This amplitude measurement is known simply as the average value of the waveform. If we average all the points on the waveform algebraically that is, to consider their sign , either positive or negative , the average value for most waveforms is technically zero, because all the positive points cancel out all the negative points over a full cycle:.
In other words, we calculate the practical average value of the waveform by considering all points on the wave as positive quantities, as if the waveform looked like this:. Conversely, polarity-sensitive meter movements vibrate uselessly if exposed to AC voltage or current, their needles oscillating rapidly about the zero mark, indicating the true algebraic average value of zero for a symmetrical waveform. Although the mathematics of such an amplitude measurement might not be straightforward, the utility of it is.
Consider a bandsaw and a jigsaw, two pieces of modern woodworking equipment. Both types of saws cut with a thin, toothed, motor-powered metal blade to cut wood. But while the bandsaw uses a continuous motion of the blade to cut, the jigsaw uses a back-and-forth motion. The comparison of alternating current AC to direct current DC may be likened to the comparison of these two saw types:.
The problem of trying to describe the changing quantities of AC voltage or current in a single, aggregate measurement is also present in this saw analogy: how might we express the speed of a jigsaw blade? A bandsaw blade moves with a constant speed, similar to the way DC voltage pushes or DC current moves with a constant magnitude. A jigsaw blade, on the other hand, moves back and forth, its blade speed constantly changing. What is more, the back-and-forth motion of any two jigsaws may not be of the same type, depending on the mechanical design of the saws.
One jigsaw might move its blade with a sine-wave motion, while another with a triangle-wave motion. To rate a jigsaw based on its peak blade speed would be quite misleading when comparing one jigsaw to another or a jigsaw with a bandsaw! Despite the fact that these different saws move their blades in different manners, they are equal in one respect: they all cut wood, and a quantitative comparison of this common function can serve as a common basis for which to rate blade speed.
Picture a jigsaw and bandsaw side-by-side, equipped with identical blades same tooth pitch, angle, etc. We might say that the two saws were equivalent or equal in their cutting capacity. More specifically, we would denote its voltage value as being 10 volts RMS. RMS amplitude measurement is the best way to relate AC quantities to DC quantities, or other AC quantities of differing waveform shapes, when dealing with measurements of electric power.
For other considerations, peak or peak-to-peak measurements may be the best to employ. For instance, when determining the proper size of wire ampacity to conduct electric power from a source to a load, RMS current measurement is the best to use, because the principal concern with current is overheating of the wire, which is a function of power dissipation caused by current through the resistance of the wire.
Peak and peak-to-peak measurements are best performed with an oscilloscope, which can capture the crests of the waveform with a high degree of accuracy due to the fast action of the cathode-ray-tube in response to changes in voltage.
Because the mechanical inertia and dampening effects of an electromechanical meter movement makes the deflection of the needle naturally proportional to the average value of the AC, not the true RMS value, analog meters must be specifically calibrated or mis-calibrated, depending on how you look at it to indicate voltage or current in RMS units.
The accuracy of this calibration depends on an assumed waveshape, usually a sine wave. Electronic meters specifically designed for RMS measurement are best for the task. Some instrument manufacturers have designed ingenious methods for determining the RMS value of any waveform.
The heating effect of that resistance element is measured thermally to give a true RMS value with no mathematical calculations whatsoever, just the laws of physics in action in fulfillment of the definition of RMS. The accuracy of this type of RMS measurement is independent of waveshape. In addition to RMS, average, peak crest , and peak-to-peak measures of an AC waveform, there are ratios expressing the proportionality between some of these fundamental measurements.
The crest factor of an AC waveform, for instance, is the ratio of its peak crest value divided by its RMS value. Square-shaped waveforms always have crest and form factors equal to 1, since the peak is the same as the RMS and average values. Sinusoidal waveforms have an RMS value of 0. Triangle- and sawtooth-shaped waveforms have RMS values of 0. Bear in mind that the conversion constants shown here for peak, RMS, and average amplitudes of sine waves, square waves, and triangle waves hold true only for pure forms of these waveshapes.
The RMS and average values of distorted waveshapes are not related by the same ratios:. Since the sine-wave shape is most common in electrical measurements, it is the waveshape assumed for analog meter calibration, and the small multiple used in the calibration of the meter is 1. Any waveshape other than a pure sine wave will have a different ratio of RMS and average values, and thus a meter calibrated for sine-wave voltage or current will not indicate true RMS when reading a non-sinusoidal wave.
Depicted above, is a very simple AC circuit. One such concern is the size and cost of wiring necessary to deliver power from the AC source to the load. However, in the real world, it can be a major concern. If we give the source in the above circuit a voltage value and also give power dissipation values to the two load resistors, we can determine the wiring needs for this particular circuit:.
As a practical matter, the wiring for the 20 kW loads at Vac is rather substantial A. From the example above, Bear in mind that copper is not cheap either! It would be in our best interest to find ways to minimize such costs if we were designing a power system with long conductor lengths.
One way to do this would be to increase the voltage of the power source and use loads built to dissipate 10 kW each at this higher voltage.
The loads, of course, would have to have greater resistance values to dissipate the same power as before 10 kW each at a greater voltage than before. The advantage would be less current required, permitting the use of smaller, lighter, and cheaper wire:. Now our total circuit current is This is a considerable reduction in system cost with no degradation in performance.
