What Is Electric Power?

If we are going to recall our Physics subject, it is said that whenever a force is applied that causes motion the work is said to be done. Take a look on the illustration below:

 

Forces that work is done and  forces not doing work.

The first figure shown above are combination of forces which work is done and forces which work is not done. (a)The picture in which the shelf is held under tension does not cause motion, thus work is not done. (b) The second picture in which the woman pushes the cart causes motion, thus the work is done. (c) The man applied tension in the string is not working since as there is no movement in the direction of the force. (d) The track applied horizontal force on the log is doing work. 

The potential difference between any two points in an electric circuit, which gives rise to a voltage and when connected causes electron to move and current to flow. This is one of a good example in which forces causing motion, thus causing work to be done. 

Talking about work in electric circuit, there is also a electric power which is the time rate of doing work done of moving electrons from point to point. It is represented by the symbol P, and the unit of power is watt, which is usually represented by the symbol W. Watt is practically defined as the rate at which work is being done in a circuit in which the current of 1 ampere is flowing when the voltage applied is 1 volt.

The Useful Power Formula

Electric Power can be transmitted from place to place and can be converted into other forms of energy. One typical energy conversion of electrical energy are heat, light or mechanical energy. Energy conversion is what the engineers really mean for the word power.

The power or the rate of work done in moving electrons through a resistor in electric circuit depends on how many electrons are there to moved. It only means that, the power consumed in a resistor is determined by the voltage measured across it, multiplied by the current flowing through it. Then it becomes,

Power = Voltage x Current

Watts  = Volts x Amperes

P = E x I  or P = EI ------> formula no.1

The power formula above can be derived alternatively in other ways in terms of resistance and current or voltage and resistance using our concept of Ohm's Law. Since E=IR in Ohm's Law, the E in the power formula above can be replaced by IR if the voltage is unknown. Therefore, it would be:

P = EI

P = (IR)I or P = I²R ------------> formula no.2

Alternatively if I = E/R in Ohm'Law, we can also substitute it to E in the power formula which is terms of voltage if the resistance is unknown. 

P = EI

P = E(E/R) or P = E²R ---------> formula no. 3

For guidance regarding expressing of units of power are the following:

a. Quantities of power greater than 1,000 watts are generally expressed in (kW).

b. Quantities greater than 1,000,000 watts are generally expressed as megawatts (MW).

c.  Quantities less than 1 watt are generally expressed in (mW).

The Power Rating of Equipment

Most of the electrical equipment are rated in terms of voltage and power - volts and watts. For example, electrical lamps rated as 120 volts which are for use in 120 volts line are also expressed in watts but mostly expressed in watts rather than voltage. Probably you would wonder what wattage rating all about.

The wattage rating of an electrical lamps or other electrical equipment indicates the rate at which electrical energy is changed into another form of energy, such as heat or light. It only means the greater the wattage of an electrical lamp for example, the faster the lamp changes electrical energy to light and the brighter the lamp will be.

The principle above also applies to other electrical equipment like electric soldering irons, electrical motors and resistors in which their wattage ratings are designed to change electrical energy into some forms of energy. You will learn more about other units like horsepower used for motors when we study motors. 

Take a look at the sizes of carbon resistors below. Their sizes are depends on their wattage rating. They are available with same resistance value with different wattage value. When power is used in a material having resistance, electrical energy is changed into heat. When more power are used, the rate at which electrical energy changed into heat increases, thus temperature of the material rises. If the temperature of the material rises too high, the material may change it composition: expand, contract or even burn. In connection to this reason, all types of electrical equipment are rated for a maximum wattage. 

 

Carbon resistors with comparative sizes of different wattage ratings
of 1/4 watt, 1/2 watt,1 and 2 watts

If the resistors greater then 2 watts rating are needed, wire-wound resistors are used. They are ranges between 5 and 200 watts, with special types being used for power in excess of 200 watts.

 

Use wire wound resistors if higher than 2 watts are needed

Fuses

We all know that when current passes through the resistors, the electrical energy is transformed into heat which raises the temperature of the resistors. If the temperature rises too high, the resistor may be damaged thereby opening the circuit and interrupting the current flow. One answer for this is to install the fuse. 

Fuses are resistors using special metals with very low resistance value and a low melting point. When the power consumed by the fuses raises the temperature of the metal too high, the metal melts and the fuse blows thus open the circuit when the current exceeds the fuse's rated value. What is the identification of blown fuse? Take a look on the picture below.

 

This is the good fuse

 

 

This is the blown fuse

 In other words, blown fuses can be identified by broken filament and darkened glass. You can also check it by removing the fuse and using the ohmmeter.

There are two types of fuses in use today - conventional fuses, which blow immediately when the circuit is overloaded. The slow-blowing (slo-blo) fuses accepts momentary overloads without blowing, but if the overload continues, it will open the circuit. This slo-blo fuses usually used on motors and other appliances with a circuit that have a sudden rush of high currents when turned on.

Fuses are rated in terms of current. Since various types of equipments use different currents, fuses are also made with different sizes, shapes and current ratings.

Various types of fuses are made for various equipments

Proper rating of fuse is needed and very important. It should be slightly higher than the greatest current you expect in the circuit because too low current rating of fuse will result to unnecessary blowouts while too high may result to dangerously high current to pass.

Later we will be study circuit breaker which is another protective devices for over current protection.

Electrical Power in Series, Parallel and Complex Circuits

The principle of getting the total power of the circuit is just simple. There is no need to elaborate this topic. 

The total power consumed by the circuit is the sum of all power consumed in each resistance.

Therefore, we just only sum up all power consumed in each resistance whether it a series, parallel or a complex circuits. Thus,

P_t= P₁+P₂+P₃+P_n watts  ---------->formula no. 4

From the problem in my previous post about complex circuit, try to calculate each power of the resistance and the total power as well. Constant practice always makes you perfect!

Career in Electrical Engineering

One of the many electrical engineering careers includes working with digital technology. This career allows electrical engineers to work with digital technology and to develop ways to make digital technology small enough to be easy to use. Workers in this career may be able to work with cell phone companies to make the required technology small enough to fit into the smallest cell phone or they may design technology to make cell phones more efficient. This can be an exciting career for an electrical engineer and can be quite lucrative as well. 

Electrical engineering is another rewarding type of engineering that is available for individuals today. Just like computer hardware engineering, an electrical engineer is instrumental in every aspect of building any electrical product. The electrical engineer is closely related to every part of the building cycle of any electric product. The electrical engineer is also instrumental in building, installing, repairing and servicing any of the electrical instruments. Therefore, it can be said that the electrical engineer is the backbone of any electrical engineering product. 

Usually, electrical engineering jobs require that engineers work with electrical systems on quite a large scale, but one branch, electronic engineering, deals with the electrical systems on a very small scale. Usually, these types of electrical engineering jobs require dealing with small integrated circuits and computer systems. Whether an electrical engineer deals with small electrical systems or large electrical systems, there are a variety of electrical engineering jobs available. 

How to become an electrical engineer?

If you want to embrace a career as an electrical engineer, you are generally required to graduate from college in engineering. Just like any other engineering career, you will need to have excellent grade in mathematics and science to study in an engineering schools. Being a science-oriented student is not enough, you will be required to have good skills in English, social studies, and computers. Most recruiters also expect their engineers to be creative, curious, logical, detail-oriented and good team-workers.

