Generation of a Sine Wave of Voltage

There are two facts that the voltage developed in a coil of a generator changes; the first one is it changes in magnitude from instant to instant as varying values of flux are cut per second and the other one is it changes in direction as coil side change positions under north and south poles, implies that alternating emf is generated. This means that the voltage is maximum as mentioned in our last topic here when the position of the coil is just like shown in the figure below:

Initial position of the coil

and will diminish to zero as the coil rotates clockwise toward the position as shown below:

As the coil rotates clockwise

Then, as the coil continues to rotate clockwise, the polarities will change. Assuming uniform flux distribution between north and south poles, the generated voltage in a coil located from the vertical will be:

e = Em sin α

Consider the figure below for us to analyze why this relationship mentioned above happened.

Illustrating the generated voltage is proportional to sin alpha 

It was come up to the relationship between instantaneous voltage e and maximum voltage Em is that a coil side such as a, moving tangentially to a circle as indicated, cut lines of force in proportion to its vertical component of the motion. If the vector length ay in the figure above represents a constant rotating velocity, it should be obvious that vector xy is, its vertical component; the vector length ax is the horizontal component and it emphasize that motion in this direction involves no flux- cutting action. Since the velocity ratio xy/ay=sinα is also a measure of the voltage in coil side a with respect to the maximum voltage (when the coil is located horizontally) it follows that sinα is a varying proportionality factor that equates e to Em.

The equation above may be used to determine a succession of generated voltage values in a coil as it rotates through a complete revolution. This is just by computing with its selected angular displacements.

A more convenient way of representing the instantaneous voltage equation mentioned above is to draw a graph to illustrate a smooth variation of voltage with respect to the angular position of the coil, this graph is called a sine wave. The wave repeats itself and it is called a periodic, then each complete succession of values is called a cycle, while each positive or negative half of the cycle is called alternation.

Sinusoidal Voltage Wave

Now, we can say that an alternating voltage as an emf that varies in magnitude and direction periodically. Then, when the emfs are proportional to the trigonometric sine function, it is referred to a sinusoidal alternating voltage. However, there are also some periodic waves which do not follow this shape and they are called non sinusoidal waves. This topic will be covered when we reached more complicated analysis is AC Circuits.

Lets have a practical example of a problem using the equation above just for you to appreciate the presented  formula above:

Problem : The voltage in an ac circuit varies harmonically with time with a maximum of 170V. What is the instantaneous voltage when it has reached 45 degree in its cycle?

Using, e = Em sin α = 170V x sin (45 degree) = 170V x 0.71 = 120 V.

In the common 60 cycle ac circuit, there are 60 complete cycle each second; i.e. the time interval of 1 cycle is 1/60 sec. It should be noted that this corresponds to a reversal in a direction of the current every 1/120 sec. (since the direction reverses twice during each cycle). 

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Generation of Alternating EMF's

A voltage can be developed in a coil of wire in one of the three ways:

1. By changing the flux through the coil.
2. By moving the coil through the magnetic field.
3. By altering the direction of the flux with respect to the coil.

The first one is that voltage is said to be induced emf and in accordance with Faraday's law, its magnitude at any instant of time is given by the formula as shown below:

e = N(dΦ/dt) x 10 ^-8 volts

where N is the number turns in a coil
dΦ/dt = rate at which the flux in maxwells changes through the coil

Please take note that in this method of developing an emf, there is no physical motion of coil or magnet; the current through the exciting coil that is responsible for the magnetism is altered to change the flux through the coil in which the voltage is induced. For the second and third method mentioned above, there is actual physical motion of coil or magnet, and in altered positions of coil or magnet flux through the coil changes. A voltage developed on these ways is called a generated emf and is given by the equation:

e = Blv x 10^-8 volts

where B is the flux density in lines per square inch
l is the length of the wire, in., that is moved relative to the flux
v is the velocity of the wire, in.per sec., with respect to the flux

Two-pole single AC Generator

The figure above illustrates an elementary a-c generator. The single turn coil may be moved through the magnetic field created by two magnet poles N and S. As you can see, the ends of the coil are connected to two collectors upon which two stationary brushes rest on it. For the clockwise rotation as shown, the side of the coil on north pole N is moving vertically upward to cut the maximum flux under north pole N, while the other side of the coil on south pole S is moving vertically downward to cut the maximum flux under south pole S. After the coil is rotated one quarter of a revolution to the position as shown below:

