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Thread: Household electrical sockets

  1. #1 Household electrical sockets 
    Forum Freshman ScubaDiver's Avatar
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    I am a freshman in EE. I have some questions about a standard 120VAC electrical socket.
    (some are labeled as 110vac though)
    I basic understanding of what is happening but I still have some questions.

    I want to understand everything that is happening at a deep level.

    My questions are basically these..
    1. It is truly a "sine wave"?

    Sometimes when signals are oscillatory and have a rounded shape people just start calling them sine waves even though they aren't.
    I would think that it would have to be a pure sine wave in order for other concepts like power factor to make sense, as power factor for a sinusoidal voltage is just the cosine of the phase difference between the voltage waveform and current waveform. If the voltage was just some arbitrary oscillating waveshape then things like power factor wouldn't make much sense.


    2. What is the significance of the RMS value?
    I do understand the following. A sinusoidal voltage will produce the same power dissipation as just having the rms voltage instead. (like if you short both across a resistor)

    Also, isn't the rms value higher than the AVERAGE value because of the power dissipation factor coming into play. I believe you can't just assume that a sine wave will produce the same amount of power as another voltage of the sine waves average value. This is because power dissipation really starts to take off when the voltage is near the peak of the sine wave (or when the current is highest), because the current is squared in the power term, so the rms value is needed to compensate for this, in a sense. (I hope that was clear)


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  3. #2  
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    Ask Harold.


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    1) yes it is a nearly pure sine wave, with just a little noise and higher harmonics.

    2) yes the rms value of an AC voltage is the DC voltage that will produce the same amount of power in a purely Ohmic (resistive) load. Yes you are right that the part of the sine wave near the maximum or minimum contributes most to AC power. The maths in the definition of rms takes care of that.

    For other loads, the effect of AC voltage and the "equivalent" DC voltage can be dramatically different.
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    Yep, what Leszek said. By the way, if you have a voltmeter, its a-c voltage readout probably just gives you .707 of the peak, and could be significantly off for non-sinusoidal voltages. A "true rms" voltmeter is a little more expensive.

    Here is how the voltage at your electrical outlet might not be a perfect sinusoid. Let's say you have a nice, clean, sinusoidal 120/240 voltage at the transformer feeding your house. The voltage at the outlet won't be exactly the same. There is a voltage drop through the wiring that is proportional to the current and the wiring impedance. Now, as long as your loads are linear, like resistance heaters or ordinary electrical motors, it's still sinusoidal, though reduced in voltage and possibly phase shifted. Nonlinear loads could cause a distortion, though. Things like the power supplies for electronic equipment would tend to do that.
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    One arrives at the .707 of peak RMS value by integrating under the sine curve,
    this magically gives .5 * sqroot of 2...
    and we all thought that pure math was too abstract for real engineering, eh?

    On the distortion produced by loads issue: I've never heard of this, it seems that it is more than noise? Can you elucidate a bit.

    thx
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  7. #6 Re: Household electrical sockets 
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    Quote Originally Posted by ScubaDiver
    I am a freshman in EE. I have some questions about a standard 120VAC electrical socket.
    (some are labeled as 110vac though)
    I basic understanding of what is happening but I still have some questions.

    I want to understand everything that is happening at a deep level.

    My questions are basically these..
    1. It is truly a "sine wave"?
    It is very close, and you will discover the reason if you take a class in rotating machinery.

    Quote Originally Posted by ScubaDiver
    Sometimes when signals are oscillatory and have a rounded shape people just start calling them sine waves even though they aren't.
    I would think that it would have to be a pure sine wave in order for other concepts like power factor to make sense, as power factor for a sinusoidal voltage is just the cosine of the phase difference between the voltage waveform and current waveform. If the voltage was just some arbitrary oscillating waveshape then things like power factor wouldn't make much sense.
    Nothing is a perfect sine wave. But what you get out of the wall is very very close. It is far from "just some artitrary oscillating waveshape."

    Power factors and phasor representations work extremely well, particulary in power engineering applications.

    When you have to consider the effects of noise on sensitive electronics, you may need to utilize a more precise description and look hard at transients. "Dirty" power can be an issue with some electronics, but it is just noise in terms of electric power, pun intended.


    [quote="ScubaDiver"]2. What is the significance of the RMS value?
    I do understand the following. A sinusoidal voltage will produce the same power dissipation as just having the rms voltage instead. (like if you short both across a resistor)

    Also, isn't the rms value higher than the AVERAGE value because of the power dissipation factor coming into play. I believe you can't just assume that a sine wave will produce the same amount of power as another voltage of the sine waves average value.[/tex]

    You clearly understand the mathematical definition of the rms value of a sinusoidal signa. No one has just assumed that a sine wave will produce the same amount of power as another voltage of the rms value.