It is essential for an engineer to effectively communicate their ideas and suggestions to others in their field. A successful Electrical Engineer is a person who has perfect understanding and knowledge about his field and also possesses good grasp of principles of engineering in general as well. That's why you are going to study fundamentals of engineering in beginning. After getting perfect mastery over fundamentals, you can now start focusing on your area of expertise.

Large personal gains and contributions to the community make electric engineering a very useful major that a young person could study. Electric engineers have already contributed to many sectors of life, including the applications in the aerospace industry and the military. Such influence will only enlarge as technology advances and becomes an important factor in our daily life. As electric engineers' influences grow, the importance of electric engineering also becomes more significant. 

The field then subdivides into eight primary areas:

Power, control, electronics, microelectronics, signal, telecommunications,instrumentation and, probably the fastest growing of the areas, computers. There are many who practice more than one of these sub-disciplines, but it's possible to specialize in just one of them and make quite a career out of it. There's also one very popular cross discipline called mechatronics that combines mechanical and electronic engineering. 

Digital and analog electronics is another form of electrical engineering technology that engineers must be well acquainted with to perform their jobs. Both digital and analog electronics are used in computers and phones, however, digital electronics are becoming more widely used as analog electronics is becoming more and more outdated. This form of electrical engineering technology requires that engineers understand Boolean algebra, digital circuits, and how logic gates work. Even those that deal with digital electronics must also understand the electrical engineering technology of analog electronics as well. Digital electronics are usually built with various analog components, so understanding how analog electronics work is essential. 

You should understand that electrical engineers is not the same as electronic engineers. While the two may sound the same, there are great differences between the two. An electrical engineer will deal with electricity and electrical things on a large scale, where electronic engineers will deal with smaller electronics such as cell phones and computers and the components that are inside them.

Electrical Engineering Basics

INTRODUCTION

Electrical engineering is a field of engineering that generally deals with the study and application of electricity, electronics and electromagnetism. The field first became an identifiable occupation in the late nineteenth century after commercialization of the electric telegraph and electrical power supply. It now covers a range of subtopics including power, electronics, control systems, signal processing and telecommunications.

Electrical engineering may or may not include electronic engineering. Where a distinction is made, usually outside of the United States, electrical engineering is considered to deal with the problems associated with large-scale electrical systems such as power transmission and motor control, whereas electronic engineering deals with the study of small-scale electronic systems including computers and integrated circuits. Alternatively, electrical engineers are usually concerned with using electricity to transmit energy, while electronic engineers are concerned with using electricity to transmit information. More recently, the distinction has become blurred by the growth of power electronics.

POWER SYSTEM

Power engineering, also called power systems engineering, is a subfield of engineering that deals with the generation, transmission and distribution of electric power as well as the electrical devices connected to such systems including generators, motors and transformers. Although much of the field is concerned with the problems of three-phase AC power - the standard for large-scale power transmission and distribution across the modern world - a significant fraction of the field is concerned with the conversion between AC and DC power as well as the development of specialized power systems such as those used in aircraft or for electric railway networks.

BASICS OF ELECTRIC POWER

Electric power is the mathematical product of two quantities: current and voltage. These two quantities can vary with respect to time (AC power) or can be kept at constant levels (DC power).

Most refrigerators, air conditioners, pumps and industrial machinery use AC power whereas most computers and digital equipment use DC power (the digital devices you plug into the mains typically have an internal or external power adapter to convert from AC to DC power). AC power has the advantage of being easy to transform between voltages and is able to be generated and utilized by brushless machinery. DC power remains the only practical choice in digital systems and can be more economical to transmit over long distances at very high voltages.

The ability to easily transform the voltage of AC power is important for two reasons: Firstly, power can be transmitted over long distances with less loss at higher voltages. So in power networks where generation is distant from the load, it is desirable to step-up the voltage of power at the generation point and then step-down the voltage near the load. Secondly, it is often more economical to install turbines that produce higher voltages than would be used by most appliances, so the ability to easily transform voltages means this mismatch between voltages can be easily managed.

Solid state devices, which are products of the semiconductor revolution, make it possible to transform DC power to different voltages, build brushless DC machines and convert between AC and DC power. Nevertheless, devices utilizing solid state technology are often more expensive than their traditional counterparts, so AC power remains in widespread use.

POWER

Power Engineering deals with the generation, transmission and distribution of electricity as well as the design of a range of related devices. These include transformers, electric generators, electric motors and power electronics.

The power grid is an electrical network that connects a variety of electric generators to the users of electric power. Users purchase electricity from the grid avoiding the costly exercise of having to generate their own. Power engineers may work on the design and maintenance of the power grid as well as the power systems that connect to it. Such systems are called on-grid power systems and may supply the grid with additional power, draw power from the grid or do both.

Power engineers may also work on systems that do not connect to the grid. These systems are called off-grid power systems and may be used in preference to on-grid systems for a variety of reasons. For example, in remote locations it may be cheaper for a mine to generate its own power rather than pay for connection to the grid and in most mobile applications connection to the grid is simply not practical.

Today, most grids adopt three-phase electric power with alternating current. This choice can be partly attributed to the ease with which this type of power can be generated, transformed and used. Often, the power is split before it reaches residential customers whose low-power appliances rely upon single-phase electric power. However, many larger industries and organizations still prefer to receive the three-phase power directly because it can be used to drive highly efficient electric motors such as three-phase induction motors.

Transformers play an important role in power transmission because they allow power to be converted to and from higher voltages. This is important because higher voltages suffer less power loss during transmission. This is because higher voltages allow for lower current to deliver the same amount of power, as power is the product of the two. Thus, as the voltage steps up, the current steps down. It is the current flowing through the components that result in both the losses and the subsequent heating. These losses, appearing in the form of heat, are equal to the current squared times the electrical resistance through which the current flows, so as the voltage goes up the losses are dramatically reduced.

For these reasons, electrical substations exist throughout power grids to convert power to higher voltages before transmission and to lower voltages suitable for appliances after transmission.

COMPONENTS

Power engineering is a network of interconnected components which convert different forms of energy to electrical energy. Modern power engineering consists of three main subsystems: the generation subsystem, the transmission subsystem, and the distribution subsystem. In the generation subsystem, the power plant produces the electricity. The transmission subsystem transmits the electricity to the load centers. The distribution subsystem continues to transmit the power to the customers.

GENERATION

Generation of electrical power is a process whereby energy is transformed into an electrical form. There are several different transformation processes, among which are chemical, photo-voltaic, and electromechanical. Electromechanical energy conversion is used in converting energy from coal, petroleum, natural gas, uranium, water flow, and wind into electrical energy. Of these, all except the wind energy conversion process take advantage of the synchronous AC generator coupled to a steam, gas or hydro turbine such that the turbine converts steam, gas, or water flow into rotational energy, and the synchronous generator then converts the rotational energy of the turbine into electrical energy. It is the turbine-generator conversion process that is by far most economical and consequently most common in the industry today.

The AC synchronous machine is the most common technology for generating electrical energy. It is called synchronous because the composite magnetic field produced by the three stator windings rotate at the same speed as the magnetic field produced by the field winding on the rotor. A simplified circuit model is used to analyze steady-state operating conditions for a synchronous machine. The phasor diagram is an effective tool for visualizing the relationships between internal voltage, armature current, and terminal voltage. The excitation control system is used on synchronous machines to regulate terminal voltage, and the turbine-governor system is used to regulate the speed of the machine.

