Basic of Electricity

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Voltmeter: A voltmeter is an instrument used for measuring electrical potential difference between two points in an electric circuit. Analog voltmeters move a pointer across a scale in proportion to the voltage of the circuit; digital voltmeters give a numerical display of voltage by use of an analog to digital converter. Potential difference: Voltage, electrical potential difference, electric tension or electric pressure (denoted ∆V and measured in units of electric potential: volts, or joules per coulomb) is the electric potential difference between two points, or the difference in electric potential energy of a unit charge transported between two points. Electric field: An electric field is generated by electrically charged particles and time-varying magnetic fields. The electric field describes the electric force experienced by a motionless electrically charged test particle at any point in space relative to the source(s) of the field. The concept of an electric field was introduced by Michael Faraday. Electron flow concept: When Benjamin Franklin made his conjecture regarding the direction of charge flow (from the smooth wax to the rough wool), he set a precedent for electrical notation that exists to this day, despite the fact that we know electrons are the constituent units of charge, and that they are displaced from the wool to the wax -- not from the wax to the wool -- when those two substances are rubbed together. This is why electrons are said to have a negative charge: because Franklin assumed electric charge moved in the opposite direction that it actually does, and so objects he called "negative" (representing a deficiency of charge) actually have a surplus of electrons. Negative or positive direction:

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Current flow: An electric current is a flow of electric charge. Electric charge flows when there is voltage present across a conductor. In electric circuits this charge is often carried by moving electrons in a wire. It can also be carried by ions in an electrolyte, or by both ions and electrons such as in a plasma. The SI unit for measuring an electric current is the ampere, which is the flow of electric charges through a surface at the rate of one coulomb per second. Electric current can be measured using an ammeter. Electric currents cause many effects, notably heating, but also induce magnetic fields, which are widely used for motors, inductors and generators.

Resistor symbol: Carbon-composition resistor: Carbon composition resistors (CCR) are fixed form resistors. They are made out of fine carbon particles mixed with a binder (for example clay). After baking it has a solid form. Although carbon composition resistors are widely applied in circuits, the majority of resistors are nowadays made by deposition of a metal or carbon film over a ceramic carrier.

Ohm's law states that the current through a conductor between two points is directly proportional to the potential difference across the two points. Introducing the constant of proportionality, the resistance, one arrives at the usual mathematical equation that describes this relationship:

DC circuits: The basic tools for solving D C circuit problems are Ohm's Law, the power relationship, the voltage law, and the current law. The following configurations are typical; details may be examined by clicking on the diagram for the desired circuit. Magnetism is a class of physical phenomena that includes forces exerted by magnets on other magnets. It has its origin in electric currents and the fundamental magnetic moments of elementary particles. These give rise to a magnetic field that acts on other currents and moments. All materials are influenced to some extent by a magnetic field

In alternating current (AC, also ac), the flow of electric charge periodically reverses direction. In direct current (DC, also dc), the flow of electric charge is only in one direction. The abbreviations AC and DC are often used to mean simply alternating and direct, as when they modify current or voltage. AC is the form in which electric power is delivered to businesses and residences. The usual waveform of an AC power circuit is a sine wave. In certain applications, different waveforms are used, such as triangular or square waves. Audio and radio signals carried on electrical wires are also examples of alternating current. In these applications, an important goal is often the recovery of information encoded (or modulated) onto the AC signal.

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Key terms discussed on the download file: Elements of an Atom, Free Electrons, Conductors, Insulators, Semiconductors, Voltage, Current, Direction of Current Flow, Kirchhoff's current law, LED (light-emitting diodes), IC (integrated circuit), An integrated circuit ,monolithic integrated circuit , Electromotive force, emf, Inductance and Capacitance, Reactance and Impedance, Series and Parallel RLC Circuits, Power and Power Factor in an AC circuit, Transformers, Review Questions, current in a series circuit, magnetic field, magnetic lines of force, compass needle, iron filings, left-hand rule, clockwise magnetic flux, definition of magnetic flux, current-carrying coil, generators, direct current, alternating current, dc voltage, negative and positive terminals,

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Basic of Electricity

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Table of content Introduction...................................................................................................... 4 Conductors and insulators................................................................................ 5 Current, Voltage, and Resistance..................................................................... 6 Ohm's Law ....................................................................................................... 9 DC circuits ....................................................................................................... 10 Magnetism........................................................................................................ 15 Alternating Current .......................................................................................... 19 Inductance and Capacitance............................................................................. 27 Reactance and Impedance................................................................................ 35 Series and Parallel RLC Circuits ..................................................................... 37 Power and Power Factor in an AC circuit ....................................................... 43 Transformers .................................................................................................... 46 Review Questions ............................................................................................ 55

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Introduction Upon completion of Basics of Electricity you will be able to: ° Explain the difference between conductors and insulators ° Use Ohm's law to calculate current, voltage, and resistance ° Calculate equivalent resistance for series, parallel, or series-parallel circuits ° Calculate voltage drop across a resistor ° Calculate power given other basic values ° Identify factors that determine the strength and polarity of a current-carrying Coil's magnetic field ° Determine peak, instantaneous, and effective values of an AC sine wave ° Identify factors that effect inductive reactance and capacitive reactance in an AC circuit ° Calculate total impedance of an AC circuit ° Explain the deference between real power and apparent power in an AC Circuit ° Calculate primary and secondary voltages of single-phase and three-phase transformers ° Calculate the required apparent power for a transformer

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Conductors and Insulators Elements of an Atom As you probably know, everything in the world, whether solid, liquid, or gas, is made up of atoms. Each atom contains some number of electrons, protons, neutrons, and other sub-atomic stuff. The nucleus (central region) of each atom contains the protons (positive charge) and neutrons (no charge). Electrons (negative charge) live in a cloud around the outside. Since electrons and protons are charged particles, each atom prefers to have the same number of electrons as protons. In the normal state of an atom, the number of electrons is equal to the number of protons and the negative charge of the electrons is balanced by the positive charge of the protons. Free Electrons Electrons move about the nucleus at different distances. The closer to the nucleus, the more tightly bound the electrons are to the atom. Electrons in the outer band can be easily force out of the atom by the application of some external force such as a magnetic filed, friction, or chemical action. Conductors An electric current is produced when free electrons move from atom to atom in a material. Some materials are willing to let a few electrons move from molecule to molecule. Materials that let electrons move through them are called "conductors". Although some are better than others, most metals are good conductors of electricity. Silver, Gold, and Platinum are good conductors but are expensive, so they are only used when price is not important compared to function. Copper and Aluminum are also good conductors and are fairly inexpensive. Thus the wiring in our houses is copper, and the high voltage electric lines that we see crossing the country use aluminum cables. Insulators Materials that allow few free electrons are called insulators. These substances keep their electrons under very tight control. Materials that do not let electrons move through them are called "insulators". Materials such as plastic, rubber, glass, mica, and ceramic are good insulators. Glass is an example of a type of material that keeps its electrons tightly controlled. Glass is made of silicon molecules, organized very tightly in to crystalline structures. Glass is an extremely good insulator. Many plastics are good insulators too. Plastics are cheap, flexible, and durable. That is why the wiring in our houses is covered with a layer of plastic.

