling air to flow around the transformer.

• The induction of eddy currents in metal parts of transmission towers is kept to a minimum by the distance at which the wires are held away from the tower by the insulators.

3.6 Assess the effects of the development of AC generators on society and the environment• The development of AC generators has led to the widespread application of some of the useful features of AC

electricity. AC generators are simpler and cheaper to build and operate than DC generators. Because AC electricity can easily be transformed, it can be transmitted cheaply over great distances, allowing a wide range of primary energy sources to be exploited. This has allowed the development of extensive, reliable AC electricity networks for domestic and industrial use throughout much of the world. This in turn has had both positive and negative effects on society and the environment.

• The affordability of electricity has promoted the development of a wide range of machines, processes and appliances that depends on electricity. Many tasks that were once performed by hand are now accomplished with a purpose-built electrical appliance and most domestic and industrial work requires less labour. Other new tasks can now be achieved that were formerly impossible, such as electronic communication. However, this has led to a reduction in the demand for unskilled labour and an increase in long-term unemployment. The ready availability of electricity has led to increasing dependency on electricity. Essential services such as hospitals are forced to have a back-up electricity supply, “just in case”. Any disruption to supply compromises safety and causes widespread inconvenience and loss of production. A major electricity failure can precipitate an economic crisis. The global electricity industry lobby is very powerful but is not always just. Social values may give way to economic pressures, especially in developing countries where often the poorest people lose their livelihood to make way for new energy developments.

• AC power generating plants can be located well away from urban areas, shifting pollution away from homes and workplaces, thus improving the environment of cities. However, many environmental effects of the growth in the electricity industry are negative. Power transmission lines criss-cross the country with a marked visual impact on the environment, often cutting a swathe through environmentally sensitive areas. Remote wilderness areas can easily be tapped for energy resources such as their hydro-electric potential. Air pollution from thermal power stations burning fossil fuels may be a cause of acid rain. In addition it contributes to the global increase of atmospheric carbon dioxide which is linked to long-term global climate change. Nuclear power stations leave an environmental legacy of radioactive waste that will last many thousands of years.

• The effects of the development of AC generators on society and the environment have been far-reaching. Some effects have changed the way people live, but not always for the better. Many people now enjoy increased convenience and leisure, many new industries flourish on new technologies made possible by electricity, but the dislocation and unemployment experienced by some can be devastating. Many aspects of the development of electricity have led to environmental degradation, often in remote areas where the long-term effects are poorly understood. These effects seem likely to be ongoing, as the compromise between economic interests and social and environmental values often favours the economic. We have not yet learned to live with AC electricity in a sustainable way.

3.7 Analyse secondary information on the competition between Westinghouse and Edison to supply electricity to cities

• The competition was about the distribution of electrical energy for consumer use. Edison wanted to maintain and increase his existing DC networks, and Westinghouse wanted to attempt to set up AC distribution networks.

• Whilst Edison had tried to lobby the government to pass laws capping the amount of volts the could pass through an AC distribution system and conducted highly publicised experiments electrocuting hundreds of animals with AC in order to prove it was unsafe, he suffered blow after blow to the DC distribution system.

• Westinghouse had won the bid for illuminating the Chicago World Fair and harnessed the water power from Niagara Falls as AC electricity, he continued to defeat Edison and impress the public.

• The AC distribution system was supplying New York City with lights, running street railways and the subway system by 1896.

• AC is preferred because it can be transformed and therefore transmitted to run appliances of many different voltages whereas different voltage DC supplies would have to be provided for every different voltage appliance. DC cannot be transformed, so an equivalent network cover would require many small generating stations scattered all over towns and cities.

• AC generators are also slightly more reliable as they do not require split-ring commutators that are necessary for DC generators.