    Once can PROVE that the average power dissipation of a sinusoidal signal is the product of the rms current, the rms voltage and the power factor. I am surprised that this was not done when the concept was introduced in class.


    Quote Originally Posted by ScubaDiver
    This is because power dissipation really starts to take off when the voltage is near the peak of the sine wave (or when the current is highest), because the current is squared in the power term, so the rms value is needed to compensate for this, in a sense. (I hope that was clear)
    You are arguiing intuitively. Try writing out the actual mathematical expressions, integrals and all and you will see that it works.

    The exact expression for power, of course is the amperage times the power drop. This is an instantaneous value. Now average that expression for a given load, and you will see that it becomes rms voltage*rms amperage * cosine of phase angle between them and that cosine term is the power factor.
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    Quote Originally Posted by schip666
    On the distortion produced by loads issue: I've never heard of this, it seems that it is more than noise? Can you elucidate a bit.

    thx
    It is a form of noise and sometimes referred to as harmonics. The general idea is that a periodic waveform can be represented by a number of superimposed sine waves of different frequency and amplitude called harmonics.
    There is a pretty good discussion of the topic here.
    http://ecmweb.com/mag/electric_effec...onics_power_2/
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    You are arguiing intuitively. Try writing out the actual mathematical expressions, integrals and all and you will see that it works.
    Once can PROVE that the average power dissipation of a sinusoidal signal is the product of the rms current, the rms voltage and the power factor. I am surprised that this was not done when the concept was introduced in class.
    I realize these things can be shown mathematically, (although I don't exactly know how yet) I just wanted to make sure my intuition was correct about why the average value is lower than rms value and things like that. I haven't taken any EE courses yet though.

    The wikipedia article for "rms" actually shows a lot of the math involved. I will look through it and try to get the math down so I can prove it to myself.
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    Harold: I'm still not entirely clear on the "harmonics" thing. Your ref'd article has a lot of information about what happens when there is harmonic "distortion" in the power feed, but starts out with this:

    Normally, current distortions produce voltage distortions. However, when there is a stiff sinusoidal voltage source (when there is a low impedance path from the power source, which has sufficient capacity so that loads placed upon it will not effect the voltage), one need not be concerned about current distortions producing voltage distortions.

    Examples of nonlinear loads are battery chargers, electronic ballasts, variable frequency drives, and switching mode power supplies. As nonlinear currents flow through a facility's electrical system and the distribution-transmission lines, additional voltage distortions are produced due to the impedance associated with the electrical network. Thus, as electrical power is generated, distributed, and utilized, voltage and current waveform distortions are produced.
    Which seems kind of equivocal on the subject of how and how much non-linear loads will distort the up-stream power feed. For inductive/capacitive loads I can understand a phase-shift but not harmonic generation. I suppose one can't assume nearly-zero impedance sources, so you might get distortion in a local distribution system?

    thanks again
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  11. #10  
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    The average value of a pure sine wave is zero.
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  12. #11  
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    Quote Originally Posted by schip666
    Harold: I'm still not entirely clear on the "harmonics" thing. Your ref'd article has a lot of information about what happens when there is harmonic "distortion" in the power feed, but starts out with this:

    Normally, current distortions produce voltage distortions. However, when there is a stiff sinusoidal voltage source (when there is a low impedance path from the power source, which has sufficient capacity so that loads placed upon it will not effect the voltage), one need not be concerned about current distortions producing voltage distortions.

    Examples of nonlinear loads are battery chargers, electronic ballasts, variable frequency drives, and switching mode power supplies. As nonlinear currents flow through a facility's electrical system and the distribution-transmission lines, additional voltage distortions are produced due to the impedance associated with the electrical network. Thus, as electrical power is generated, distributed, and utilized, voltage and current waveform distortions are produced.
    Which seems kind of equivocal on the subject of how and how much non-linear loads will distort the up-stream power feed. For inductive/capacitive loads I can understand a phase-shift but not harmonic generation. I suppose one can't assume nearly-zero impedance sources, so you might get distortion in a local distribution system?

    thanks again
    Linear circuits -- and the concept of impedance depends on linearity -- transform sinusoids to sinusoids.

    Nonlinear circuit elements can do almost anything. That should be expected since telling you that an element is nonlinear does not tell you what it is, only what it is not.

    You do not require zero or nearly-zero impedance to maintain sinusoidal signals, you only need linearity.