Figure 1

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Semiconductors Semiconductor materials, such as silicon, can be used to manufacture devices that have characteristics of both conductors and insulators. So a semiconductor is a material which has electrical conductivity to a degree between that of a metal (such as copper) and that of an insulator (such as glass). Many semiconductor devices act like a conductor when an external force is applied in one direction and like an insulator when the external force is applied in the opposite direction. This principle is the basis for transistors, diodes, and other solid-state electronic devices. Hence, semiconductors are the foundation of modern solid state electronics, including transistors, solar cells, light-emitting diodes (LEDs), quantum dots and digital and analog integrated circuits.

Figure 2

Current, Voltage, and Resistance

Voltage Every atom has its own complement of electrons. In a conductor, some of those electrons can jump from atom to atom. But electrons don't move from atom to atom without a reason. When electrons are flowing there is always an electrical force pushing them along. We refer to this force as "Voltage". Therefore, a voltage may represent either a source of energy (electromotive force), or lost, used, or stored energy (potential drop). A voltmeter can be used to measure the voltage (or potential difference) between two points in a system; usually a common reference potential such as the ground of the system is used as one of the points. Voltage can be caused by static electric fields, by electric current through a magnetic field, by time-varying magnetic fields, or some combination of these three. Everyone uses this term, even though they might not understand it. You probably know that a single cell from a flashlight creates an electrical force of 1.5 Volts. You also know that a transistor radio battery (with the snaps on the top) creates an electrical force of 9 Volts. (There are six little cells of 1.5 Volts each inside of the 9 Volt battery) You know that household electrical outlets are 110 or 120 Volts, and you know that "High Voltage" is dangerous.

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The force required to make electricity flow through a conductor is called a difference in potential, electromotive force (EMF), or voltage. Voltage is designated by the letter E or the letter V. the unit of measurement for voltage is the volt which is also designated by the letter V.

Current

An electric current is a flow of electric charge. Electric charge flows when there is voltage present across a conductor. In electric circuits this charge is often carried by moving electrons in a wire. In other words, the flow of free electrons in a material from one atom to the next atom in the same direction is referred to as current and is designated by the symbol I. the amount of current flowing in is determined by the number of electrons that pass through a cross-section of a conductor in one second. The SI unit for measuring an electric current is the ampere, which is the flow of electric charges through a surface at the rate of one coulomb per second. Electric current can be measured using an ammeter. Electric currents cause many effects, notably heating, but also induce magnetic fields, which are widely used for motors, inductors and generators.

Direction of Current Flow The conventional current flow approach ignores the flow of electrons and states that current flows from positive to negative. In this manual, the electron flow concept which states that electrons flow from negative to positive.

Figure 3

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Resistance Resistance is the friction in an electrical circuit that controls the flow of current. As previously mentioned, voltage causes current. When a voltage is present and there is a path (circuit) for electron flow, then there will be a current. And the amount of current flow depends on Voltage which is working against the friction (Resistance) of the circuit. If you open all of the faucets in your house, a lot of water will flow, but not enough to instantly empty the water tank on the hill above your house. The faucet valves that the water must flow through tend to limit the flow rate of the water. In a sense, they have friction that works against the water pressure to limit the flow. You can adjust the flow by how far you open each faucet. In electrical terms, the faucet is an adjustable resistor. As a rule of thumb, the resistance of a conductor increases with an increase of length or a decrease of cross-section. Resistance is designated by the symbol R. the unit of measurement for resistance is the ohm.

A resistor is an electrical component that limits or regulates the flow of electrical current in an electronic circuit. Resistors can also be used to provide a specific voltage for an active device such as a transistor. A resistor is usually shown symbolically on an electrical drawing in one of two ways, a zigzag line or an unfilled rectangle.

Figure 4

All other factors being equal, in a direct-current (DC) circuit, the current through a resistor is inversely proportional to its resistance, and directly proportional to the voltage across it. This is the well-known Ohm's Law. In alternating-current (AC) circuits, this rule also applies as long as the resistor does not contain inductance or capacitance.

Resistors can be fabricated in a variety of ways. The most common type in electronic devices and systems is the carbon-composition resistor. Fine granulated carbon (graphite) is mixed with clay and hardened. The resistance depends on the proportion of carbon to clay; the higher this ratio, the lower the resistance.

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Another type of resistor is made from winding Nichrome or similar wire on an insulating form. This component, called a wire-wound resistor, is able to handle higher currents than a carbon-composition resistor of the same physical size. However, because the wire is wound into a coil, the component acts as an inductors as well as exhibiting resistance. This does not affect performance in DC circuits, but can have an adverse effect in AC circuits because inductance renders the device sensitive to changes in frequency.

Ohm's Law

Ohm's law shows that the current through a conductor between two points is directly proportional to the voltage across the two points. Introducing the constant of proportionality, the resistance, one arrives at the usual mathematical equation that describes this relationship:

I = V ÷ R

Where I is the current through the conductor in units of amperes, V is the potential difference measured across the conductor in units of volts, and R is the resistance of the conductor in units of ohms. More specifically, Ohm's law states that the R in this relation is constant, independent of the current.

Ohm's Law Example

A nine volt battery supplies power to a cordless curling iron with a resistance of 27 ohms. How much current is flowing through the curling iron?

Figure 5 As the following simple example shows, if any two values are known, you can determine the other value using ohm's law. Since V and R are known, solve for I using ohm's law. V = R × I or I = V ÷ R = 9 ÷ 27 = 1/3 A or ~ 0.33 A.

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DC Circuits

Series Circuits: When all the resistive components of a DC circuit are connected end to end to form a single path for flowing electric current, then the circuit is referred as series DC circuit. The manner of connecting components end to end, is known as series connection.

Figure 6

Total resistance = R1 + R2 + R3 + R4 + R5 = 10K + 12K+5K+15K+1K (1000 ohm) = 43 K ohm

The total resistance RT in a series circuit cab be determined by adding all the resistor values. Although the unit for resistance is the ohm, different metric unit prefixes, such as kilo (K) or mega (M) are often used. Therefore, it is important to convert all resistance values to the same units before adding.

Current in a series circuit can be determined using Ohm's law. First, total the resistance and then divide the source voltage by the total resistance. This current flows through each resistor in the circuit.

The voltage measured across each resistor can also be calculated using Ohm's law. The voltage across a resistor is often referred to as a voltage drop. The sum of the voltage drops across each resistor is equal to the source voltage.

Figure 7

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In figure 7 Given: V (source) = 12 V, R1 = 3 K Ohm, R2 = 4 K Ohm, R3 = 5 K Ohm.

Find: RT (total resistance), IT, and voltage measured across each resistor.

Solution: RT = R1 + R2+ R3 = 3+4+5= 12 K Ohm.