The operating costs of generating electrical energy is determined by the fuel cost and the efficiency of the power station. The efficiency depends on generation level and can be obtained from the heat rate curve. We may also obtain the incremental cost curve from the heat rate curve. Economic dispatch is the process of allocating the required load demand between the available generation units such that the cost of operation is minimized.

TRANSMISSION

The electricity is transported to load locations from a power station to a transmission subsystem. Therefore we may think of the transmission system as providing the medium of transportation for electric energy. The transmission system may be subdivided into the bulk transmission system and the sub-transmission system. The functions of the bulk transmission are to interconnect generators, to interconnect various areas of the network, and to transfer electrical energy from the generators to the major load centers. This portion of the system is called "bulk" because it delivers energy only to so-called bulk loads such as the distribution system of a town, city, or large industrial plant. The function of the sub-transmission system is to interconnect the bulk power system with the distribution system.

Transmission circuits may be built either underground or overhead. Underground cables are used predominantly in urban areas where acquisition of overhead rights of way are costly or not possible. They are also used for transmission under rivers, lakes and bays. Overhead transmission is used otherwise because, for a given voltage level, overhead conductors are much less expensive than underground cables.

The transmission system is a highly integrated system. It is referred to the substation equipment and transmission lines. The substation equipment contain the transformers, relays, and circuit breakers. Transformers are important static devices which transfer electrical energy from one circuit with another in the transmission subsystem. Transformers are used to step up the voltage on the transmission line to reduce the power loss which is dissipated on the way. A relay is functionally a level-detector; they perform a switching action when the input voltage (or current) meets or exceeds a specific and adjustable value. A circuit breaker is an automatically-operated electrical switch designed to protect an electrical circuit from damage caused by overload or short circuit. A change in the status of any one component can significantly affect the operation of the entire system. There are three possible causes for power flow limitations to a transmission line. These causes are thermal overload, voltage instability, and rotor angle instability. Thermal overload is caused by excessive current flow in a circuit causing overheating. Voltage instability is said to occur when the power required to maintain voltages at or above acceptable levels exceeds the available power. Rotor angle instability is a dynamic problem that may occur following faults, such as short circuit, in the transmission system. It may also occur tens of seconds after a fault due to poorly damped or undamped oscillatory response of the rotor motion.

DISTRIBUTION

The distribution system transports the power from the transmission system to the customer. The distribution systems are typically radial because networked systems are more expensive. The equipment associated with the distribution system includes the substation transformers connected to the transmission systems, the distribution lines from the transformers to the customers and the protection and control equipment between the transformer and the customer. The protection equipment includes lightning protectors, circuit breakers, disconnectors and fuses. The control equipment includes voltage regulators, capacitors, relays and demand side management equipment.

ELECTRICAL MACHINES

An Electrical machine is a device that converts mechanical energy to electrical energy or vice versa, and changes AC voltage from one level to another level.

Electrical machines are divided into three parts:

GENERATOR

A generator is the device that converts mechanical energy at its prime mover to produce constant electrical energy at its output. In more technical words, it is a dynamic electrical energy machine. Generator is classified into two types: AC generator and DC generator.

The basic requirements for a dynamically induced emf to exist are the following: (1) A steady magnetic field (2) A conductor capable of carrying current (3) The conductor to move in the magnetic field

AC Generator

AC generator is the generator that converts mechanical energy at its prime mover into AC electricity.

AC generator is classified into several types:

• Asynchronous AC generator or induction AC generator, an AC generator whose field current is supplied by magnetic induction into the field windings.
• Synchronous AC generator, an AC generator whose magnetic field current is provided by a separate DC current source, either external DC source or mounted DC source.

 DC Generator

DC generator is the generator that produces DC power i.e., constant power P=V*I by taking mechanical energy as input. Example of a DC generator is dynamo.

MOTOR

Motor is the device that converts electrical energy at its input to produce mechanical energy. Motor is classified into two types: AC motor and DC motor.

AC motor is the motor that converts AC electrical energy at its input into mechanical energy. AC motor is classified into several types:

• Asynchronous motor or induction AC motor
• Synchronous motor

DC motor is the motor that converts DC electricity into mechanical energy. Its main components are stator, rotor, windings (field windings and armature windings) and commutator.

DC motor is classified into five types:

• Compounded DC motor
• Permanent magnet DC motor
• Separately excited DC motor, a DC motor whose field circuit receives power from a separate constant voltage supply.
• Series DC motor, a DC motor whose field windings consist of relatively few turns and connected in series with the armature circuit.
• Shunt DC motor, a DC motor whose field circuit receives power directly across the armature terminals.

Losses in DC motor are brush drop losses, core losses, mechanical losses and stray losses.

TRANSFORMER

Transformer is the device that converts AC voltage from one level to another level higher or lower, or even to the same level without changing the frequency. It works based on the principle of mutual induction, so its power remains approximately constant, where as frequency also remains the same.

IMAGES

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How Electric Motors Work

     Magnetic Fields

Magnetic fields exert a force on ferrous metals (like iron) and magnets as well as on electric currents without any physical contact. Lines of force or flux were invented to help us visualize the magnetic field. Stronger magnetic fields are shown with more lines of flux. Magnetic flux density is proportional to the number of flux lines per unit area. See Figure 1.

DC Motor Action

An electric current produces a magnetic field. The flux lines of a staight, current carrying conductor are concentric rings around the conductor. See Figure 2. The direction of the magnetic field lines are determined by the direction of the current. Your right hand can be used to show this relationship. Your thumb points in the direction of current and your fingers curl in the direction of magnetic field.

Current flowing through a conductor in a magnetic field exerts a sideways force on the conductor. In Figure 3, the permanent magnetic field and the induced magnetic field oppose each other in the region above the wire, reducing the total flux. Below the wire, the two fields are in the same direction and the total flux is increased. The resulting magnetic force causes the conductor to move upwards into the area of the weaker magnetic field.

If an armature loop is placed in a magnetic field, the field around each conductor is distorted. See Figure 4.

These repulsion forces are proportional to the flux density and the current in the armature loop. The repulsion forces push the armature upwards on the left and downwards on the right. These forces are equal in magnitude and opposite in direction and produce a torque which causes the armature to rotate clock-wise.

Commutation

The magnitude of this torque is equal to the force multiplied by the perpendicular distance between the two forces. It is maximum when the conductors are moving perpendicular to the magnetic field. When the loop is in any other position, the torque decreases. When the plane of the loop is perpendicular to the magnetic flux (we call this the neutral plane), the torque equals zero. As soon as the armature passes this point, it experiences a force pushing it in the opposite direction and is eventually magnetically held at the neutral position. In order to maintain the motion of the armature, the battery connections to the armature loop must be reversed as the loop rotates past the neutral plane. This is the basic principle behind a DC electric motor. Electrical energy (current) supplied to the armature is transformed into mechanical motion (the loop rotates).

With the type of motor described above, the torque varies from zero to its maximum twice in each revolution. This variation in torque can cause vibration in the motor and the equipment it drives. Also, a motor stopped with thearmature in the neutral plane is very difficult to start. Additional armature coils solve both of these problems.

Figure 5 shows a motors with one coil, two coils, and 16 coils. The more coils that an armature has (each with two commutator segments), the smoother the torque output. Torque never drops to zero when there are two or more coils.