3.8 Analyse secondary information to identify how transmission lines are:- insulated from supporting structures- protected from lightening strikes

• The ways in which transmission lines are insulated from supporting structures and protected from lightening strikes include:• Shield conductors: these are two non-current carrying wires at the very top of the tower• Earth cable: this runs from the top of the pole down into the Earth• Insulation chains: these are saucer-shaped stacks of ceramic material used whenever the transmission wires

need to be joined to any other metal structure, like the supporting tower• Metal tower: being metal, and set deeply into the ground, the tower itself is an earth protection against

lightening strikes• Distance: the distance between towers is at least 150m, which is enough to protect each tower from adjacent

towers in case one is hit by lightening

4. Transformers allow generated voltage to either be increased or decreased before it is used

4.1 Describe the purpose of transformers in electrical currents• A transformers is a magnetic circuit with two multi-turn coils wound onto a common core whose purpose is to

increase or decrease AC voltages• The domestic supply voltage in Australia is 240V single-phase AC. Industrial and commercial supply is usually

415 V three-phase AC. Whilst many appliances are designed to directly operate on this supply, there are machines that require either an increase or decrease from standard supply.

• Many domestic and industrial appliances have components that require voltages typically between 3V and 24V. In addition, some imported appliances run on voltages common to the country of manufacture.

4.2 Compare step-up and step-down transformers• A step-down transformer is placed in the circuit between the AC supply and the component to reduce supply

voltage required for the component.• A step-up transformer is placed in the circuit to raise the voltage to the required amount, for example a TV

which generally requires 1500V.• It is common for a step-up and step-down transformer to be built into the appliance as apart of its power supply.

Many appliances contain both step-up and step-down transformers to supply voltages required by different components. Many step-down transformers are multi-tapped transformers capable of supplying a range of secondary voltages from the same primary input voltage.

• Main differences are:Step-down Transformer Step-up Transformer

* Consists of two inductively coupled coils wound on a laminated iron core

* Consists of two inductively coupled coils wound on a laminated iron core

* Fewer turns in the secondary coil than the primary coil

* More turns in the secondary coil than the primary coil

* Lower output voltage than input * Higher output voltage than input

* Higher output current than input current * Lower output current than input current

* Used at substations and in towns to reduce transmission line voltage for domestic/industrial use

* Used at power stations to increase voltage and reduce current for long-distance transmission

* Used in computers, radios, CD players etc. to reduce household electricity to very low voltages

* Used in television sets to increase voltage used in picture tube

4.3 Identify the relationship between the ratio of the number of turns in the primary to secondary coils and the ratio of primary and secondary voltage

• Transformers consist of two coils of insulated wire called the primary and secondary coils. These coils can be wound together onto the same, soft iron core, or linked by a soft iron core.

• Transformers are designed so that almost all the magnetic flux produced in the primary coil threads the secondary coil. When an alternating current flows through the primary coil, a constantly changing magnetic flux threads the secondary coil. This constantly changing magnetic flux passing through the secondary coil produces an AC voltage at the terminals of the secondary coil with the same frequency as the AC voltage supplied at the terminals of the primary coil

• The difference between the primary voltage, VP , and the secondary voltage, VS, is in their magnitudes. 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 on the primary coil and secondary coil.

• If the transformer is ideal, hen it is 100% efficient and the energy input at primar ycoil equals energy output of the secondary coil.

• The rate of change of flux (ΔФ/Δt) through both coils is the same. • VP = np (ΔФ/Δt) and VS = nS (ΔФ/Δt)• VP/VS = np /nS

• If the number of primary coils is greater than number of secondary coils, then the output voltage will be less than the input voltage, i.e. step-down transformer. If the number of secondary coils exceeds the number of primary coils, then the output will be greater than the

4.4 Explain why voltage transformations are related to the conservation of energy• The Law of Conservation of Energy states that energy cannot be created or destroyed, merely transformed from

one form to another. Hence, a step-up and step-down transformer must get the extra energy from some where or give off the extra energy.