IT = VT ÷ RT= 12 ÷ 12 = 1 mA

Voltage measured across each resistor = VR1 = 3 K Ohm ×1 mA = 3 V, VR2 = 4 × 1 mA = 4 V, VR3 = 5 K × 1 mA = 5 V

Figure 8

Figure 8 illustrate 4 voltmeters measuring total voltage, the voltage across R1, R2, and R3.

Parallel Circuits

If two or more components are connected in parallel they have the same potential difference (voltage) across their ends. The potential differences across the components are the same in magnitude, and they also have identical polarities. The same voltage is applicable to all circuit components connected in parallel. The total current is the sum of the currents through the individual components, in accordance with Kirchhoff’s current law. See figure 9

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Figure 9

Voltage

In a parallel circuit the voltage is the same for all elements.

Total resistance for a parallel circuit with any number of resistors can be calculated using the formula shown in the next illustration. See figure 10

Figure 10

If R1 = 5, R2 = 10, and R3 = 20 Ohm, then calculation of total resistance shown in figure 10 is equal to:

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Current in each of the branches of a parallel circuit can be calculated by dividing the circuit voltage, by the resistance of the branch. The total circuit current can be calculated by adding the current for all branches or by dividing the circuit voltage by the total resistance. Figure 11 displays calculation of total current for the figure illustrated in figure 10.

Figure 11

Series-Parallel Circuits: if circuit components are series-connected in some parts and parallel in others, we won't be able to apply a single set of rules to every part of that circuit. Instead, we will have to identify which parts of that circuit are series and which parts are parallel, then selectively apply series and parallel rules as necessary to determine what is happening. Take the circuit shown in figure 12 for instance, this circuit is neither simple series nor simple parallel. Rather, it contains elements of both. The current exits the bottom of the battery, splits up to travel through R3 and R4, rejoins, then splits up again to travel through R1 and R2, then rejoins again to return to the top of the battery. There exists more than one path for current to travel (not series), yet there are more than two sets of electrically common points in the circuit (not parallel).

Figure 12

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Series-parallel circuits are usually more complex than the circuits shown previously, but by using the circuit formulas discussed earlier in this course, you can easily determine circuit characteristics. In the circuit shown in figure 12, the total resistance can be determined for two parallel and on series circuit in 3 easy steps. BUT each step is relatively simple. In addition, since the source voltage is known, by using Ohm's law you can also solve for current and voltage thought each circuit. In the figure 13, calculate VR1, VR2…VR4, IR1, IR2..IR4, RT and fill out the table given in figure 13.

Figure 13

Power in a DC Circuit

The electric power in watts associated with a complete electric circuit or a circuit component represents the rate at which energy is converted from the electrical energy of the moving charges to some other form, e.g., heat, mechanical energy, or energy stored in electric fields or magnetic fields. For a resistor in a DC Circuit the power is given by the product of applied voltage and the electric current:

P = VI

The following example shows how power can be calculated using power formula.

Figure 14

P = VI = 12 × 2 = 24 W

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Magnetism

Magnetism is a force of attraction or repulsion that acts at a distance. It is due to a magnetic field, which is caused by moving electrically charged particles. It is also inherent in magnetic objects such as a magnet.

A magnet is an object that exhibits a strong magnetic field and will attract materials like iron to it. Magnets have two poles, called the north (N) and south (S) poles. Two magnets will be attracted by their opposite poles, and each will repel the like pole of the other magnet. Magnetism has many uses in modern life.

When we think of a permanent magnet, we often envision a horse-shoe or bar magnet or a compass needle, but permanent magnets come in many shapes. All magnets have two characteristics. They attract iron, and if free to move, a magnet assumes a north-south orientation.

Magnetic Lines of Force

There are lines of force surrounding a magnet. You can trace the lines of force around a magnet by using a small compass, as shown in fig.15.

Figure15 A small compass can be used to trace magnetic lines of force near a permanent magnet.

When you bring the compass near the north pole of the magnet, the south pole of the compass will be attracted to it. The compass needle will line up with the magnetic lines of force. If you move the compass, as shown in fig.15, you will be able to trace out the lines of force. It is generally believed that the lines of force come from the north pole as shown, and travel to the south pole. You can also see the path made by the lines of force around a magnet by placing a thin sheet of cardboard over the magnet and then sprinkling iron filings evenly over the cardboard. Tap the cardboard

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gently and the iron filings will arrange themselves in a definite pattern as shown in fig.16.

Figure 16. If iron filings are placed on a sheet of cardboard over permanent Magnets, they will trace out lines of force. Interaction Between Magnets

When two magnets are brought together, the magnetic flux around the magnets causes some form of interaction. When two unlike poles are brought together the magnets attract each other. When two like poles brought together the magnets repeal each other. See figure 17.

Figure 17 Electromagnetism An electric current flowing through a wire produces a magnetic field in the space around the wire. This is called electromagnetism. The concentration of the

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lines of force close to the wire will be much greater than those at some distance from the wire as shown in fig. 17A

Figure 17A. Hence, electromagnetic field is a magnetic field generated by current flow in a conductor. Every electric current generates a magnetic filed and a relationship exists between the direction of current flow and the direction of the magnetic field. The left-hand rule for conductors demonstrates this relationship. If a current-carrying conductor is grasped with the left hand with the thumb pointing in the direction of electron flow, the fingers point in the direction of the magnetic lines of flux. Hence, when current flows in a wire, and an external magnetic field is applied across that flow, the wire experiences a force perpendicular both to that field and to the direction of the current flow. A left hand can be held, as shown in fig. 18, so as to represent three mutually orthogonal axes on the thumb, first finger and middle finger. Each finger is then assigned to a quantity (electric current, magnetic field and mechanical force). The right and left hand are used for generators and motors respectively.

Figure 18 Note that, when an electron flows away from you, causes counterclockwise magnetic flux and when it flow towards you causes clockwise magnetic flux. Definition of Magnetic Flux

Magnetic flux is the product of the average magnetic field times the perpendicular area that it penetrates. It is a quantity of convenience in the statement of Faraday's Law and in the discussion of objects like transformers and solenoids. In the case of an electric generator where the magnetic field penetrates a rotating coil, the

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area used in defining the flux is the projection of the coil area onto the plane perpendicular to the magnetic field. See equation illustrated in figure 19.

Figure 19

Current-Carrying Coil

A coil of wire carrying a current, acts like a magnet. Individual loops of wire act as small magnets. The individual fields add together to form one magnet. The strength of the field can be increased by adding more turns to the coil, increasing the amount of current, or winding the coil around a material such as iron that conducts magnetic flux more easily than air.

When the wire is formed into a coil, the circular magnetic rings pass through the center of the coil in the same direction and reinforce each other as shown. This type of magnet is called an electromagnet. The magnetic effect exists only as long as current is flowing through the wire. The electromagnet shown in fig. 20 can be made much stronger by inserting an iron bar, or a bar of some magnetic material, inside the coil. The bar is called a core. The actual increase in the strength of the magnet will depend upon the type of core material used.

Figure 20

A large variety of electrical devices such as motors, circuit breakers, contactors, relays and motors starters use electromagnetic principles.