Rotated 90 degree

the coil sides have no flux to be cut and no voltage is generated. As the coil proceeds to rotate, the side of the coil on south pole S will cut the maximum flux on north pole N. Then, the side of the coil previously on north pole N will cut the maximum flux on south pole S. With this change in the polarity that are cut by the conductors, reversal in brush potential will occur. There are two important points that would like to emphasize in connection with the rotation of the coil of wire through a fixed magnetic field:

1. The voltage changes from instant to instant.
2. The electrical polarity (+) and minus (-) changes with alternating positions under north and south poles.

In actual, ac generator rotate a set of poles that is placed concentrically within a cylindrical core containing many coils of wires. However, a moving coil inside a pair of stationary poles applies equally well to the rotating poles construction; in both arrangements there is a relative motion of one element with respect to the other.

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Introduction to Alternating Current

Last time, we studied the first part of Learn Electrical Engineering for Beginners and this is all about DC Circuits. Today, we will be dealing with our Part 2 of our module and this is all about Alternating Current Circuits.

So, you may now start to learn what this ac is and how it behaves. Alternating Current does not flow through a conductor in the same direction as what dc does. Instead, it flows back and forth in the conductor at the regular interval, continually reversing its direction of flow and can do so very quickly. It is measured in amperes, just as dc is measured too. Remember, one couloumb of electrons is passing a given point in a conductor in one second. This definition also applies when ac is flowing- only now some of the electrons during that 1 second flow past the given point going in one direction, and the rest flow past it going in the opposite directions.

Difference between DC and AC

The industrial applications of alternating current are widespread. These include the many types of induction motor, ranging in size employed in wind tunnels and reclamation projects, transformer equipment used in connection with welders and many kinds of control devices, communication systems, and many others.

The advantages of ac generation are, however, apparent when it is recognized that it can be accomplished economically in large power plants where fuel and water are abundant. But nowadays, solar power is becoming popular as power plants through solar panels. Moreover, generators and associated equipment may be large, an important matter in so far as cost per kilowatt is concerned; also transmission over networks of high-voltage lines to distant load centers is entirely practicable.

Transmission Lines to distant load centers

In Part 2 of Learn Electrical Engineering for Beginners, you will study the nature, behavior and uses of time-varying or alternating current. You will study the for the first time two components - the inductor and the capacitor which are frequently used to control direct as well as alternating current and voltage. The resistors, in which we all know acted in such a way as to restrict the flow of current directly. In other words, the bigger the resistor you put in, the more you restrict the current flow. The inductor and the capacitor, on the other hand, act to control the current and voltage in different ways, and you will see that they do depends on how often the current is reversed. These three components - the resistor, inductor and the capacitor are basic elements of electric and electronic circuits.

Resistor, Capacitor and Inductor Behavior in AC Circuits

As of now, you will not understand the meaning of the behavior of the given diagram shown above. But as we started the first topic of AC Circuits on my next post, you will appreciate and understand gradually what really mean by AC Circuits.

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What is Electric Circuit? - Part 2

Before I proceed with our new topic for today, I just want to give thanks for those who are currently subscribed here in Learn Electrical Engineering for Beginners. I hope this will be a helpful site for you which I will always give a full and detail information for every subject matter.

Well, it's enough for my short introduction because I'm already running out of time for the updates. Yesterday I had mentioned on my previous post about our topic on full definition of Electric Circuits that I will going to differentiate between DC and AC Circuits. Please keep in mind that after discussing the difference between the two, I will going to discuss first to you all DC Circuits related topics so that we would not be confused. The principles that we will be discussing here in DC Circuits will also be used again when we touch AC Circuits. Please keep that in mind and this is very important. I just want to keep my ideas and discussions organize here in Electrical Engineering site. I was also trying to catch up the attention of those Electrical Engineering who study online as well as those non- electrical engineers.

Moving on...

Still remember on our review on Physics on my previous post in Voltage, Current, Power and Energy. I already give the definition of DC and AC Current. But for those recent readers, here is the short definition and which is almost the same when dealing with circuits.