• The amount of electrical energy entering a transformer in a certain time must equal the total energy exiting the transformer in the same period of time, i.e. power in equals power out. In an 'ideal' transformer, all of the magnetic flux in the primary coil threads the secondary coil, (this is not the case as some energy is usually transformed into thermal energy due to the occurrence of eddy currents in iron core).

• Thus, the rate of change of magnetic flux induced by the primary voltage is equal to the rate of change of magnetic flux inducing an emf in the secondary coil. The relationship between voltage, number of turns and rate of change of flux in the primary coil is given by Faraday's Law: e = N.Df

Dt• The same equation links the number of turns, the rate of change of flux and the induced voltage in the secondary

coil. Combining equations from both sides, and allowing for equal rates of change of flux gives the 'transform equation': Vp = np

Vs ns

• Thus, the voltage transformation that occurs in a transformer is a consequence of the Law of Conservation of Energy. Another consequence of the law in an 'ideal' transformer is that the power of the secondary coil Ps is

equal to the power in the primary coil Pp: P = VI, Pp = VPIP = VsIs = Ps or Is = VP = np

IP Vs ns

• This means that the ratio of secondary current to primary current is the inverse of the ratio of secondary voltage to primary voltage. The secondary current is less than the primary current in a step-up transformer, and greater in a step-down transformer.

• Real transformers produce heat because of the resistance of the iron core to induced eddy currents. This represents an energy loss to the system as heat is a form of energy. The power output of a transformer cannot exceed the power input, and the useful electrical power output is less than the input by the amount of the power loss through heating within the transformer.

4.5 Explain the role of transformers in electricity sub-station• Electricity from power stations is transmitted through the national grid at very high voltages (up to 500kV in

Australia). The high voltages are necessary to minimise energy loss due to resistance in the conducting transmission wires as energy is carried over great distances

• Transmission lines operate under significantly higher voltages than those required to operate most industrial and domestic equipment and appliances. The role of transformers in sub-stations is to progressively reduce the voltage as it comes closer to the consumer. At each stage, the output voltage is chosen to match the power demand and the distances over which the supply is needed.

4.6 Discuss why some electrical appliances in the home that are connected to the mains domestic power supply use a transformer

• Electricity supplied to the domestic households is typically 240V AC. Many domestic appliances are designed to run most efficiently at this voltage. Such appliances are directly connected to the main domestic power supply without a transformer.

• Other appliances have components that require a transformer because they operate best at lower voltages than the mains supply.

• Many small portable appliances, such as personal CD players and mobile telephones, have been designed to run on batteries. These require low DC voltages, either as an alternative to batteries or to recharge the batteries. When the whole appliance is designed to run at the same low voltage, a step-down transformer-rectifier may be built into the plug of the power supply lead that connects to the mains supply. Alternatively, a normal power lead connects the mains to a built-in power supply unit that contains a step-down transformer and a rectifier.

• Appliances such as television receivers and computer monitors contain cathode ray tubes that require voltages well above the mains supply, up to around 25 kV, to accelerate electrons toward the screen. These use a built-in step-up transformer to provide the necessary voltage. The power supply unit may contain both a step-up and a step-down transformer.

4.7 Discuss the impact of transformer on society• The development of transformers has made it possible to transmit electrical energy efficiently over large

distances.• Even very remote communities now have access to grid-supplied high-voltage electricity which is stepped-down

locally by transformers. This has raised living standards in rural communities through the provision of, electrical lighting, refrigeration and air conditioning, and increased the scope of rural industries.

• Large cities have been allowed to spread, because electricity is readily available as an energy source, thanks to transformers. This has led to social dislocation in urban “deserts”, as people have moved further from family and friends and workplaces.

• Industry is no longer clustered around power stations or other sources of energy. Power stations can be in remote locations and high-voltage electrical energy can be distributed almost anywhere, to be stepped down near the point of use. This has allowed industries to be decentralised and has facilitated the development of industrial areas away from residential areas. This has relocated pollution away from homes, but it means that many people now spend significant time travelling between home and work.