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Alternating Current GENERATORS

Although batteries are very useful, their ability to supply large amounts of power is limited. If a battery, even a lead-acid storage battery, is called upon to supply large amount of current, it will soon be exhausted and must be removed from the circuit and recharged.

Before studying generators, let us learn about two important kinds of current you will have to deal with: direct current and alternating current.

Direct Current and Alternating Current

The current supplied by a battery always flow from the negative terminal of the battery through the external circuit and back to the positive terminal of the battery. The current always flows in one direction. We call this kind of current direct current. We usually abbreviate this dc. The voltage supplied by a battery that causes a direct current to flow is referred to as a dc voltage. On a battery, one terminal is always the negative terminal and the other terminal is always the positive terminal. The terminals have always the same polarity.

A dc generator is a device that generates a direct current. In other words, the current coming from a dc generator always flows in the same direction. This means that the terminals of the generator must always have the same polarity. One terminal will always be the negative terminal and the other terminal will always be the positive terminal.

The device or devices connected to the generator are called the load. The load could be a number of light bulbs or it could be a motor or a combination of light bulbs and a motor. The dc generator and the load connected to it are called the dc circuit. In a dc circuit where the generator voltage is constant and the resistance of the load is constant, the current flowing in the circuit will be constant. In other words, the polarity of the generated voltage does not change nor does the strength of the dc current flowing in the circuit change.

Besides direct current, there is another important type of current with which you must be familiar. This type of current is called alternating current, or simply ac. Alternating current differs from direct current in that the strength of the current is continually changing. The current starts at 0 and flows in one direction, building up to a maximum value, which depends upon the voltage being generated and the resistance of the load. Then the current decreases to 0 and begins flowing in the opposite direction, once again building up to a maximum value and dropping to 0. in order for the current to go through this change, the polarity of the voltage generated must change. The voltage starts at 0 with one polarity, builds up to a maximum value, drops to 0 and then reverses polarity, builds and drops with this opposite polarity. This is called a cycle.

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While there are many devices that will operate only on direct current, alternating current has many useful applications. Indeed, our modern industries depend upon large amount of alternating current being readily available.

AC Sine Wave

AC is the form in which electric power is delivered to businesses and residences. The usual waveform of an AC power circuit is a sine wave. In certain applications, different waveforms are used, such as triangular or square waves. Audio and radio signals carried on electrical wires are also examples of alternating current. Alternating voltage and current vary continuously. The graphic representation for AC is a sine wave. A sine wave can represent current or voltage. There are two axes. The vertical axis represents the direction and magnitude of current or voltage. The horizontal axis represents time. See figure 21.

Figure 21

When the waveform is above the time axis, current is flowing in one direction. This is referred to as the positive direction. When the waveform is below the time axis, current is flowing in the opposite direction. This is referee to as the negative direction. A sine wave moves through a complete rotation of 360 degrees, which is referred to as one cycle. Alternating current goes through many of these cycles each second.

Basic AC Generator

Alternating current is produced by a generator when a conductor cuts through magnetic flux lines. In this case, a voltage is induced into the conductor, which causes current to flow. See next figure.

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Figure 21

The polarity of the induced voltage and direction the resulting current flows is determined by the direction the conductor moves through the magnetic field. Reversing the direction of movement reverses the polarity of the voltage and the direction current flows through the wire.

The generator in figure 21 consists of the following: 1- North and South Pole magnets, which create magnetic flux lines between them. 2- A single-loop conductor called the armature. 3- Slip rings mounted on a shaft to which each end of the wire is connected. 4- Brushes on which the slip rings ride to enable current to be carried to the circuit that uses the AC current. A sine wave will be used to illustrate how the generator produces the voltage as the armature rotates through the magnetic field. See figure 21. In the position shown in figure 22, the armature conductor moves in the same direction as the flux lines.

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Figure 22

Nothing is induced into the armature conductor because no cutting action takes place. Hence, the generator, as shown on the graph (figure 23), produces zero voltage.

Figure 23

As the shaft turns, the armature segments begin cutting through the flux lines. See figure 24. In this case shaft has turned 90 degrees and the armature segments cuts the flux lines at a right angle.

Figure 24

As the shaft continues to turn, the positive voltage decreases because the flux lines are no longer cut at a right angle.

When the armature loop has made a half turn, none of the flux lines are cut and zero volts are induced, as shown at 180 degrees of the sine wave. See figure 25.

The voltage induced into the armature reverses and becomes negative.

The maximum voltage is induced when the segments of the armature cut through the flux lines at a right angle.

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Figure 25

The peak negative voltage is produced at 270 degrees of the rotation and of the sine wave. As the shaft continues to turn, the negative voltage decreases because the flux lines are no longer cut at a right angle. See figure 26.

Figure 26

When the armature loop has made a full rotation, none of the flux lines are cut and zero volts are induced, as shown at 360 degrees of the sine wave.

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Figure 27

Question:

The polarity of the voltage induced into a conductor ---------- determined by the direction at which it moves through a magnetic field.

A: is B: is not

Four-Pole AC generator

An AC generator produces one cycle per revolution for each pair of poles. An increase in the number of poles, causes an increase in the number of cycles completed in a revolution. A four-pole generator completes two cycles per revolution.

Figure 28

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Frequency

Frequency is the number of cycles per second of voltage induced in the armature. If a two-pole generator armature rotates at a speed of 60 revolutions per second, the generated voltage have a frequency of 60 cycles per second. The recognized unit for frequency is hertz, abbreviated Hz. 1 Hz is equal to 1 cycle per second.

Power supply companies generate and distribute electricity at very low frequencies. The standard power line frequency in the United States and many other countries is 60 HZ. 50 HZ is also common power line frequency used throughout the world.

Period

The period, usually denoted by T, is the length of time taken by one cycle, and is the reciprocal of the frequency f. The SI unit for period is the second

Amplitude

As it was previously discussed, voltage and current in an AC circuit rise and fall over time in a pattern referred to as a sine wave. In addition to frequency, an AC sine wave also has amplitude, which is the range of variation. Amplitude can be specified in there ways: peak value, peak-to-peak value, and effective value. See figure 29.

Figure 29

From figure 29, the maximum voltage that the ac reaches during a half-cycle is called the peak voltage. The peak-to-peak value is the range from the positive peak to the negative peak. This is twice the peak value. The effective value of AC is defined in terms of an equivalent heating effect when compared to DC. Instruments designed to measure AC voltage and current usually display the effective value. The effective value of an AC voltage or current is approximately equal to 0.707 times the peak value.

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The effective value is also referred to as the RMS value. This name is derived from the root-mean-square mathematical process used to calculate the effective value of a waveform.

Instantaneous Value

This is the value (voltage or current) of a wave at any particular instant. Often chosen to coincide with some other event. E.g. The instantaneous value of a sine wave one quarter of the way through the cycle will be equal to the peak value. See point X in Fig 30.

The voltage waveform produced as the armature of a basic two-pole AC generator rotates 360 degrees is called a sine wave because the instantaneous voltage or current is related to the sine trigonometric function.

