Intro to AC Circuits using Phasors and RMS Voltage and Current | Doc Physics

okay everything we've done in electricity so far has been leading to this point we are now going to discuss AC circuits so this was the big battle between Edison and Tesla Edison favored the DC circuit where it's all very simple you make electrons go this direction and the current goes this direction and nothing's weird and Tesla said no let's have it go this way in the net line this one that wind and this wind and that way sloshing back and forth and as you can see Tesla one out for household distribution and there are a lot of reasons for that one of them is the idea of transformers one of them we'll talk about in a little bit but transformers work require constantly changing flux so if you've got it constantly changing flux a consistently changing flux right there then you can make a transformer this is the simplest one right you just put two coils near each other and you have them share a flux like I've got a soft magnetic material in here and then any any flux change in one is the same as the flux change and the other so you can make voltages dramatically change and converting from one voltage to another is a really practical thing so this is one of the reasons that AC went out and the other one is for a later time for us to discuss but with AC we take this definition we say that the voltage as a function of time is the maximum voltage I don't care what it is but it's going to be multiplied by a sine function and it's of course going to be the sine of Omega times T that's going to be in radians per second so be careful we're going to be taking the sine of something in radians and that gives us a graph of let me get you the v-max this is voltage and this is time and it's going to start out here and go like that so if the voltage is doing that then this level right here would be the max if the voltage is doing that and you've just got a simple resistor like I don't know a hot plate or a toaster or something then the current will be doing in fact exactly the same thing the current will be changing as a function of time this is how hard you're pushing and this is the way the system responds so it's kind of like a stress-strain relationship again and you're going to have well certainly you won't have the same value but will expect the zeros to line up and we'll expect it to have the same structural performance here this is current as a function of time and this is I max right here and we've still got all of our favorite relationships like V is I R but all of these become a function of time you assume that the resistance doesn't change with time but if the voltage is going up and down then the current is similarly going up and down so inside of my hot plate I actually have current going this direction and then that direction in this direction in that direction clockwise and counter clockwise and in the United States it changes 60 times every second it's going forward and back 60 times in every single second and in Europe and India shout out to India I think they've got 50 times every second that it switches direction and so if if ooh look at this look at this what if we say what which we try to find out what v-max is no let's not try to find out with the axes let's just say that current as a function of time is going to be well I guess it'll be V as a function of time divided by R so it's v-max over R times the same sine function sine of Omega times T and now it's time to introduce a really neat concept these things are called phasers and a phaser looks like this first you get yourself a coordinate system and I'm just going to define X here and Y here and a phasor is a vector a phasor simply put is just a vector and the vector is continuously spinning around the origin that's the definition of a phasor and this phasor I'm going to say is v-max long that's how long it is and I want to say that the projection projection of phaser on y-axis is instantaneous value it helps to look at simulations of these at this point because I'm not going to be able to rotate that vector around there but if you know that that sucker is rotating and I guess we need to label some of these angles this angle is going to be Omega times T because well that's what's happening here we initially have a y component a Y projection of zero and it goes to a Y projection of V Max and it takes the time the time that it takes to do one quarter of a revolution gets us up to right here because that's a quarter wave right and then as it goes around it goes back to zero again yeah that's right here this maybe I can draw you some lines that correspond to various points when yeah yeah I can do that I can show you the phasor in its orientation so here the phasor is directly up here the phasor is directly to the left here the phasor is directly down here the phasers directly to the right now it doesn't matter whether it's left or right at this point but but whether it's up or down tells us whether we have a positive or a negative projection of the vector so we can put little tick marks all along here and sort of acknowledge that it's these points that we're getting maximum or zero values for our voltage but remember I said that the current is doing the same thing but of course it's it's V Max divided by R so I don't know what R is but I can draw you a similar phasor maybe right next to that other phasor it actually should be right on top of it and this phasor is length right here is V Max over R and V Max over R defines IMAX so in a similar way at each of these tick mark times I can say that we have the same orientation for the IMAX vector what that means is when there is a maximum current there is a maximum voltage and vice versa because those guys oh you got language for this these guys are said to be in phase they're said to be in phase because the phasers line up with each other so that means if one change is the other changes and they have the same time dependence uh-huh uh-huh now let's think about the definition of well I don't like the changing all the time I would like a value to describe what it actually is and I'm going to use a value called average the problem is the app what's the average of this graph well let's see it spends half its time up and half its time down the average of that graph over one full rotation