In electricity, we deal both on direct current (DC) and alternating current (AC). In DC Circuits, the current always flows in the same or one direction. In AC Circuits, the direction of current flow reverses periodically- this means at one instant the current flow in one direction and in the next instant, in the opposite direction. Remember in our review? this flow reversal in AC current is usually done regularly. What does it mean? If we talk about 60Hz AC power, we mean that the direction of flow reverses 60 times ( or cycles) per second. Graphically, here are the difference for you to comprehend it well. ( You may click the image to enlarge)


Ohhh... before I forgot there are other types of current such as Exponential Current and Dumped Sinusoidal Current. But these are somewhat on the deeper concepts that we might be able to touch on our future discussion. But to give you an idea here are the graphical difference between the two. ( You may click the image to enlarge)



As what I had mentioned earlier, on the first part of the circuitry discussion we will deal with the function of direct current in circuits containing resistance (resistive circuits) and we will use Ohms Law and Kirchhoff's Laws as the tools for analysis and understanding the relationship between current, voltage and resistance. This will be your foundation for your future understanding of ac circuitry. Therefore, it is very important that you completely understand every concept I presented here in dc circuitry.

Continuing our understanding of Electric Circuit.

It may help you to grasp the concept of an electric current flowing through a closed circuit. Imagine that the electrons which make up the current form a moving stream which revolves through the complete circuit.

This moving streams of electrons maintains a constant density throughout its entire length. The number of electrons entering the positive terminal of a battery from a wire is always exactly balanced by the number of electrons which the battery forces to move its own negative terminal and out into the wire.

Therefore, there is no way either the conductor wire or the battery possess either more or less electrons in a complete circuit. If the circuit loop is broken, the electron orbiting stream instantly stops revolving through the circuit; but both wire and battery will still hold exactly same number of electrons as they did when the circuit was made. The only difference is that the wire is now holding some of the electrons which was previously in the battery. Likewise, the battery had taken an equal number from the wire.

The number of electrons in the electron stream is depends on the strength of the voltage applied forcing the electrons to move. The lower the voltage, the weaker.

I will just tell you this in advance that when a resistance of any kind is inserted into the circuit loop, it also restrict the number of electrons flowing therefore reduces the current. You will notice that in some of our applications when we touch different circuitry laws. The flow of current is restricted by this resistance.

Also keep in mind a closed loop of wire is not always an electric circuit. Remember that in our definition of Electric Circuits, I had mentioned there the 2 conditions that makes up an electric circuit. Current, voltage and resistance are present in any electric circuit where electrons move around the close loop. The pathway for current flow is actually the circuit, and its resistance controls the amount of current flow around the circuit.

DC circuits consists of a source of DC voltage, such as batteries plus the combined resistance of the electrical load connected across this voltage. While working with DC circuits, you will find out how the total loads can be changed with various combinations of resistances, and how these combination of resistances control the circuit current and affect the voltage. This concept will also be applied in AC circuitry.

There will be two types of circuits that we will be dealing with: these are series circuits and parallel circuits. No matter how complex the circuit is, still it can be simplified down into series connection to or a parallel circuit connection.

One last thing.

The Load

Previously on our last topic we had mentioned about the load in the electric circuit. So what the heck is the load? How does it works in the electric circuit?

In basic electric circuit the device that transforms the electrical energy from the source of power (emf) into some useful function -such as heat, light, mechanical power, etc.- is called the load. The load aside from transforming and electrical energy into some useful purposes, can be utilized to changed or control the amount of energy being delivered from the source.

A load could be a motor, a telephone, a lamp, a heater or some other appliances -( name it ). the term load means the electric power delivered by the source. If you don't get it, I will give you an example. When it is stated that the load is increased or decreased, it means that the source is delivering less or more power. Remember a load can be: a device which utilizes the power from the source and the power that is taken from the source.

One more last thing...

The Switches

I included this because this is one of the common part of electric circuitry either on DC or AC Circuitry. We have been using switches everyday and all our life. We could see it in our lamps, a radios, flahlights etc. It is a controlling device which open and close the circuit. There are many types of switches you will encounter in your study of Electrical Engineering. But this will be discussing separately when we touch practical applications in our course outline.

This is where it ends our topic discussing what an electric circuit is. On my succeeding post, we will now begin to study in detail the relationship between voltage, current and resistance.

Hope you appreciate this post today presenting it in my own little way. Learning is fun here in Electrical Engineering for Beginners.

Cheers!

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