Figure 30

As shown in the following illustration, the instantaneous voltage (e) and current (i) at any point on the sine wave are equal to the peak value times the sine of the angle. The sine values shown in the illustration are obtained from trigonometric tables. Keep in mind that each point has an instantaneous value, but this illustration only shows the sine of the angle at 30 degree intervals. The sine of an angle is represented symbolically as sin , where the Greek letter theta represents the angle.

Instantaneous current I = I(peak) × sin

Instantaneous voltage (e) = E (peak) × sin

Example: if E (peak) = 170 v, at 150 degrees then e = 170 × (0.5) = 85 v

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Inductance and Capacitance

Inductance

Inductance is typified by the behavior of a coil of wire in resisting any change of electric current through the coil. Inductance is the property of an electric circuit that opposes any change in electric current. Resistance opposes current flow, inductance opposes changes in current flow. Inductance is designated by the letter L. the unit of measurement for inductance is the Henry (h); however, because the Henry is a relatively large unit, inductance is often rated in millihenries or micro henries.

Arising from Faraday's law, the inductance L may be defined in terms of the emf generated to oppose a given change in current. Increasing current in a coil of wire will generate a counter emf which opposes the current. Applying the voltage law allows us to see the effect of this emf on the circuit equation. The fact that the emf always opposes the change in current is an example of Lenz's law.

All conductors and many electrical devices have a significant amount of inductance, but inductors are coils of wire wound for a specific inductance. For some applications, inductors are wound around a metal core to further concentrate the inductance. The inductance of a coil is determined by the number of turns in the coil, the coil diameter and length, and the core material. As shown in the following illustration, an inductor is usually indicated symbolically on an electrical drawing as a curled line.

Inductors are components manufactured to have a specific inductances. All electrical products have inductance, but the products shown in figure 31 are examples of products that are primarily inductive.

Figure 31

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Inductors in Series

Inductors can be connected together in either a series connection, a parallel connection or combinations of both series and parallel together, to produce more complex networks whose overall inductance is a combination of the individual inductors. However, there are certain rules for connecting inductors in series or parallel and these are based on the fact that no mutual inductance or magnetic coupling exists between the individual inductors.

Inductors are said to be connected in "Series" when they are daisy chained together in a straight line, end to end. In the Resistors in Series we mentioned that the different values of the resistances connected together in series just "add" together and this is also true of inductance. Inductors in series are simply "added together" because the number of coil turns is effectively increased, with the total circuit inductance LT being equal to the sum of all the individual inductances added together.

In the figure 32, an AC source supplies electrical power to four inductors. Total inductance of series inductors is equal to the sum of the inductors.

Figure 32

Inductors in Parallel

The total inductance of inductors in parallel is calculated using a formula similar to the formula for resistance of parallel resistors. The following illustration shows the calculation for a circuit with three parallel inductors.

Figure 33

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L (total) = 2.86 mh

Capacitance and Capacitors

Capacitance is the ability of a body to store an electrical charge. Any object that can be electrically charged exhibits capacitance. A common form of energy storage device is a parallel-plate capacitor. In a parallel plate capacitor, capacitance is directly proportional to the surface area of the conductor plates and inversely proportional to the separation distance between the plates.

Capacitance is typified by a parallel plate arrangement and is defined in terms of charge storage:

Where

• Q = magnitude of charge stored on each plate. • V = voltage applied to the plates.

Figure 34

As you see from figure 34, the capacitance of a capacitor depends on the area of the plates, the distance between the plates, and type of dielectric material used. The symbol for capacitance is C and the unit of measurement is the farad (F). However, because the farad is a large unit, capacitors are often rated in microfarads or picofarads .

One farad is the value of capacitance that produces a potential of one volt when it has been charged by one coulomb. A coulomb is equal to the amount of charge (electrons) produced by a current of one ampere flowing for one second. For most applications, the farad is an impractically large unit of capacitance, although capacitors measured in farads are now used, especially for backing up memory. The most commonly used SI prefixes for electrical and electronic applications are:

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1 millifarad (mF) = one thousandth (10−3) of a farad or 1000 μF 1 microfarad (μF, or MFD)

= one millionth (10−6) of a farad, or 1000000 pF, or 1000 nF

1 nanofarad (nF) = one billionth (10−9) of a farad, or 1000 pF 1 picofarad (pF) = one trillionth (10−12) of a farad

Capacitors in Series

Capacitors are one of the standard components in electronic circuits. Moreover, complicated combinations of capacitors often occur in practical circuits. It is, therefore, useful to have a set of rules for finding the equivalent capacitance of some general arrangement of capacitors. It turns out that connecting capacitors in series decreases total capacitance. The formula for series capacitors is similar to the formula for parallel resistors. In the following example, an AC source supplies electrical power to three capacitors in figure 35.

Figure 35

Capacitors in Parallel

1- Parallel connected Capacitors always have the same voltage drop across each of them.

2- They do not have the same charge unless they have the same capacitance C.

3- The Charge on the equivalent capacitor is the sum of the charges on both capacitors.

4- The Voltage on the equivalent capacitor is the same as the voltage across either capacitor. In figure 36:

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Figure 36

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Reactance and Impedance

V = voltage in volts (V)

I = current in amps (A)

Z = impedance in ohms (ohm)

R = resistance in ohms (ohm)

Impedance (symbol Z) is a measure of the overall opposition of a circuit to current, in other words: how much the circuit impedes the flow of current. It is like resistance, but it also takes into account the effects of capacitance and inductance. Impedance is measured in ohms, symbol ohm . Impedance is more complex than resistance because the effects of capacitance and inductance vary with the frequency of the current passing through the circuit and this means impedance varies with frequency! The effect of resistance is constant regardless of frequency.

Total opposition to current flow in an AC circuit that contains both reactance and resistance is called impedance, designated by the symbol Z.The term 'impedance' is often used (quite correctly) for simple circuits which have no capacitance or inductance - for example to refer to their 'input impedance' or 'output impedance'. This can seem confusing if you are learning electronics, but for these simple circuits you can assume that it is just another word for resistance.

Inductive Reactance X

Reactance (symbol X) is a measure of the opposition of capacitance and inductance to current. Reactance varies with the frequency of the electrical signal. Reactance is measured in ohms, symbol . There are two types of reactance: capacitive reactance (Xc) and inductive reactance (XL).

The total reactance (X) is the difference between the two: X = XL - Xc

Capacitive reactance, Xc

Xc is large at low frequencies and small at high frequencies. For steady DC which is zero frequency, Xc is infinite (total opposition), hence the rule that capacitors pass AC but block DC. For example: a 1µF capacitor has a reactance of 3.2k for a 50Hz signal, but when the frequency is higher at 10kHz its reactance is only 16 .