nothing and the average of that over a next rotation nothing so the average isn't going to help us at all but what if we square it do you know what the square of the sign function looks like square the sine functions like so that's time and that's voltage for instance but it's voltage squared and so voltage squared is uh let's look at that it would be v-max squared times sine square of Omega times T so these squared still depends on time but what if I take the average of that now take mean and if I take the mean of that sucker right there I'm going to say the squared averaged no I can't average in then square because then it just gets zero but if I take the square and then average it then I'm looking for this value right here what do you think that is you see this value up at the top this top value is what that top value is simply Vmax square right that's what it means the squared max is v-max squared so that's fine but these squared averaged is just half that big look at it isn't it half that big of course it's half that big it's symmetric around the halfway point so this is one half now careful I'm going to write 1/2 v-max squared ok all right now here's my next plan my next plan is to take the square root of this business right here so I'm going to say V squared averaged and then screwed it is well the screwed of that business right there so this is 1 over screw 2 times V Max oh that's a lovely conclusion Wow turns out that every excuse me huh every relationship where you've got a sign has the same functionality right here if you square it and then average it and then screwed it you will get 1 over root 2 of the maximum value of that function that's really lovely so I can say in a general sense this will work for current and it will work for well frankly anything that is changing sinusoidal e or cosinusoidal e I take any variable and I square it and I average the square and I screwed it and this is 1 over root 2 times the maximum value of that variable and this thing right here this squaring and then meaning and screwing is called the RMS value stands for root mean squared because I'm taking the root and I'm taking the mean and I'm squaring it not in that order though I'm square mean rooting it but it's called root mean square so you have to get used to that and this is just whatever the maximum value of that sucker is divided by root 2 so let's let's say a couple things and then I'll make some some shout outs to you there's um Wow well there's power right and you know that power in a resistor like my hot plate power is I score times R and if power is I squared times R then it's simply going to be I max square times R oh and then there's this sine square of Omega T but that you see this works instantaneously this is the power at any instant but the voltage and the current are changing sinusoidally so at these instants right here the power delivered by the circuit to my resistor is actually zero and here this is huge power and this is also huge power doesn't matter that the currents going the other direction in a resistor it's going to heat up either way huge power huge power no power no power no power no power this is another advantage of decent of AC / DC actually even though it seems like it just makes it more complicated it makes it really lovely so this is true instantaneously but I can tell you another equation like power average equals current RMS square times R and so that means wait a second the average power wait if I take I RMS this thing right here and I square it I'm going to get I square wait a second that's IMAX square times R divided by 2 into resting alright and this is true at any time this doesn't have any time dependence because I'm looking for average the beautiful thing is we've had all this complication and we get back all of our standard equations power is I V as long as I use RMS RMS I'm still good I can find the average power and I get power is I squared times R if I use ms current and then I will get average power and we can also say that power is v square over R if you use RMS voltage then you'll get average power yeah everything we knew already oh and also V is IR it's true that this is true instantaneously but also the RMS voltage is the RMS current times the resistance of our resistor yay we got everything back now the only oh shoot this right here average power this right here I squared max times R is maximum power so the maximum power divided by 2 is the average power because power depends on the square of the current function or depending on how you look at it I guess it depends on the square of the voltage function so you've sometimes got zero power and you sometimes got maximum power but your average power is right smack in the middle of the average and the maximum and that makes sense I think so let's look at just one example of this beautiful equation here the RMS voltage in fact us says that V RMS is uh what do they say they say the RMS voltage is 120 volts from my electrical supplier and I know that the RMS voltage is the maximum voltage divided by the scroot of 2 so I can find that the maximum voltage is Oh what do you get 170 volts or so whoa so they've been telling me it's 120 volts but really it's 170 no it's 170 some of the time here's voltage as a function of time and it's making this sine graph the maximum value is 170 but the RMS is 1 over root 2 of that so the RMS is like right here that's the RMS voltage and of course it's not the same thing as the average because the average voltage is 0 but it's a way to indicate to us the amount of voltage that is there on a root mean squared kind of level I any better way to say it and hello everybody in India they tell me that your RMS voltage is what do they say I think they say that it's 220 volts and that's your maximum voltage divided by the screw of two so the v-max in India is about 311 volts Wow okay so I think in Europe they'd find it to be 320 or 330 volts that's just the difference between the maximum value here and the RMS value that I've shown in green goodbye

Channel: Doc Schuster

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Keywords: schuster, solve, voltage, transformer, electricity, root mean square, current, tutor, wghs, ap physics, problem, help, understand

Id: FrRmihdF52o

Length: 16min 11sec (971 seconds)

Published: Mon Feb 04 2013