    The nonlinearity to which Harold is referring can come from inductive devices such as transformers which can operate with cores nearly saturated and therefore are not linear. When they operate in a linear range you do not get the distortion of sinusoids. There are other sources of noise and non-linearity as with arcing that might occur in a switch, or in malfunctioning equipment.
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    Quote Originally Posted by schip666
    Which seems kind of equivocal on the subject of how and how much non-linear loads will distort the up-stream power feed. For inductive/capacitive loads I can understand a phase-shift but not harmonic generation. I suppose one can't assume nearly-zero impedance sources, so you might get distortion in a local distribution system?

    thanks again
    How much really depends on the impedance of the distribution system, the location of the nonlinear loads, the current etc. How it works would be like this. Suppose you had a controller such as this:
    http://en.wikipedia.org/wiki/Phase_control
    which controls the power to a device by rapidly switching the circuit on at a certain point in the sine wave and off as the voltage crosses through zero. The current would not be a sine wave. Therefore any voltage drop due to this current, by Ohm's law, would have a shape like the chopped up current waveform. So if the voltage at the transformer starts out as a perfect 120 volt sinusoid, you would find the voltage at the receptacle where this device is plugged in, is not quite sinusoidal. It would be the algebraic sum of the 120 v sinusoid and the non-sinusoidal voltage drop.
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  14. #13  
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    Quote Originally Posted by Harold14370
    Quote Originally Posted by schip666
    Which seems kind of equivocal on the subject of how and how much non-linear loads will distort the up-stream power feed. For inductive/capacitive loads I can understand a phase-shift but not harmonic generation. I suppose one can't assume nearly-zero impedance sources, so you might get distortion in a local distribution system?

    thanks again
    How much really depends on the impedance of the distribution system, the location of the nonlinear loads, the current etc. How it works would be like this. Suppose you had a controller such as this:
    http://en.wikipedia.org/wiki/Phase_control
    which controls the power to a device by rapidly switching the circuit on at a certain point in the sine wave and off as the voltage crosses through zero. The current would not be a sine wave. Therefore any voltage drop due to this current, by Ohm's law, would have a shape like the chopped up current waveform. So if the voltage at the transformer starts out as a perfect 120 volt sinusoid, you would find the voltage at the receptacle where this device is plugged in, is not quite sinusoidal. It would be the algebraic sum of the 120 v sinusoid and the non-sinusoidal voltage drop.
    Once you depart from linearity or start sending in chopped signals, all bets are off. It may not be as simple as a 120v sinusoid plus something that looks like the original chopped signal. A linear circuit is basically a linear integro-differential operator. The thing that makes it preserve sinusoids is that dereivatives of sinusoids are sinusoids of the same frequency and sums of sinusoids of a single frequency are sinusoids again. If you start chopping and differentiating you get all kinds of stuff.

    You will get a sum of the 120v sinusoid and god knows what else. The god knows what else may win, particular if there is alot of capacitance or reactance in the system in the right (or wrong) configuration. To compensate one needs capacitance in a compensating configuration (a filter).
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    You're right, what I said would only be strictly true if the wiring was purely resistive. I suppose you could do a Fourier analysis to break the current waveform down into its constituent frequencies and solve it that way.
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    The average value of a pure sine wave is zero.
    I knew someone was going to say this. When I said average value earlier I just meant the average voltage in the positive direction. (which would also be the same as the average voltage in the negative direction.

    (I guess the rms value takes care of this confusion because you are squaring the numbers)

    The nonlinearity to which Harold is referring can come from inductive devices such as transformers which can operate with cores nearly saturated and therefore are not linear. When they operate in a linear range you do not get the distortion of sinusoids. There are other sources of noise and non-linearity as with arcing that might occur in a switch, or in malfunctioning equipment.
    Yeah, thats what I got from what he said. He was just trying to get me to realize that components that the electrical power must travel through before it gets to my house, such as a pole distribution transformer, may distort the waveforms even more, so by the time the "sine wave" gets to my house, its not a perfect sine wave anymore.
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    firstly...I think the distortion thing must necessarily be related to impedance as it would be "impossible" to couple a load non-linearity back into a zero impedance source. Of course there are no zero impedance sources, especially over "infinite" bandwidth, so one can expect some junk in the power feed. The treatment in the ECM article indicated that one might need to deal with a LOT of harmonic distortion which surprised me. I guess that's why I'm not a power distribution engineer, ne?

    secondly...On the sine averaging to zero thing. Well sure, everything eventually averages to zero -- or actually around 4 deg K -- but RMS has nothing to do with that. RMS is a measure of the effective power one can extract from an AC source, compared to the equivalent DC voltage on a resistive load. Since the common sink point is nominally at 0-volts the +/-ness of the instantaneous signal isn't really of interest (again, for resistive loads), so one can think of it as "full-wave-rectified" --where the negative going portion is "flipped-over" into the positive (or v-versa) -- and then take the integral of the waveform. That works for all waveforms, but most meters just assume a sine with no DC offset...
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    Schip666 is correct about the RMS (root mean square) value. If I recall, it's something like 0.636 rather 0.707. Wiki has a good writeup on it:

    Root Mean Square

    What I haven't noticed in this discussion is why AC power is used to begin with or why it is three-phase.