Inductive reactance, XL

XL is small at low frequencies and large at high frequencies. For steady DC (frequency zero), XL is zero (no opposition), hence the rule that inductors pass DC

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but block high frequency AC. For example: a 1mH inductor has a reactance of only 0.3 for a 50Hz signal, but when the frequency is higher at 10kHz its reactance is 63 . As an second example, for a 60 Hz circuit containing a 10 mh inductor, the inductive reactance is: XL = 2 fL = 2 × 3.14 ×60 Hz × 0.010 h = 3.768 Ohm

For this example, the resistance is zero, so the impedance is equal to the reactance. If the voltage is known, Ohm's law can be used to calculate the current. If, for example, the voltage is 10 V, the current is calculate as follows: I = E ÷ Z = 10 V ÷ 3.768 Ohm = 2.65 A Current and Voltage Phases

In a purely resistive AC circuit, current and voltage are said to be in phase current because they rise and fall at the same time as shown in the following example. See figure 37.

Figure 37

In a purely inductive AC circuit, current and voltage are said to be out of phase because voltage leads current by 90 degrees as shown in following example. Another way of saying that voltage leads current by 90 degrees is to say that current lags voltage by 90 degrees. See figure 38.

Figure 38

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In an AC circuit with both resistance and inductance, current lags voltage by more than 0 degrees and less than 90 degrees. The exact amount of lag depends on the relative amounts of resistance and inductive reactance. The more resistive a circuit is, the closer it is to being in phase. The more reactive a circuit is, the more current and voltage are out of phase. In the following example, resistance and inductive reactance are equal and current lags voltage by 45 degrees. See figure 39.

Figure 39

Hence when capacitors or inductors are involved in an AC circuit, the current and voltage do not peak at the same time. The fraction of a period difference between the peaks expressed in degrees is said to be the phase difference. The phase difference is <= 90 degrees. It is customary to use the angle by which the voltage leads the current. This leads to a positive phase for inductive circuits since current lags the voltage in an inductive circuit. The phase is negative for a capacitive circuit since the current leads the voltage phase. The phase relation is often depicted graphically.

Calculating Impedance in an Inductive circuit

The impedance in a circuit with resistance and inductive reactance can be calculated using the following equation. If capacitive reactance was present in the circuit, its value would be added to the inductance term before squaring.

Vectors

A common way to represent AC circuit values is with a vector diagram. A vector is a quantity that has magnitude and direction. For example, the following vector diagram illustrates the relationship between resistance and inductive reactance for a circuit containing 10 ohm of each. The angle between the vectors is the phase angle represented by the symbol . When inductive reactance is equal to resistance the resultant angle is 45 degrees. This angle represents how much current lags voltage for this circuit. See figure 40.

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Figure 40

Capacitive Reactance

Capacitive Reactance has the electrical symbol "Xc" and has units measured in Ohms the same as resistance, (R). It is calculated using the following formula:

Example No1

Calculate the capacitive reactance of a 220nF capacitor at a frequency of 1kHz and again at 20kHz.

At a frequency of 1kHz,

Xc = 1 ÷ ( 2 × 3.14 × 1000 × 220 × = 723.4 ohm

And if the voltage is 10 V, the current is calculated as follows.

I = E ÷ Z = 10 V ÷ 723.4= 0.0138 A

Current and Voltage Phases

The phase relationship between current and voltage in a capacitive circuit is opposite to the phase relationship in an inductive circuit. In a purely capacitive circuit, current leads voltage by 90degrees.

In a circuit with both resistance and capacitance reactance, AC current leads voltage by more than 0 degrees and less than 90 degrees. The exact amount of lead depends on the relative amounts resistance and capacitive reactance.

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Series and Parallel R-L-C Circuits

Circuits often contain resistance, inductance, and capacitance. In an inductive AC circuit, current lags voltage by 90 degrees. In a capacitive AC circuit, current leads voltage by 90 degrees. Therefore, when represented in vector form, inductive and capacitive reactance is 180 degrees apart. The net reactance is determined by taking the difference between the two quantities.

Figure 41

An AC circuit is:

1- resistive if XL and Xc are equal

2- Inductive if XL is greater than Xc

3- Capacitive if Xc is greater than XL

The following formula is used to calculate total impedance for a circuit containing resistance, capacitance, and inductance.

Series R-L-C Circuit

The following example shows a total impedance calculation for a series R-L-C circuit. Once total impedance has been calculated, current is calculated using Ohm's law.

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Figure 44

Keep in mind that because both inductive reactance and capacitive reactance are dependant upon frequency, if the frequency of the source changes, the reactance

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change. For example, if the frequency increases, the inductive reactance increases, but the capacitive reactance decreases.

For the special case where the inductive reactance and capacitive reactance are equal, the inductive and capacitive reactance cancel and the net impedance is resistance. In this case, the current is equal to the voltage divided by the resistance. This is referred to as a series resonant circuit.

Resonance

Resonance in AC circuits implies a special frequency determined by the values of the resistance , capacitance , and inductance . For series resonance the condition of resonance is straightforward and it is characterized by minimum impedance and zero phase. Parallel resonance , which is more common in electronic practice, requires a more careful definition. See figure 44A.

Figure 44A

The Parallel RLC Circuit is the exact opposite to the series circuit we looked at in the previous tutorial although some of the previous concepts and equations still apply. However, the analysis of parallel RLC circuits can be a little more mathematically difficult than for series RLC circuits so in this tutorial about parallel RLC circuits only pure components are assumed in this tutorial to keep things simple.

In a capacitive AC circuit, current leads voltage by 90 degrees. In an inductive AC circuit, current lags voltage by 90 degrees. When represented in vector form, capacitive current and inductive current and are platted 180 degrees apart. The net reactive current is determined by taking the difference between the reactive currents. The total current for the circuit can be calculated as shown in the following example. Once the total current is known, the total impedance is calculated using Ohm's law.

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Figure 45

In the above parallel RLC circuit, we can see that the supply voltage, E is common to all three components whilst the supply current It consists of three parts. The current flowing through the resistor, IR, the current flowing through the inductor, IL and the current flowing through the capacitor, IC. But the current flowing through each branch and therefore each component will be different to each other and to the supply current, It. The total current drawn from the supply will not be the mathematical sum of the three individual branch currents but their vector sum.

IR = E ÷ R = 24 ÷ 4 = 6 A , IC = E ÷ Xc = 24 ÷ 6 = 4 A , Il = E ÷ Xl = 24 ÷ 2 = 12 A

Figure 46

Like the series RLC circuit, we can solve this circuit using the phasor or vector method but this time the vector diagram will have the voltage as its reference with the three current vectors plotted with respect to the voltage. The phasor diagram for a parallel RLC circuit is produced by combining together the three individual phasors for each component and adding the currents vectorially.

For the special case where the inductive and capacitive reactance are equal, the inductive and capacitance currents cancel and the net current is the resistive current. In this case, the inductor and capacitor form a parallel resonant circuit.

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Parallel Resonance

The resonance of a parallel RLC circuit is a bit more involved than the series resonance. The resonant frequency can be defined in three different ways, which converge on the same expression as the series resonant frequency if the resistance of the circuit is small. See figure 46A.

One of the ways to define resonance for a parallel RLC circuit is the frequency at which the impedance is maximum. The general case is rather complex, but the special case where the resistances of the inductor and capacitor are negligible can be handled readily by using the concept of admittance.