Back EMF

Whenever a conductor moves through magnetic lines of flux, voltage (emf) is induced in the conductor which is opposite to the voltage you applied to the motor to make it spin. The magnitude of this emf depends on the speed of rotation. It is called the back emf or contervoltage. The difference between the applied voltage and the back emf determines the current in the motor circuit. So, the back emf helps to limit the current flowing in the armature.

DC Motor Types — Permanent Magnet Motors

Permanent magnet (PM) motors are comparably small, light, efficient motors. Their high efficiency and small size are due to the use of permanent magnets to produce the magnetic field. They do not have the added bulk and electrical losses of the field windings normally required to produce the magnetic field.

Permanent magnets are produced by ferromagnetic materials that have been magnetized by an external magnetic field. Ferromagnetic materials can produce magnetic fields several times greater than the external field and will remain magnetized even after the applied magnetic field is removed.

Speed Regulation

Speed regulation is easily accomplished in a PM motor because the speed is linearly related to the voltage. The speed can be increased simply by increasing the voltage. The speed is inversely proportional to the torque. This means that the torque increases as the motor slows down for heavy loads.

See Figure 6. The torque a motor can apply at start up (starting torque) and the torque which causes the motor to breakdown (breakdown torque) are the same

for these motors. PM motors have a high starting torque for starting large loads. This torque results from a high starting current, 10 to 15 times normal running current. PM motors cannot be continuously operated at these currents, though, since overheating can occur. Runaway in a motor occurs when the motor builds up speed under no load until its bearings or brushes are destroyed. Runaway is unlikely in PM motors.

Dynamic Braking

Sometimes it’s necessary for a motor to stop rotating quickly after power is disconnected from the motor. This can be achieved by mechanical braking (friction) or electrical braking (dynamic braking). Dynamic breaking is accomplished in a PM motor by shorting the armature connections and converting the motor into a generator. The rotational mechanical energy is converted to electrical energy and then to heat. PM motors can be braked very quickly using this method without the use of brake shoes which wear out. PM motors are also be easily reversible when the motor is running or stopped.

The most serious disadvantage of PM motors is that the PM fields can be demagnetized by the high armature currents that result from stalling or “locked rotor operation.” This problem becomes more of a concern at temperatures below 0°C. Also, permanent magnet motors are normally small motors because permanent magnets can’t supply enough magnetic field to produce large PM motors.

PM motors can be used for applications requiring small, efficient motors which have high starting torques and low running torques (inertial loads). They are commonly used in well pumps and appliances in RV systems. Jim Forgette of Wattevr Works uses PM motors in his washing machine retrofit kits.

Shunt Motors

In shunt motors, the magnetic field is supplied by an electromagnet which is connected in parallel with the armature loop. The primary advantage of shunt motors is good speed regulation.

Variations in torque by the load do not have a big effect on the speed of the motor unless it is overloaded. Shunt motors have lower starting torques and lower starting currents (three times running currents) than other motors of same horse power. See Figure 7.

Figure 7

The National Electrical Manufacturer’s Assn has agreed on four standard speeds for shunt motors: 1140, 1725, 2500, and 3450 rpm. The speed is normally controlled by varying the armature supply voltage. Speed varies linearly with armature supply voltage and torque is unaffected.

Shunt motors are typically used for loads which require good speed regulation and fair starting torque. If very heavy loads are to be started, a starting circuit may be required. Starting circuits connect progressively smaller resistances in series with the armature. Runaway can occur in shunt motors if the field current is interrupted when the motor is turning but not loaded. Dynamic braking and reversibility are both options with shunt motors.

Series Motors

In series motors, the field coil is connected in series with the armature loop. The field coil has a large current (the full armature current). Heavier copper is used for the field coil but not many turns are needed. Series motors are usually less expensive and smaller in size than other motors of the same horsepower because less copper is used.

Due to the small number of turns and the resulting low inductance, series motors can operate on both ac and DC power. For this reason, series motors are often called universal motors. Power to both the field and armature loops reverses at the same time when operated on ac power and so the resulting magnetic force remains the same. Series motors may perform differently on ac than DC because of the difference in impedance of the windings. One shouldn’t assume all series motors are universal. Some may be optimized for a particular power supply and perform poorly or fail prematurely if not operated on the correct supply.

As the motor’s speed is decreased by heavy loads, the motor supplies high torque to drive the load. This helps prevent stalling and provides high starting torque. Starting currents are also high but are not usually a problem because series motors are normally small motors. See Figure 8. The speed of series motors can be adjusted by varying the supply voltage with a rheostat, variable transformer or electronic controls. Series motors are not normally used if constant speed over a range of loads is required.

Series motors are very common motors in household appliances and power tools. They are used in blenders, juicers, food processors, and hand power tools such as drills. They are very versatile and have the highest horsepower per pound and per dollar of any motor that operates on standard single phase ac power. They deliver high motor speed, high starting torque and wide speed capability. Series motors are usually operated at speeds over 7000 rpm or more. In routers, small grinders and sanders, speeds of 25,000 rpm are not uncommon. Series motors are often connected to a built-in gear train to reduce shaft speed and/or provide more torque. Gear trains also provide loading which prevents runaway.

Series motors have comparatively high maintenance. Brushes and bearings need to be regularly replaced. They are the only motors that are usually given an intermittent duty rating. Other disadvantages of series motors are that they are not usually designed for dynamic braking and reversibility. They should not be run without a load as runaway can occur.

Series motors have a moderately low power factors — normally between 0.5 and 0.7. Resistors have a power factor of one. The more reactive a component, the lower its power factor. Low power factors can be a problem for modified sine wave inverters. Appliances with low power factors may run three quarter speed. Sine wave inverters do not have trouble with power factors less than one. Series motors are typically small motors and so their high starting currents are not usually a problem for inverters.

Compound Motors

A compound motor provides a mixture of the characteristics of both shunt and series motors. Its field coil is split into a series field which is connected in series

with the armature and a shunt field which is connected in parallel with the armature. The magnetic fields can either aid (cumulative compound) or oppose each other (differential compound).

Cumulative and differential compound motors have different speed/torque characteristics. Cumulative compound motors provide more torque than shunt wound motors and better speed regulation than series wound motors. Differential compound motors have almost perfect speed regulation but lower starting torque. See Figure 9.

Compound motors were often used in the past. Inexpensive electronic controls has made it possible to replace them in many cases with lower cost series and shunt motors. They are still used sometimes in large DC equipment which require high torque and good speed regulation.

Brushless DC Motors

Brushless DC motors are actually not DC motors at all. They are ac motors with built-in micro inverters to change the DC supplied to the motor into ac to be fed to the field windings. A logic circuit senses the position of the permanent magnet rotor and controls the distribution of current to the field windings. Field windings are energized in sequence to produce a revolving magnetic field.

The greatest advantage of brushless DC motors is the replacement of carbon graphite brushes and commutators with long life solid state circuitry. They provide low maintenance, low electrical noise motors with good speed control and constant torque. They cannot, however, be easily reversed and are not easily adaptable to dynamic braking. They are also more expensive than conventional DC motors. They are used frequently in audio-visual equipment and “muffin” cooling fans, such as the ones found in inverters, charge controllers, and computer equipment. They are also used in Sun Frost refrigerators.

