Chapter One, alternating current. In a previous course called basic electrical theory, we were looking at DC circuits that is where the voltages and currents are for the most part constant at least as far as the supplied sources are concerned. We are now going into the realms of AC circuits where voltages and currents are not constant but changing rapidly. In our system in North America, it's changing 60 times a second, at least as far as the supplied sources are concerned with AC or alternating current is possible to build electrical generators, motors and power distribution systems that are far more efficient than DC systems. And so we find AC use predominantly across the world in high power Applications and the diagram in front of you here kind of illustrates the comparison between AC and DC the circuit on the left is switched to DC which is indicated by a battery, the the yellow dots circulating in a counterclockwise direction are indicating electrons and the arrows are pointing to the electron flow.

We we know in from our previous study that that is the flow of electrons, but convention says the current flow the adopted conventional current flow is the clockwise direction with the battery. In the case of the circuit on the right where we've switched to AC and and the generator is an AC or an alternating current generator the you can see Electrons are shifting back and forth as well as the flow is going back and forth. And that is happening in a 60 hertz sec system 60 times a second. If a machine is constructed to rotate a magnetic field around a set of stationary wire coils with a turning of the shaft, AC voltage will be produced across the coils of that shaft in accordance with Faraday's law of electromagnetic induction, which we are introduced in our previous course, this is the basic operating principle of an AC generator.

Ac generators are sometimes also referred to as alternators. There is effect of electromagnetism known as mutual inductance, whereby two or more coils of wire are placed so that the changing magnetic field created by one induces a voltage in the other. If we have two mutually inductive coils and we energize one coil with AC, we will create AC voltage in the other coil. When used as such, this device is known as a transformer. The fundamental significance of a transformer is its ability to step voltages down or to step it up from the powered coils to the unpowered coils. The AC voltage induced in an unpowered secondary coil is equal to the AC voltage across the powered or primary coil multiplied by the ratio of the secondary coil turns to the primary coil.

Turns. The Transformers ability to step AC voltages up or down with ease gives AC an advantage unmatched by DC in the realms of power distribution. When transmitting electrical power over long distances, it is far more efficient to do so, with stepped up voltages and step down currents, then step the voltages back down, and the current back up for industry and businesses or consumer use. The advantage here is you can use smaller diameter wire for transmission, with less resistive power losses. transformer technology has made long range electrical power distribution practical, without the ability to efficiently step voltages up and down. It would be cost prohibitive to construct power systems for anything but close range.

As useful as transformers are they only work with a story Not DC because the phenomenon of mutual inductance relies on changing magnetic fields. A direct current DC can only produce steady magnetic fields, Transformers simply will not work with direct current, the alternating current or AC power, AC voltages and it seems like a misnomer to call a voltage alternating current or AC voltages but there there is a tendency to refer to anything in regard to producing alternating current as a seat. So, anyway, it's going to be helpful to understand what these AC quantities look like and generators of AC quantities or AC power Ultimately, AC voltage and AC current are designed in a special way such that the voltages the open circuit voltage is produced by these AC generators and the current follow what is known as a sinusoidal wave form. And sinusoidal wave forms lend themselves to trigonometric functions that help in the analysis of AC circuits.

So, we're going to look at the structure of AC voltages and AC current now, and they are referred to as sinusoidal waves. We are then going to look at what those AC quantities mean in terms of the power they're capable of producing and we're going to define a term Relative to these sinusoidal waveforms, called RMS values and RMS stands for root mean square, but we'll get into the explanation that in a few slides. As I said before, an alternator is designed to produce AC voltage in this specific shape over time, the voltage switches polarity over time but does so in a very practical manner. When graphed over time, the wave traced by the voltage of alternating polarity from an alternator takes on a distinct shape known as a sine wave, or we can describe the wave form as sinusoidal. In the voltage plot, from the electromechanical alternator, the change from one polarity to the other is a smooth one.