Figure 46A

Admittance

Although the impedance Z is a far more common way to characterize the voltage-current relationships in an AC circuit, there are times when the admittance is a valuable construct. For a given circuit element, the admittance is just the reciprocal of the impedance.

The admittance has its most obvious utility in dealing with parallel AC circuits where there are no series elements. The equivalent admittance of parallel elements is the sum of the admittances of the components.

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Power and Power factor in an AC circuit

Power consumed by a resistor is dissipated in heat and not returned to the source. This is called true power because it is the rate at which energy is used. Hence, For a DC circuit the power is P=VI, and this relationship also holds for the instantaneous power in an AC circuit. However, the average power in an AC circuit expressed in terms of the rms voltage and current is

Where is the phase angle between the voltage and current. The additional term is called the power factor.

From the phasor diagram for AC impedance, it can be seen that the power factor is R/Z. For a purely resistive AC circuit, R=Z and the power factor = 1.

Importance of Power Factor

A power factor of one or "unity power factor" is the goal of any electric utility company since if the power factor is less than one, they have to supply more current to the user for a given amount of power use. In so doing, they incur more line losses. They also must have larger capacity equipment in place than would be otherwise necessary. As a result, an industrial facility will be charged a penalty if its power factor is much different from 1.

Current in an AC circuit rises to peak values and diminishes to zero many times a second. The energy stored in the magnetic field of an inductor, or plates of a capacitor, is returned to the source when current changes direction.

Although reactive components do not consume energy, they do increase the amount of energy that must be generated to do the same amount of work. The rage at which this non-working energy must be generated is called reactive power. If voltage and current are 90 degrees out of phase, as would be the case in a purely capacitive or purely inductive circuit, the average value of true power is equal to zero. In this case, there are high positive peak values of power, but when added together the result is zero.

Industrial facilities tend to have a "lagging power factor", where the current lags the voltage (like an inductor). This is primarily the result of having a lot of electric induction motors - the windings of motors act as inductors as seen by the power supply. Capacitors have the opposite effect and can compensate for the inductive motor windings. Some industrial sites will have large banks of capacitors strictly for the purpose of correcting the power factor back toward one to save on utility company charges.

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In electric power transmission and distribution, volt-ampere reactive (var) is a unit used to measure reactive power in an AC electric power system. Reactive power exists in an AC circuit when the current and voltage are not in phase. The correct symbol is var. The term var was proposed by the Romanian electrical engineer Constantin Budeanu and introduced in 1930 by the IEC in Stockholm, which has adopted it as the unit for reactive power. Apparent Power

Power in an AC circuit is the vector sum of true power and reactive power. This is called apparent power. The true power is equal to apparent power in a purely resistive circuit because voltage and current are in phase. Voltage and current are also in phase in a circuit containing equal values of inductive reactance and capacitive reactance. In most circuits, however, apparent power is composed of both true power and reactive power.

Power Formulas

The formula for apparent power is shown below. The unit of measure for apparent power is the volt-ampere (VA). P = E I.

True power is calculated from another trigonometric function, the cosine of the phase angle (COS ). The formula for true power is shown below. The unit of measure for true power is the watt (W).

P = E I COS

Power Calculation Example

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Figure 47

Power Factor

Power factor is the ratio of true power to apparent power in an AC circuit. As previously indicated, this ratio is also the cosine of the phase angle.

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Transformers

A transformer is a static electrical device that transfers energy by inductive coupling between its winding circuits. A varying current in the primary winding creates a varying magnetic flux in the transformer's core and thus a varying magnetic flux through the secondary winding. This varying magnetic flux induces a varying electromotive force (emf) or voltage in the secondary winding. Transformers are thus used to vary the relative voltage of circuits, which, in some cases, also isolates them.

In the following a single-phase transformer circuit, the AC generator provides electrical power to the primary coil. The magnetic field produced by the primary induces a voltage into the secondary coil. Which supplies power to a load. See figure 47A.

Transformers range in size from thumbnail-sized used in microphones to units weighing hundreds of tons interconnecting the power grid. A wide range of transformer designs are used in electronic and electric power applications. Transformers are essential for the transmission, distribution, and utilization of electrical energy. See figure 48.

Generators used by power companies typically generate voltages of 30 KV or less. While this is a relatively high voltage compared to the voltages used by power customers, it is more efficient for utilities to transmit this power at still higher voltages, up to as high at 765 kv. See figure 49.

The electrical power is received at substation transformers may miles away where it is stepped down and distributed locally. When it arrives at the customer's location, it is further stepped down to the level needed for the type of customer. Even within a customer's facility, voltage may need to be stepped down further to meet requirements of some equipment.

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Figure 48

Figure 48 shows a Pole-mounted distribution transformer with center-tapped secondary winding used to provide 'split-phase' power for residential and light commercial service, which in North America is typically rated 120/240 volt.

Figure 49

Coefficient of coupling

The Coefficient of coupling of a transformer is dependent on the portion of the total flux lines that cuts both primary and secondary windings.

Ideally, all the flux lines generated by the primary should cut the secondary, and all the lines of the flux generated by the secondary should cut the primary.

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The coefficient of coupling would then be one (unity), and maximum energy would be transferred from the primary to the secondary. Practical power transformers use high-permeability silicon steel cores and close spacing between the windings to provide a high coefficient of coupling.

Lines of flux generated by one winding which do not link with the other winding are called LEAKAGE FLUX. Since leakage flux generated by the primary does not cut the secondary, it cannot induce a voltage into the secondary.

The voltage induced into the secondary is therefore less than it would be if the leakage flux did not exist. Since the effect of leakage flux is to lower the voltage induced into the secondary, the effect can be duplicated by assuming an inductor to be connected in series with the primary. This series

LEAKAGE INDUCTANCE is assumed to drop part of the applied voltage, leaving less voltage across the primary.

Transformer Formulas

There are a number of useful formulas for calculating voltage, current, and the number of turns between the primary and secondary of a transformer. These formulas can be used with either step-up or step-down transformers. The following legend applies to the transformer formulas:

Notice the equation shows that the ratio of secondary voltage to primary voltage is equal to the ratio of secondary turns to primary turns.

The equation can be written as:

The following formulas are derived from the above equation:

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If any three of the quantities in the above formulas are known, the fourth quantity can be calculated.

Example 1. A transformer has 200 turns in the primary, 50 turns in the secondary, and 120 volts applied to the primary (Ep). What is the voltage across the secondary (E

s)?

Example 2. There are 400 turns of wire in an iron-core coil. If this coil is to be used as the primary of a transformer, how many turns must be wound on the coil to form the secondary winding of the transformer to have a secondary voltage of one volt if the primary voltage is five volts?

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Note: The ratio of the voltage (5:1) is equal to the turns ratio (400:80). Sometimes, instead of specific values, you are given a turns or voltage ratio. In this case, you may assume any value for one of the voltages (or turns) and compute the other value from the ratio. For example, if a turn ratio is given as 6:1, you can assume a number of turns for the primary and compute the secondary number of turns (60:10, 36:6, 30:5, etc.).