AC Motors — Induction Motors

The majority of motors in service today are ac motors. Many of these are universal motors. Induction motors,

though more expensive, are also very common due to their high reliability. Polyphase induction motors are cheaper, more efficient, more reliable, and have a higher starting torque than single phase induction motors. We are only discussing single phase induction motors here though because only single phase power is available to most homes.

Induction motors use a squirrel cage rotor construction. This means that the rotor is made of thick aluminum or copper that is one turn only and is joined at each end by an aluminum or copper ring. This frame is then filled in with laminated iron to provide a low reluctance magnetic path. The bars of the rotor are angled with respect to the shaft to provide a smoother output torque and more uniform starting performance.

Voltage is induced in the rotor when it is placed in a rotating magnetic field. The induced voltage produces a high current because of the rotor’s very low resistance. This high current flowing in the rotor produces its own magnetic field. The magnetic interaction of the rotor and the rotating stator field exerts a torque on the rotor, making it follow the magnetic field. Thus an induction motor produces a torque on the rotor without any electrical connections to the rotor. This eliminates the use of brushes and bearings and is the reason for the induction motor’s high reliability.

Normally, the rotating magnetic field in induction motors is produced with three-phase power. A magnetic field established with single phase power will pulse with intensity but will not rotate. A squirrel cage rotor placed between the poles of a single phase motor will therefore not rotate either. Once the rotor begins rotating, however, it will continue to rotate. Thus some means must be employed to create a rotating magnetic field to start the rotor moving. This method determines the type of single phase ac induction motor.

Split-phase Motors

In split-phase motors, a rotating magnetic field is produced with a start winding and a run winding. The start winding is made of smaller gauge wire. The resulting higher resistance and lower reactance produces an approximately 60° phase difference between the currents in the two windings.

This phase difference produces a rotating magnetic field which causes the rotor to start rotating. See Figure 10 below.

DC Motor Characteristics

Motor Type	Starting Torque	Starting Current	Revers-ibility	Speed	Dynamic Braking	Size/ Weight	Cost	Horsepower Range
PM	high	high	easy	varying	yes	smallest	low	under 1
Shunt	low	low	easy	constant	yes	normal	moderate	any
Series	high	very high	not usually	high & varying	no	small	low	under 2
Compound (Dif)	low	low	easy	very constant	yes	large	high	any
Compound (Cum)	high	high	easy	fairly constant	yes	large	high	any
Brushless	high	high	difficult	constant	no	small	high	low

 

The start winding is disconnected from the circuit when the motor reaches 70% of operating speed.

The start winding will overheat if it conducts current continuously. Once the rotor begins turning, the distortion of the stator magnetic field by the rotor’s magnetic field produces enough magnetic field rotation to keep the rotor turning.

Split-phase motors are very common and not very expensive. Oxidation of centrifugal switches was once the most common type of failure. Solid state devices have improved the motor’s reliability. They have a moderate starting torque and a high starting current (8–10 times running current).

They are a good choice for easy to start application such as large fans, blowers, washing machines and some power tools, including bench grinders and large table saws. Overheating can occur if the motor is heavily loaded and the speed kept too low for the switch to open. Heat builds up with the high starting current and the high start winding resistance. Overheating can also result from frequent starting and stopping.

Split-phase motors operate at practically constant speed and come up to rated speed very quickly. The motor’s speed varies from 1780 rpm at no load to 1725–1700 rpm at full load for a 4 pole 60 Hz motor. Split-phase motors can be reversed while at rest but not during operation. Dynamic braking can be accomplished by supplying DC power to the field coils via either an external DC supply or a rectifier, resistor and charging capacitor.

Split-phase motors can cause problems on inverters because of their very high starting currents. Richard learned a trick after damaging many inverters trying to start his bench grinder. If you start the wheel turning with your finger, you can get the grinder started with a lower current. Be sure to get your finger out of the way before you turn the switch on.

Capacitor-Start Motors

Capacitor-start motors have a higher starting torque and lower starting current than split-phase motors. They do this by connecting a capacitor in series with the start winding which increases the phase difference between the start and run fields. Low cost ac electrolytic capacitors are normally used since they are only used for a few seconds when starting.

Capacitor-start motors are used to start very heavy loads such as refrigerators, pumps, washing machines and air compressors. The starting currents can be quite high when the motor is operated with large loads. This much current is hard on centrifugal switch contacts and so many capacitor-start motors use a current or potential relay instead of a centrifugal switch.

Capacitor-start motors often have problems on modified sine wave inverters. The field coils and the capacitor make up a tuned circuit which requires 60 Hz frequency for proper operation. Although modified sine wave inverters have an average 60 Hz frequency, the instantaneous frequency is sometimes much, much higher. Richard’s found in his experience that substituting the capacitor for a higher or lower value may solve the problem. It’s a matter of testing different values. Sine wave inverters do not have any problems starting capacitor-start motors.

Permanent-Split-Capacitor (PSC) Motors

Centrifugal switches and relays are the most likely part of the capacitor-start motor to fail. They can be removed if slightly larger wire is used for the start windings so that they can be left connected without overheating. A higher capacitor value is required to compensate for the higher inductance of the larger windings. Oil-bath type capacitors are usually used because the capacitor is now used during start and run operation.

AC Motor Characteristics

Motor Type	Starting Torque	Starting Current	Reversibility	Speed	Dynamic Braking	Cost	Horsepower Range
Split-phase	moderate	high	easy, at rest	relatively constant	yes	normal	up to 2
Capacitor-start	high	medium	easy, at rest	relatively constant	yes	high-normal	up to 5
PSC	mod. high	med. low	easy	relatively constant	yes	high-normal	up to 5
Two-capacitor	high	medium	easy, at rest	relatively constant	yes	high-normal	up to 5
Shaded-pole	low	low	not reversible	relatively constant	yes	low	up to 1/2

PSC motors operate in much the same way as a two phase ac motor. The capacitor ensures that the capacitor winding is out of phase with the main winding. There is now a rotating magnetic field during start and run operation. This gives the motor greater efficiency and quieter and smoother operation than ac induction motors that only have a rotating magnetic field during start operation. The capacitor value is a compromise between the optimum value for starting and running. This results in a lower starting torque than the capacitor-start motor.

PSC motors are used in applications where frequent starts and stops and quiet smooth operation is required. Examples are instrumentation and low noise equipment fans.

Two-Capacitor Motors

Two capacitor start, one capacitor run motors use an electrolytic capacitor for starting and an oil-type capacitor for starting and running.

The two capacitors are connected in parallel. This motor type preserves the efficiency and smooth, quiet operation of PSC motors while running and provides the high starting torque characteristic of the capacitor-start motors. Optimum starting and running characteristics are obtained at the expense of using some sort of switch again.

Shaded-Pole Motors

Shaded-pole motors’ magnetic fields are made to rotate by the inductive effect of two or more one-turn coils next to the main windings in the stator. The time varying magnetic field set up by the alternating current in the main winding induces current in the shading coils. The induced current in turn establishes a magnetic field in the shading coils which lags behind the main field by about 50°. This sets up a rotating magnetic field in the stator.

Shaded-pole motors are simple in design and construction. They have no internal switches, brushes, or special parts. These motors offer substantial cost savings in applications which require constant speed and low power output.

Shaded-pole motors are inefficient, have low starting torque and can have unsmooth running torque. They are nonetheless cheap and reliable and are used in countless consumer applications ranging from inexpensive blowers to room air conditioner fans. Shaded-pole motors run without problems on sine wave inverters but may run slow on modified sine wave inverters.