    AC is used because it is then easily "stepped up" through a transformer for carrying it several miles and "stepped down" to the consumer voltage. This wasn't available for the commercial market when electricity use was beginning fr DC, and is still impractical for the consumers at large. The reason why we need several thousands of volts to carry power from the generation source to consumer has to do with resistive loss.

    Three phase power is used because AC power is a sine wave. If you add three sine waves that are 120 degrees apart, the net result is zero. Magnetic vibrations, etc. cancel each other out. Makes for a very smooth transition of power. Even automobile alternators use three phase power, and a six diode full wave rectifier to create the DC power. In our homes, a single phase is used through a step down transformer. We get two hot wires and a neutral, to give us the 120 volts for most uses, and the 240 volts for heating, dryer, range, etc.

    As for 110volt/120 volt... Minor variations don't matter. You'll often find incandescent lamps marked at 130 volts.
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    Quote Originally Posted by Wild Cobra
    Schip666 is correct about the RMS (root mean square) value. If I recall, it's something like 0.636 rather 0.707. Wiki has a good writeup on it:

    Root Mean Square

    What I haven't noticed in this discussion is why AC power is used to begin with or why it is three-phase.

    AC is used because it is then easily "stepped up" through a transformer for carrying it several miles and "stepped down" to the consumer voltage. This wasn't available for the commercial market when electricity use was beginning fr DC, and is still impractical for the consumers at large. The reason why we need several thousands of volts to carry power from the generation source to consumer has to do with resistive loss.

    Three phase power is used because AC power is a sine wave. If you add three sine waves that are 120 degrees apart, the net result is zero. Magnetic vibrations, etc. cancel each other out. Makes for a very smooth transition of power. Even automobile alternators use three phase power, and a six diode full wave rectifier to create the DC power. In our homes, a single phase is used through a step down transformer. We get two hot wires and a neutral, to give us the 120 volts for most uses, and the 240 volts for heating, dryer, range, etc.

    As for 110volt/120 volt... Minor variations don't matter. You'll often find incandescent lamps marked at 130 volts.
    Three phase is used because you can create a rotating magnetic field with 3-phase power which is what makes large electric motors work. Smaller motors use a capacitor to create a 2-phase rotating field that works, but not as well. It is equally useful on the generating end, and permits the use of synchronous rotating machines, both generators and motors.
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    Quote Originally Posted by Wild Cobra
    Schip666 is correct about the RMS (root mean square) value. If I recall, it's something like 0.636 rather 0.707. Wiki has a good writeup on it:

    Root Mean Square
    I don't know where you are getting 0.636. The link you provided says its the amplitude divided by square root of 2, and that's .707.
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    Schip666 is correct about the RMS (root mean square) value. If I recall, it's something like 0.636 rather 0.707.
    I don't know where you are getting 0.636. The link you provided says its the amplitude divided by square root of 2, and that's .707.
    Whew...for a moment there I thought I had forgotten everything...
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    AC is used because it is then easily "stepped up" through a transformer for carrying it several miles and "stepped down" to the consumer voltage.
    Yes, but you left off the part about why its so important to step it up. As far as I know, the reason why it is stepped up is to cut down on the losses in the wires. (If they double the voltage and cut the current in half then its still the same amount of power)

    So just the simple act of cutting the current in half for power transmission would cut the heat losses in the wires by 75%.

    About the thing for RMS. I always thought that was just an approximation. Like if your peak voltage was 170 then you would divide by the square root of two to roughly figure out the rms voltage.
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    Quote Originally Posted by ScubaDiver

    About the thing for RMS. I always thought that was just an approximation. Like if your peak voltage was 170 then you would divide by the square root of two to roughly figure out the rms voltage.
    No it is not an approximation, at least for truly sinusoidal signals. It is an exact relationship that comes from doing the relevant mathematics. See any introductory textbook on circuit analysis.
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  24. #23  
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    Quote Originally Posted by Wild Cobra
    In our homes, a single phase is used through a step down transformer. We get two hot wires and a neutral, to give us the 120 volts for most uses, and the 240 volts for heating, dryer, range, etc.
    In which country?
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    Quote Originally Posted by Leszek Luchowski
    Quote Originally Posted by Wild Cobra
    In our homes, a single phase is used through a step down transformer. We get two hot wires and a neutral, to give us the 120 volts for most uses, and the 240 volts for heating, dryer, range, etc.
    In which country?
    It's that way in the USA.
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