The voltage level changes most rapidly at the zero point or The crossover and most slowly at either of the peaks. Because this is repetitive we describe the wave form in terms of cycles where one cycle is made up of 360 degrees. Here we have plotted a sinusoidal wave form over time. And that wave form varies over time, but what we're doing is taking a snapshot of it right now, if, if you could visualize that, and we're going to state that the sine wave begins at zero degrees, and it starts as rice. So zero degrees is the beginning of the cycle of the wave could be voltage or current, and the voltage or current at this point is zero. 90 degrees, which is a quarter of the wave way through the wave form.

The voltage or current is at a maximum. And for convenience purposes, we're saying it is one at 180 degrees through the cycle, the wave form, comes back down and goes through its crossover point. And at that point it the wave with voltage or current is zero. Once again, at 270 degrees, the waveform voltage occurred is at a negative maximum. And at 360 degrees, we've gone through one complete cycle. And essentially we're going to start all over again so the angle is 360, or zero degrees.

And we are once again Back at zero. If we were to follow the changing voltage produced by a coil of an alternator from any point on the sine wave graph to that point where the sine wave shape begins to repeat itself, we would have marked exactly one cycle of that wave. This is most easily shown by spanning the distance between identical peaks, but maybe measured between any corresponding points on the graph. The degree marks on the horizontal axis of the graph represents the domain of the trigonometric sine function and also the angular position of a simple two pole alternator shaft as it rotates and produces CAC quantity. Since the horizontal axis of this graph, can mark the passage of time as well as shaft position in degrees. The dimensions marked for one cycle is often measured in units of time, most often seconds or fractions of a second.

When we expressed as a met when expressed as a measure of as a measurement, this is often called the period of a wave, the period of a wave in degrees is all always 360 degrees. But the amount of time one period occupies Of course depends on the rate voltage oscillates back and forth. A more popular measure for describing the alternating rate of an AC voltage or current wave, then period is the rate Have that back and forth oscillation. This is called frequency. The modern unit for frequency is the Hertz, or abbreviated h Zed, which represents the number of wave cycles completed during one second of time. In North America the standard powerline frequency as I said before is 60 hertz, meaning that the AC voltage often oscillates at a rate of 60 complete back and forth cycles every second.

In Europe where the power system frequency is 50 hertz, the AC voltage only completes 50 cycles every second. a radio station transmitter broadcasting at a frequency of 100 megahertz generates an AC voltage for transmission, oscillating at the rate of 100 million cycles every second. Prior to the canonization of the Hertz unit frequency was simply expressed as cycles per second older meters and electronic equipment often bore frequency units of CPS or cycles per second instead of hertz. period and frequency are mathematical reciprocals of one another that is to say, if a sine wave has a period of 10 seconds its frequency will be point one hertz or one 10th of a cycle per second frequency in hertz equals one over the period in seconds. We encounter a measurement problem if we try to express how large or how small an AC quantity is, with DC or quantities of voltage and current are generally constant.

We have little trouble expressing how much voltage or current we have in any part of the circuit. But how do you grant a single measurement magnitude of something that is constantly changing. One way is to express the intensity or the magnitude also called amplitude of an AC quantity is to measure its peak height on a waveform graph. This is also known as the peak or crest value of an AC wave for another way is to measure the total height between the opposite peaks. This is known as peak to peak measurement or P to P value of an AC wave form. Another way of expressing the magnitude of a wave is to mathematically average the value of all the points on the waveform graph to a single aggregate number.

This amplitude measurement is known simply as the average value of the wave form. If we average all the points on the wave form algebraic algebraically that is to consider their signs either positive or negative, the average value of most wave forms is technically zero, because all the positive points cancel out all the negative points over a full cycle. However, a practical measure of a waveforms aggregate value average is usually defined as the mathematical mean of all the points, absolute values over a cycle. In other words, we calculate the practical average value of a waveform by considering all the points in the waveform as positive quantities. As if the waveform looked like this. The average value would then have some value other than zero, that would be related to the intensity of the wave.