Speed Control of ac Motors

Speed control of ac series motors can be accomplished by using SCR’s and triacs to turn ac power on for only part of each cycle, reducing the average voltage to the motor without dissipating large amounts of power.

Induction motors are usually designed to run at a single speed controlled by the frequency of the ac power supply driving them (which is usually a constant 60 Hz). At a higher cost, they are sometimes specially designed to provide speed variations. This is usually accomplished by changing the number of poles. A motor with two coils per phase will run half as fast as a motor with one coil per phase. Thus a motor can be made with two or three coils per phase and the number of coils can be switch selected.

Energy Efficient Electric Motors

Split-phase, capacitor-start, PSC and two-capacitor motors are all available in energy efficient models. Improvements in efficiency are mainly due to increased conductor and rotor areas, improved grade of steel and improved ventilation. These motors are begining to be found in larger home applliances and may make these appliances an option for RE systems.    

Electric motors and generators

DC motors

A simple DC motor has a coil of wire that can rotate in a magnetic field. The current in the coil is supplied via two brushes that make moving contact with a split ring. The coil lies in a steady magnetic field. The forces exerted on the current-carrying wires create a torque on the coil.

The force F on a wire of length L carrying a current i in a magnetic field B is iLB times the sine of the angle between B and i, which would be 90° if the field were uniformly vertical. The direction of F comes from the right hand rule*, as shown here. The two forces shown here are equal and opposite, but they are displaced vertically, so they exert a torque. (The forces on the other two sides of the coil act along the same line and so exert no torque.)

* A number of different nmemonics are used to remember the direction of the force. Some use the right hand, some the left. For students who know vector multiplication, it is easy to use the Lorentz force directly:  F  =  q v X B ,  whence F  =  i dL X B . That is the origin of the diagram shown here.

The coil can also be considered as a magnetic dipole, or a little electromagnet, as indicated by the arrow SN: curl the fingers of your right hand in the direction of the current, and your thumb is the North pole. In the sketch at right, the electromagnet formed by the coil of the rotor is represented as a permanent magnet, and the same torque (North attracts South) is seen to be that acting to align the central magnet.

Throughout, we use blue for the North pole and red for the South. This is just a convention to make the orientation clear: there is no difference in the material at either end of the magnet, and they are usually not painted a different colour.

Note the effect of the brushes on the split ring. When the plane of the rotating coil reaches horizontal, the brushes will break contact (not much is lost, because this is the point of zero torque anyway – the forces act inwards). The angular momentum of the coil carries it past this break point and the current then flows in the opposite direction, which reverses the magnetic dipole. So, after passing the break point, the rotor continues to turn anticlockwise and starts to align in the opposite direction. In the following text, I shall largely use the 'torque on a magnet' picture, but be aware that the use of brushes or of AC current can cause the poles of the electromagnet in question to swap position when the current changes direction.

The torque generated over a cycle varies with the vertical separation of the two forces. It therefore depends on the sine of the angle between the axis of the coil and field. However, because of the split ring, it is always in the same sense. The animation below shows its variation in time, and you can stop it at any stage and check the direction by applying the right hand rule.

Motors and generators

Now a DC motor is also a DC generator. Have a look at the next animation. The coil, split ring, brushes and magnet are exactly the same hardware as the motor above, but the coil is being turned, which generates an emf.

If you use mechanical energy to rotate the coil (N turns, area A) at uniform angular velocity ω in the magnetic field B, it will produce a sinusoidal emf in the coil. emf (an emf or electromotive force is almost the same thing as a voltage). Let θ be the angle between B and the normal to the coil, so the magnetic flux φ is NAB.cos θ. Faraday's law gives:

emf = − dφ/dt = − (d/dt) (NBA cos θ) = NBA sin θ (dθ/dt) = NBAω sin ωt.

The animation above would be called a DC generator. As in the DC motor, the ends of the coil connect to a split ring, whose two halves are contacted by the brushes. Note that the brushes and split ring 'rectify' the emf produced: the contacts are organised so that the current will always flow in the same direction, because when the coil turns past the dead spot, where the brushes meet the gap in the ring, the connections between the ends of the coil and external terminals are reversed. The emf here (neglecting the dead spot, which conveniently happens at zero volts) is |NBAω sin ωt|, as sketched.

An alternator

If we want AC, we don't need recification, so we don't need split rings. (This is good news, because the split rings cause sparks, ozone, radio interference and extra wear. If you want DC, it is often better to use an alternator and rectify with diodes.) In the next animation, the two brushes contact two continuous rings, so the two external terminals are always connected to the same ends of the coil. The result is the unrectified, sinusoidal emf given by NBAω sin ωt, which is shown in the next animation.

This is an AC generator. The advantages of AC and DC generators are compared in a section below. We saw above that a DC motor is also a DC generator. Similarly, an alternator is also an AC motor. However, it is a rather inflexible one. )

Back emf

Now, as the first two animations show, DC motors and generators may be the same thing. For example, the motors of trains become generators when the train is slowing down: they convert kinetic energy into electrical energy and put power back into the grid. Recently, a few manufacturers have begun making motor cars rationally. In such cars, the electric motors used to drive the car are also used to charge the batteries when the car is stopped - it is called regenerative braking. So here is an interesting corollary. Every motor is a generator. This is true, in a sense, even when it functions as a motor. The emf that a motor generates is called the back emf. The back emf increases with the speed, because of Faraday's law. So, if the motor has no load, it turns very quickly and speeds up until the back emf, plus the voltage drop due to losses, equal the supply voltage. The back emf can be thought of as a 'regulator': it stops the motor turning infinitely quickly (thereby saving physicists some embarrassment). When the motor is loaded, then the phase of the voltage becomes closer to that of the current (it starts to look resistive) and this apparent resistance gives a voltage. So the back emf required is smaller, and the motor turns more slowly. (To add the back emf, which is inductive, to the resistive component, you need to add voltages that are out of phase. 

Coils usually have cores

In practice, (and unlike the diagrams we have drawn), generators and DC motors often have a high permeability core inside the coil, so that large magnetic fields are produced by modest currents. This is shown at left in the figure below in which the stators (the magnets which are stat-ionary) are permanent magnets.

'Universal' motors

The stator magnets, too, could be made as electromagnets, as is shown above at right. The two stators are wound in the same direction so as to give a field in the same direction and the rotor has a field which reverses twice per cycle because it is connected to brushes, which are omitted here. One advantage of having wound stators in a motor is that one can make a motor that runs on AC or DC, a so called universal motor. When you drive such a motor with AC, the current in the coil changes twice in each cycle (in addition to changes from the brushes), but the polarity of the stators changes at the same time, so these changes cancel out. 

Build a simple motor

To build this simple but strange motor, you need two fairly strong magnets (rare earth magnets about 10 mm diameter would be fine, as would larger bar magnets), some stiff copper wire (at least 50 cm), two wires with crocodile clips on either end, a six volt lantern battery, two soft drink cans, two blocks of wood, some sticky tape and a sharp nail.

Make the coil out of stiff copper wire, so it doesn't need any external support. Wind 5 to 20 turns in a circle about 20 mm in diameter, and have the two ends point radially outwards in opposite directions. These ends will be both the axle and the contacts. If the wire has lacquer or plastic insulation, strip it off at the ends.