The transformer in each of the above problems has fewer turns in the secondary than in the primary. As a result, there is less voltage across the secondary than across the primary. A transformer in which the voltage across the secondary is less than the voltage across the primary is called a STEP-DOWN transformer. The ratio of a four-to-one step-down transformer is written as 4:1. A transformer that has fewer turns in the primary than in the secondary will produce a greater voltage across the secondary than the voltage applied to the primary. A transformer in which the voltage across the secondary is greater than the voltage applied to the primary is called a STEP-UP transformer. The ratio of a one-to-four step-up transformer should be written as 1:4. Notice in the two ratios that the value of the primary winding is always stated first.

Transformer Ratings

Transformers are rated for the amount of apparent power they can provide. Because values of apparent power are often large, the transformer apparent power rating is frequently given in kVA (kilovolt- amperes). The kVA rating determines the current and voltage a transformer can deliver to its load without overheating.

For a single-phase transformer, the apparent power rating is calculated by multiplying secondary voltage by the maximum load current. This means that if a transformer needs to provide a secondary voltage of 240 V at a maximum load current of 75 A, the kVA rating of the transformer must be at least 18 kVA.

240 × 75 = 18000 VA = 18 kVA

Transformer Losses

Load losses vary according to the loading on the transformer. They include heat losses and eddy currents in the primary and secondary conductors of the transformer.

Heat losses, or I2R losses, in the winding materials contribute the largest part of the load losses. They are created by resistance of the conductor to the flow of current or electrons. The electron motion causes the conductor molecules to move and produce friction and heat. The energy generated by this motion can be calculated using the formula:

Watts = (volts)(amperes) or VI.

According to Ohm’s law, V=RI, or the voltage drop across a resistor equals the amount of resistance in the resistor, R, multiplied by the current, I, flowing in the resistor. Hence, heat losses equal (I)(RI) or I2R.

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Transformer designers cannot change I, or the current portion of the I2R losses, which are determined by the load requirements. They can only change the resistance or R part of the I2R by using a material that has a low resistance per cross-sectional area without adding significantly to the cost of the transformer. Most transformer designers have found copper the best conductor considering the weight, size, cost and resistance of the conductor. Designers can also reduce the resistance of the conductor by increasing the cross-sectional area of the conductor.

Three-Phase electric power

Three-phase electric power is a common method of alternating-current electric power generation, transmission, and distribution. It is a type of polyphase system and is the most common method used by electrical grids worldwide to transfer power. It is also used to power large motors and other heavy loads. A three-phase system is usually more economical than an equivalent single-phase or two-phase system at the same voltage because it uses less conductor material to transmit electrical power.

Three-phase power, as shown in the following illustration, is a continuous series of three overlapping AC cycles. Each wave represents a phase and is offset by 120 electrical degrees from each of the two other phases. See figure 50.

Figure 50

Three-phase Transformers

Up to this point in the manual, we have focused primarily upon single-phase transformers. Single-phase meaning (2) power lines as an input source; therefore, only

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(1) primary and (1) secondary winding is required to accomplish the voltage transformation. However, most power is distributed in the form of three-phase A.C.

Three-Phase transformers must have (3) coils or windings connected in the proper sequence in order to match the incoming power and therefore transform the power company voltage to the level of voltage we need and maintain the proper phasing or polarity.

Three phase electricity powers large industrial loads more efficiently than single-phase electricity. When single-phase electricity is needed, it is available between any two phases of a three-phase system, or in some systems, between one of the phases and ground. By the use of three conductors a three-phase system can provide 173% more power than the two conductors of a single-phase system. Three-phase power allows heavy duty industrial equipment to operate more smoothly and efficiently. Three-phase power can be transmitted over long distances with smaller conductor size. In a three-phase transformer, there is a three-legged iron core as shown below. Each leg has a respective primary and secondary winding.

A three-phase transformer is made of three sets of primary and secondary windings, each set wound around one leg of an iron core assembly. Essentially it looks like three single-phase transformers sharing a joined core as in Figure 51.

Figure 51 shows three phase transformer core has three sets of windings.

Delta and Wye Connections

Those sets of primary and secondary windings will be connected in either Δ or Y configurations to form a complete unit. The various combinations of ways that these windings can be connected together in will be the focus of this section.

Whether the winding sets share a common core assembly or each winding pair is a separate transformer, the winding connection options are the same:

• Primary - Secondary • Y - Y • Y - Δ • Δ - Y • Δ - Δ

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The reasons for choosing a Y or Δ configuration for transformer winding connections are the same as for any other three-phase application: Y connections provide the opportunity for multiple voltages, while Δ connections enjoy a higher level of reliability (if one winding fails open, the other two can still maintain full line voltages to the load).

Delta Connections

Delta transformers are schematically drawn in a triangle. The voltages across each winding of the delta triangle represents one phase of a three phase system. The voltage is always the same between any two wires. A single phase (such as L1 to L2 can be used to supply single phase loads. All three phases are used to supply three phase loads. See figure 52.

When current is the same in all three coils, it is said to be balanced. In each phase, current has two paths to follow. For example, current flowing from L1 to the connection point at the top of the delta can flow down though one coil to L2, and down though another coil to L3. When current is balanced, the current in each line is equal to the square root of 3 times the current in each coil.

Figure 52

Wye Connection

The wye connection also known as a star connection. Three coils are connected to form a "Y" shape. The wye transformer secondary has four leads, three phase leads and one neutral lead. The voltage across any phase (line-to-neutral) will always be less than the line-to-line voltage. The line-to-line voltage is the square root of 3 times the line-to-neutral voltage. The following example shows a wye transformer secondary with a line-to-neutral voltage is 277 volts and line-to-line voltage of 480 volts.

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Figure 53

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Review Questions

1- List of three basic particles of an atom and state the charge of each (positive, negative, or neutral).

2- Materials that permit many electrons to move freely are called --------.

3- Materials that allow few free electrons are called ------------.

4- A material that has an excess of electrons has a ----------- charge.

5- ------------ is the force that, when applied to a conductor, causes current flow.

6- Identify the basic unit of measure for each of the items shown below.

a) Resistance ---------- b) Current -------------- c) Voltage -------------

7- The voltage for a series circuit that has a current of 0.5 A and a resistance of 60 ohm is ----------- V.

8- for a DC circuit with a voltage of 24 V and a current of 5 A, the power is

----------- W.

9- The instantaneous voltage at 240 degrees for a sine wave with a peak voltage

of 150 volt is ------------ V.

10- The effective voltage for a sine wave with a peak voltage of 150 V is ------ V. 11- For a 50 Hz circuit with a 10 MF capacitor, the capacitive reactance is ------

Ohm.

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Good links

http://www.allaboutcircuits.com/worksheets/dc_s.html

The basics of how transformers work, where to shop for step down mains transformers, and how to wire one up to mains voltages.

http://www.youtube.com/watch?v=GMePE7NZcxw

http://www.physics.uoguelph.ca/tutorials/ohm/

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File name: BAS_ELC_COM

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