So far, we have looked at three ways that we can measure the intensity of an AC wave form, whether that be current or voltage, we can simply measure the peak or the crest or the amplitude of that wave. Or we can measure a quantity that is peak to peak or we can take the mean average as a quantity that measures the intensity of the AC wave. The good news is really, these are all related to each other in a way they can be just scaled one to the other. In other words, they very directly as each other So, one can be converted to the other by simply multiplying by a scaling factor. The thing or the trick we have to know is which one we're dealing with With so that we can make that conversion or we can deal with the actual measurement and it can be useful to us.

As we communicate the value of voltage and current with others in the industry of electrical power, as well as their related quantities of power energy ratings in different elements, we have to ask ourselves how useful are using any of these terms? And is there some way of measuring the values? That is the most useful way? The question was asked, asked and answered a long time ago and the answer was the RMS value before just jumping to the definition of RMS, which by the way is mathematically related proportionally to the other ways of describing the waves such as amplitude peak to peak average and mean average. Let's go through the logical steps of getting there. Starting with two simple circuits, one DC, one AC that is each with the same load, but one driven by DC source and the other driven by an AC source.

When we close the switch on the DC circuit, the Bobo light with an intensity that is dependent on the resistance are Savelle of the light and the DC current. Now, let's close the switch and adjust the AC current To the light bulb with the same intensity that is to say, both loads, both lights consume the same average power. So we now ask ourselves, what is that AC current, we can come to the conclusion that if the two bulbs light to the same brand of brightness, that is they draw the same amount of power, and it is reasonable to consider the current ay ay ay ay c to be, in some ways equivalent to the current IDC. So what is that value of AC? It would be useful if there was some meaningful way to calculate it. So let's go there.

If an AC supply is connected, A component of resistance say are the instantaneous power dissipated is given by the power equation I squared R. If we plot i squared, the instantaneous current, which itself is a sine wave, it is always positive because plus i times plus i is positive and negative i times negative i is positive, it does go to zero, but never negative. Remember that the instantaneous power dissipated is given by the equation power equals i squared R. The peak or maximum value of i squared is showing here and labeled i squared max The mean or average value of i squared is i squared max divided by two. So the average value of power is we'll call it P subscript AV is equal to IMAX squared over two times r subscript L. We just saw from the previous slide that the average power consumed in the circuit is given by this equation, which is equal to the maximum value of the current squared over two times the resistor.

Let's define Current then with that when use to calculate power gives us the average power. In other words, when that current, let's call it I with a subscript the fine for now is squared and multiplied by RL gives us the average power. But the defined our Id find squared is also equal to IMAX squared over two. Therefore, the square root of the mean current equals that define current. So we just discovered that what the value of I defined is it's equal to IMAX divided by root two and we call this current I RMS or root mean square and it is 0.707 the value of the maximum current. This is another more useful way to describe AC quantities voltage and current.

And of course it can be converted directly to amplitude peak or peak to peak or average just by multiplying by a scaling factor. However, we use RMS values for current and voltage, we can directly calculate the average power from these root mean square quantities. The RMS value of an AC supply is equal to the direct current which would dissipate the energy at the same time rate of a given resistor. We can use the same logic to define the RMS value of the voltage of an alternating voltage supply v rms is equal to the peak voltage divided by root two, where V is the maximum or peak value of the voltage. So, we have a way of calculating the RMS values of both current and voltage from the respective peak values. So, we have a way of calculating the average power consumed by a resistor or resistance in a circuit using RMS values for voltages.

And four currents. And all of the other power equations using just current and resistance and or voltage and resistance would still hold true do the due to the linearity property, we are only multiplying by a scaling factor. So we can always calculate the average power used by AC currents and voltages with resistors. Also ohms laws still holds true because of the linearity properties. And all of the other things that we do with resistors. Using AC voltages and currents still hold true.

We still calculate series loads the same parallel loads the same, we can still analyze mesh equations Current shots, voltage and current law still holds true. superposition, Thevenin, Norton, and source transformation all hold true. Remember that we have to so far only use resistors in the subsequent chapters and we're going to go on to see how we use impedances rather than just resistors. But that's further down the road. For now, all of these things still hold true. This ends chapter one