An alternative relisation of the simple motor The supports for the axle can be made of aluminium, so that they make electrical contact. For example poke holes in a soft drink cans with a nail as shown. Position the two magnets, north to south, so that the magnetic field passes through the coil at right angles to the axles. Tape or glue the magnets onto the wooden blocks (not shown in the diagram) to keep them at the right height, then move the blocks to put them in position, rather close to the coil. Rotate the coil initially so that the magnetic flux through the coil is zero, as shown in the diagram. Now get a battery, and two wires with crocodile clips. Connect the two terminals of the battery to the two metal supports for the coil and it should turn. Note that this motor has at least one 'dead spot': It often stops at the position where there is no torque on the coil. Don't leave it on too long: it will flatten the battery quickly. The optimum number of turns in the coil depends on the internal resistance of the battery, the quality of the support contacts and the type of wire, so you should experiment with different values. As mentioned above, this is also a generator, but it is a very inefficient one. To make a larger emf, use more turns (you may need to use finer wire and a frame upon which to wind it.) You could use eg an electric drill to turn it quickly, as shown in the sketch above. Use an oscilloscope to look at the emf generated. Is it AC or DC? This motor has no split ring, so why does it work on DC? Simply put, if it were exactly symmetrical, it wouldn't work. However, if the current is slightly less in one half cycle than the other, then the average torque will not be zero and, because it spins reasonably rapidly, the angular momentum acquired during the half cycle with greater current carries it through the half cycle when the torque is in the opposite direction. At least two effects can cause an asymmetry. Even if the wires are perfectly stripped and the wires clean, the contact resistance is unlikely to be exactly equal, even at rest. Also, the rotation itself causes the contact to be intermittent so, if there are longer bounces during one phase, this asymmetry is sufficient. In principle, you could partially strip the wires in such a way that the current would be zero in one half cycle.

An even simpler motor (one that is also much simpler to understand!) is the homopolar motor.

AC motors

With AC currents, we can reverse field directions without having to use brushes. This is good news, because we can avoid the arcing, the ozone production and the ohmic loss of energy that brushes can entail. Further, because brushes make contact between moving surfaces, they wear out. The first thing to do in an AC motor is to create a rotating field. 'Ordinary' AC from a 2 or 3 pin socket is single phase AC--it has a single sinusoidal potential difference generated between only two wires--the active and neutral. (Note that the Earth wire doesn't carry a current except in the event of electrical faults.) With single phase AC, one can produce a rotating field by generating two currents that are out of phase using for example a capacitor. In the example shown, the two currents are 90° out of phase, so the vertical component of the magnetic field is sinusoidal, while the horizontal is cosusoidal, as shown. This gives a field rotating counterclockwise.

(* I've been asked to explain this: from simple AC theory, neither coils nor capacitors have the voltage in phase with the current. In a capacitor, the voltage is a maximum when the charge has finished flowing onto the capacitor, and is about to start flowing off. Thus the voltage is behind the current. In a purely inductive coil, the voltage drop is greatest when the current is changing most rapidly, which is also when the current is zero. The voltage (drop) is ahead of the current. In motor coils, the phase angle is rather less than 90¡, because electrical energy is being converted to mechanical energy.)

In this animation, the graphs show the variation in time of the currents in the vertical and horizontal coils. The plot of the field components B_x and B_y shows that the vector sum of these two fields is a rotating field. The main picture shows the rotating field. It also shows the polarity of the magnets: as above, blue represents a North pole and red a South pole.

If we put a permanent magnet in this area of rotating field, or if we put in a coil whose current always runs in the same direction, then this becomes a synchronous motor. Under a wide range of conditions, the motor will turn at the speed of the magnetic field. If we have a lot of stators, instead of just the two pairs shown here, then we could consider it as a stepper motor: each pulse moves the rotor on to the next pair of actuated poles. Please remember my warning about the idealised geometry: real stepper motors have dozens of poles and quite complicated geometries!

Induction motors

Now, since we have a time varying magnetic field, we can use the induced emf in a coil – or even just the eddy currents in a conductor – to make the rotor a magnet. That's right, once you have a rotating magnetic field, you can just put in a conductor and it turns. This gives several of the advantages of induction motors: no brushes or commutator means easier manufacture, no wear, no sparks, no ozone production and none of the energy loss associated with them. Below left is a schematic of an induction motor. 

The animation at right represents a squirrel cage motor. The squirrel cage has (in this simplified geometry, anyhow!) two circular conductors joined by several straight bars. Any two bars and the arcs that join them form a coil – as indicated by the blue dashes in the animation. (Only two of the many possible circuits have been shown, for simplicity.)

This schematic suggests why they might be called squirrel cage motors. The reality is different: for photos and more details. The problem with the induction and squirrel cage motors shown in this animation is that capacitors of high value and high voltage rating are expensive. One solution is the 'shaded pole' motor, but its rotating field has some directions where the torque is small, and it has a tendency to run backwards under some conditions. The neatest way to avoid this is to use multiple phase motors.

Three phase AC induction motors

Single phase is used in domestic applications for low power applications but it has some drawbacks. One is that it turns off 100 times per second (you don't notice that the fluorescent lights flicker at this speed because your eyes are too slow: even 25 pictures per second on the TV is fast enough to give the illusion of continuous motion.) The second is that it makes it awkward to produce rotating magnetic fields. For this reason, some high power (several kW) domestic devices may require three phase installation. Industrial applications use three phase extensively, and the three phase induction motor is a standard workhorse for high power applications. The three wires (not counting earth) carry three possible potential differences which are out of phase with each other by 120°, as shown in the animation below. Thus three stators give a smoothly rotating field. 

If one puts a permanent magnet in such a set of stators, it becomes a synchronous three phase motor. The animation shows a squirrel cage, in which for simplicity only one of the many induced current loops is shown. With no mechanical load, it is turning virtually in phase with the rotating field. The rotor need not be a squirrel cage: in fact any conductor that will carry eddy currents will rotate, tending to follow the rotating field. This arrangement can give an induction motor capable of high efficiency, high power and high torques over a range of rotation rates.

Linear motors

A set of coils can be used to create a magnetic field that translates, rather than rotates. The pair of coils in the animation below are pulsed on, from left to right, so the region of magnetic field moves from left to right. A permanent or electromagnet will tend to follow the field. So would a simple slab of conducting material, because the eddy currents induced in it (not shown) comprise an electromagnet. Alternatively, we could say that, from Faraday's law, an emf in the metal slab is always induced so as to oppose any change in magnetic flux, and the forces on the currents driven by this emf keep the flux in the slab nearly constant. (Eddy currents not shown in this animation.)

Alternatively, we could have sets of powered coils in the moving part, and induce eddy currents in the rail. Either case gives us a linear motor, which would be useful for say maglev trains. (In the animation, the geometry is, as usual on this site, highly idealised, and only one eddy current is shown.)

Some notes about AC and DC motors for high power applications

This site was originally written to help high school students and teachers in New South Wales, Australia, where a new syllabus concentrating on the history and applications of physics, at the expense of physics itself, has been introduced. The new syllabus, in one of the dot points, has this puzzling requirement: "explain that AC motors usually produce low power and relate this to their use in power tools".