4.8 Gather, analyse and use available evidence to discuss how difficulties of heating caused by eddy currents in the transformers may be overcome

• The ways to overcome the difficulties of heating caused by eddy currents are:• Adding sink blades or fins to increase the rate at which heat is dissipated into surroundings• Painting the casing a dark colour so heat produced is absorbed by the casing more quickly for dissipation to

the surroundings• Putting air vents in the casing to allow air to circulate inside the transformer

• Mounting large transformers in the open air above ground so the air can flow around them• Including fans in circuits of the transformers to cool the coils• Filling the transformer with a coolant (usually oil) and circulating the oil with pumps• Constructing the soft iron core using laminations instead of one solid piece. This reduces the size of the

eddy currents and minimises the heat production from themselves• Automatic water sprinkles with thermostatic switches may be triggered by extremely warm temperature

4.9 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

• Transformers are used at generating stations to step-up transmission voltage to minimise energy losses by heating effects during transmission. Step-down transformers lower the voltage at the consumer end to safer and more usable sizes.

4.10 Solve problems and analyse information about transformers using: VP = nP VS nS

• Question 1: A battery charger is used to recharge 1.5V batteries through a 12V transformer. The transformer has 2400 turns in the primary coil. Assuming 100% efficiency, calculate:(a) The number of turns in the secondary coil

VP = nP Hence, 1.5 = nP VS nS 12 2400

nP = 2400(1.5) 12

= 300 turns(b) The output current if the input current is 10mA Is = Vp Hence, Is = 12

IP Vs 10 1.5 Is = 12(10)

1.5 = 80mA

• Question 2: A transformer changes 240V to 24 000V(a) Identify this as either a step-up or step-down transformer It is a step-up transformer(b) Calculate the ratio of the number of turns in the primary coil to the secondary coil np : nS = Vp : VS

= 240 : 24000 = 1 : 100

(c) Predict where this transformer might be used in you home Appliances which require, or have components that require, step-up transformers that increase the voltage includes the television, oven etc.

5. Motors are used in industries and the home usually convert electrical energy into more useful energy forms

5.1 Describe the main features of an AC electric motor• There are two main types of electric motors than run an AC: universal motors and induction motors. Universal

motors can run on AC or DC and are essentially similar in construction to a DC motor.• An induction motor consists of a stator and a rotor. That stator consists of a series of wire coils wound on soft

iron cores that surround the rotor. These are connected to the external power supply in such a way that they produce a magnetic field whose polarity rotates at constant speed in one direction. This is achieved in a three-phases induction motor by connecting consecutive coils in opposing pairs to the three-phase power supply. Many single-phase induction motors use capacitors to stimulate the three-phase effect.

• The rotor consists of coils wound on a laminated iron armature mounted on the axle. The rotor coils are connected to the external power supply, and an induction motor has neither commutators nor brushes. An induction motor has eddy currents that are induced in the rotor coils by rotating the magnetic field of the stator. The eddy currents produce magnetic fields which interact with the rotating field of the stator to exert a torque on the rotor in the direction of the stator field.

• The rotor coils are often simplified to single copper bars capable of carrying a large current, embedded in the surface of the armature. The bars are connected at the ends by rings or a disc of copper which allows current to flow in a loop between opposite bars. This physical arrangement is referred to as a squirrel cage because it resembles an exercise wheel for small mammals.

• An induction motor has a fixed maximum speed. The magnetic field of the stator rotates at the frequency of the AC supply. In Australia, induction motors spin at about 3000 revolutions per minute (50 Hz x 60 seconds) without a load, but the speed of the rotor slips behind that of the field as a load is applied.

5.2 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

• Electrical to heat: toaster, heater, oven, hotplates etc.• Electrical to light: light bulbs, television• Electrical to rotational kinetic energy: blender, circular saw, electric drill• Electrical to sound: radio, television• Electrical to electromagnetic energy and heat: microwave oven