This is why power distribution system designers elect to transmit electric power using very high voltages many thousands of volts : to capitalize on the savings realized by the use of smaller, lighter, cheaper wire. However, this solution is not without disadvantages. Another practical concern with power circuits is the danger of electric shock from high voltages.
Again, this is not usually the sort of thing we concentrate on while learning about the laws of electricity, but it is a very valid concern in the real world, especially when large amounts of power are being dealt with.
The gain in efficiency realized by stepping up the circuit voltage presents us with an increased danger of electric shock. Power distribution companies tackle this problem by stringing their power lines along high poles or towers and insulating the lines from the supporting structures with large, porcelain insulators.
At the point of use the electric power customer , there is still the issue of what voltage to use for powering loads. High voltage gives greater system efficiency by means of reduced conductor current, but it might not always be practical to keep power wiring out of reach at the point of use the way it can be elevated out of reach in distribution systems.
This tradeoff between efficiency and danger is one that European power system designers have decided to risk, all their households and appliances operating at a nominal voltage of volts instead of volts as it is in North America. That is why tourists from America visiting Europe must carry small step-down transformers for their portable appliances, to step the VAC volts AC power down to a more suitable VAC. Is there any way to realize the advantages of both increased efficiency and reduced safety hazard at the same time?
One solution would be to install step-down transformers at the end-point of power use, just as the American tourist must do while in Europe. However, this would be expensive and inconvenient for anything but very small loads where the transformers can be built cheaply or very large loads where the expense of thick copper wires would exceed the expense of a transformer.
An alternative solution would be to use a higher voltage supply to provide power to two lower voltage loads in series. This approach combines the efficiency of a high-voltage system with the safety of a low-voltage system:. The current through each load is the same as it was in the simple volt circuit, but the currents are not additive because the loads are in series rather than parallel. The voltage across each load is only volts, not , so the safety factor is better.
Mind you, we still have a full volts across the power system wires, but each load is operating at a reduced voltage. If anyone is going to get shocked, the odds are that it will be from coming into contact with the conductors of a particular load rather than from contact across the main wires of a power system. Being a series circuit, if either load were to open, the current would stop in the other load as well.
For this reason, we need to modify the design a bit:. Split-phase Power System. Instead of a single volt power supply, we use two volt supplies in phase with each other! This is called a split-phase power system. The astute observer will note that the neutral wire only has to carry the difference of current between the two loads back to the source. Notice how the neutral wire is connected to earth ground at the power supply end. An essential component of a split-phase power system is the dual AC voltage source.
Fortunately, designing and building one is not difficult. Since most AC systems receive their power from a step-down transformer anyway stepping voltage down from high distribution levels to a user-level voltage like or , that transformer can be built with a center-tapped secondary winding:. If the AC power comes directly from a generator alternator , the coils can be similarly center-tapped for the same effect. The extra expense to include a center-tap connection in a transformer or alternator winding is minimal.
If not for these polarity markings, phase relations between multiple AC sources might be very confusing. Why am I taking the time to elaborate on polarity marks and phase angles?
It will make more sense in the next section! In a more general sense, this kind of AC power supply is called single phase because both voltage waveforms are in phase, or in step, with each other. Apologies for the long introduction leading up to the title-topic of this chapter. The advantages of polyphase power systems are more obvious if one first has a good understanding of single-phase systems. Things start to get complicated when we need to relate two or more AC voltages or currents that are out of step with each other.
The graph in figure below illustrates an example of this. The two waves shown above A versus B are of the same amplitude and frequency, but they are out of step with each other. Log in. For a better experience, please enable JavaScript in your browser before proceeding. You are using an out of date browser. It may not display this or other websites correctly.
You should upgrade or use an alternative browser. Positive or Negative Alternation of the sine wave developed across the load. Thread starter lbmcse Start date Jun 24, Location USA. Hello everyone. This is my first post, and is a question that has plagued me from the days when I was a first year apprentice, until now, 13 years later. See the photo below. Well, I thought it would be bigger, but here goes.
I understand fwd. What I have never quite grasped, is what is the reason on these two half-wave rectifiers--that the left one develops only the negative alternation across the load, while the right figure does the opposite? I realize that in both, the cathode is negative with respect to the anode the definition of fwd.
If I could get this answered, my kingdom is yours. Not much in the way of jewels and binoculars, but boy do I feel like an ass.
Thank you. Location NE Nebraska. View attachment Well, I thought it would be bigger, but here goes. Click to expand Carultch Senior Member. Location Massachusetts. Gentlemen, thanks for the replies. I understand why and how, holes and electrons, depletion regions widening, narrowing, and the implications of both--and the check valve analogy is a familiar one. See the very small pulsed DC representation on the upper right of each diagram?
You could determine the average value by adding together a series of instantaneous values of the alternation between 0 and , and then dividing the sum by the number of instantaneous values used. The computation would show that one alternation of a sine wave has an average value equal to 0. The formula for a verage voltage is. Similarly, the formula for average current is. Do not confuse the above definition of an average value with that of the average value of a complete cycle.
Because the voltage is positive during one alternation and negative during the other alternation, the average value of the voltage values occurring during the complete cycle is zero. Custom Search.
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