AC motors are used for high power applications whenever it is possible. Three phase AC induction motors are widely used for high power applications, including heavy industry. However, such motors are unsuitable if multiphase is unavailable, or difficult to deliver. Electric trains are an example: it is easier to build power lines and pantographs if one only needs one active conductor, so this usually carries DC, and many train motors are DC. However, because of the disadvantages of DC for high power, more modern trains convert the DC into AC and then run three phase motors. Single phase induction motors have problems for applications combining high power and flexible load conditions. The problem lies in producing the rotating field. A capacitor could be used to put the current in one set of coils ahead, but high value, high voltage capacitors are expensive. Shaded poles are used instead, but the torque is small at some angles. If one cannot produce a smoothly rotating field, and if the load 'slips' well behind the field, then the torque falls or even reverses.

Power tools and some appliances use brushed AC motors. Brushes introduce losses (plus arcing and ozone production). The stator polarities are reversed 100 times a second. Even if the core material is chosen to minimise hysteresis losses ('iron losses'), this contributes to inefficiency, and to the possibility of overheating. These motors may be called 'universal' motors because they can operate on DC. This solution is cheap, but crude and inefficient. For relatively low power applications like power tools, the inefficiency is usually not economically important.

If only single phase AC is available, one may rectify the AC and use a DC motor. High current rectifiers used to be expensive, but are becoming less expensive and more widely used. If you are confident you understand the principles, it's time to go to How real electric motors work by John Storey. Or else continue here to find out about loudspeakers and transformers.

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Loudspeakers

A loudspeaker is a linear motor with a small range. It has a single moving coil that is permanently but flexibly wired to the voltage source, so there are no brushes.

The coil moves in the field of a permanent magnet, which is usually shaped to produce maximum force on the coil. The moving coil has no core, so its mass is small and it may be accelerated quickly, allowing for high frequency motion. In a loudspeaker, the coil is attached to a light weight paper cone, which is supported at the inner and outer edges by circular, pleated paper 'springs'. In the photograph below, the speaker is beyond the normal upward limit of its travel, so the coil is visible above the magnet poles. For low frequency, large wavelength sound, one needs large cones. The speaker shown below is 380 mm diameter. Speakers designed for low frequencies are called woofers. They have large mass and are therefore difficult to accelerate rapidly for high frequency sounds. In the photograph below, a section has been cut away to show the internal components. Tweeters - loudspeakers designed for high frequencies - may be just speakers of similar design, but with small, low mass cones and coils. Alternatively, they may use piezoelectric crystals to move the cone.

Speakers are seen to be linear motors with a modest range - perhaps tens of mm. Similar linear motors, although of course without the paper cone, are often used to move the reading and writing head radially on a disc drive.

Loudspeakers as microphones

In the picture above, you can see that a cardboard diaphragm (the loudspeaker cone) is connected to a coil of wire in a magnetic field. If a soundwave moves the diaphragm, the coil will move in the field, generating a voltage. This is the principle of a dynamic microphone – though in most microphones, the diaphragm is rather smaller than the cone of a loudspeaker. So, a loudspeaker should work as a microphone. This is a nice project: all you need is a loudspeaker and two wires to connect it to the input of an oscilloscope or the microphone input of your computer. Two questions: what do you think the mass of the cone and coil will do to the frequency response? What about the wavelength of sounds your use?

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Warning: real motors are more complicated The sketches of motors have been schematics to show the principles. Please don't be angry if, when you pull a motor apart, it looks more complicated!  For instance, a typical DC motor is likely to have many separately wound coils to produce smoother torque: there is always one coil for which the sine term is close to unity. This is illustrated below for a motor with wound stators (above) and permanent stators (below).

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Transformers

The photograph shows a transformer designed for demonstration purposes: the primary and secondary coils are clearly separated, and may be removed and replaced by lifting the top section of the core. For our purposes, note that the coil on the left has fewer coils than that at right (the insets show close-ups).

The sketch and circuit show a step-up transformer. To make a step-down transformer, one only has to put the source on the right and the load on the left. (Important safety note: for a real transformer, you could only 'plug it in backwards' only after verifying that the voltage rating were appropriate.) So, how does a transformer work? The core (shaded) has high magnetic permeability, ie a material that forms a magnetic field much more easily than free space does, due to the orientation of atomic dipoles. (In the photograph, the core is laminated soft iron.) The result is that the field is concentrated inside the core, and almost no field lines leave the core. If follows that the magnetic fluxes φ through the primary and secondary are approximately equal, as shown. From Faraday's law, the emf in each turn, whether in the primary or secondary coil, is −dφ/dt. If we neglect resistance and other losses in the transformer, the terminal voltage equals the emf. For the N_p turns of the primary, this gives

V_p = − N_p.dφ/dt .

For the N_s turns of the secondary, this gives

V_s = − N_s.φ/dt

Dividing these equations gives the transformer equation

V_s/V_p = N_s/N_p = r.

where r is the turns ratio. What about the current? If we neglect losses in the transformer (see the section below on efficiency), and if we assume that the voltage and current have similar phase relationships in the primary and secondary, then from conservation of energy we may write, in steady state:

Power in = power out,      so V_pI_p = V_sI_s,      whence 
I_s/I_p = N_p/N_s = 1/r.

So you don't get something for nothing: if you increase the voltage, you decrease the current by (at least) the same factor. Note that, in the photograph, the coil with more turns has thinner wire, because it is designed to carry less current than that with fewer turns. In some cases, decreasing the current is the aim of the exercise. In power transmission lines, for example, the power lost in heating the wires due to their non-zero resistance is proportional to the square of the current. So it saves a lot of energy to transmit the electrical power from power station to city at very high voltages so that the currents are only modest.

Finally, and again assuming that the transformer is ideal, let's ask what the resistor in the secondary circuit 'looks like' to the primary circuit. In the primary circuit:

V_p = V_s/r       and       I_p = I_s.r      so V_p/I_p = V_s/r²I_s = R/r².

R/r² is called the reflected resistance. Provided that the frequency is not too high, and provided that there is a load resistance (conditions usually met in practical transformers), the inductive reactance of the primary is much smaller than this reflected resistance, so the primary circuit behaves as though the source were driving a resistor of value R/r².

Efficiency of transformers

In practice, real transformers are less than 100% efficient.

• First, there are resistive losses in the coils (losing power I².r). For a given material, the resistance of the coils can be reduced by making their cross section large. The resistivity can also be made low by using high purity copper. 
• Second, there are some eddy current losses in the core. These can be reduced by laminating the core. Laminations reduce the area of circuits in the core, and so reduce the Faraday emf, and so the current flowing in the core, and so the energy thus lost.
• Third, there are hysteresis losses in the core. The magentisation and demagnetisation curves for magnetic materials are often a little different (hysteresis or history depedence) and this means that the energy required to magnetise the core (while the current is increasing) is not entirely recovered during demagnetisation. The difference in energy is lost as heat in the core.
• Finally, the geometric design as well as the material of the core may be optimised to ensure that the magnetic flux in each coil of the secondary is nearly the same as that in each coil of the primary.

More about transformers: AC vs DC generators

Transformers only work on AC, which is one of the great advantages of AC. Transformers allow 240V to be stepped down to convenient levels for digital electronics (only a few volts) or for other low power applications (typically 12V). Transformers step the voltage up for transmission, as mentioned above, and down for safe distribution. Without transformers, the waste of electric power in distribution networks, already high, would be enormous. It is possible to convert voltages in DC, but more complicated than with AC. Further, such conversions are often inefficient and/or expensive. AC has the further advantage that it can be used on AC motors, which are usually preferable to DC motors for high power applications.