Inductors Have Inductance, Reactance, AND Impedance. DANG, DAWG. | Doc Physics

in a circuit with an inductor and a power supply that's given you some AC stuff going on the power as we've discussed a little bit see the power is sometimes positive and sometimes it's negative I guess and I can identify like right here from right here to right here we're going to have the current you know power is current times voltage so the current and voltage are both positive during this instant right here so we're going to have power and in fact reaches a maximum right in between right there and then if I put another tick mark you see here the voltage is negative but the current is positive until we reach this point right here so that means we're going to have some negative power that means that the energy is leaving the inductor so here we're putting energy into the inductor that means that the power going into the inductor is positive then in a moment later we're we've got energy leaving the inductor and so the inductor is giving energy back to the power supply and then here we've got oh look we've got negative current and negative voltage during this time interval right here until that goes positive so I throw you some dotted lines right here and I tell you that then we're putting energy back into the inductor again of course the fields going the other direction that's why they're both negative but we're putting real energy into the inductor so there is a magnetic field in the inductor during this time and during that time it switches direction but look at the frequency of this the switching is dang the frequency of the switching is twice the frequency of our circuit so that's kind of cool maybe it has something to do with the square of that thing but but the wonderful thing about it is the power averaged if you average that power delivered to the inductor is there is no average power delivered of the inductor your charge in and up discharged it you're getting it right back out so that is awesome another thing I wanted to say about inductors is we can investigate the maximum voltage on the inductor and you know that's going to be a chute we've got these same things the screw is going on here the reason is you've got if you've got a what do you want you want a resistor and an inductor like that you see that you've got the voltage max from the raziel points in the direction of the current and the voltage max from the inductor points as a right angle to it so as I rotate these 2 phasers check this out they go like that sometimes we're going to be having positive power deliver at other times we're going to have negative power being delivered but the resistor is always getting some power delivered to it so we get this really cool effect where it's the voltage max across the resistor square plus the voltage max across the inductor score and I can expand that a little bit that's just going to be IMAX times ARRA score score and we're going to take a screw to all of it now this max voltage across the resistor across the inductor sorry is the maximum current that's V Max is the maximum current times well remember we called it the capacitive sorry the inductive reactance and I'm supposed to score both of these things so if I keep going to do this stuff V Max is really just I max times the scroot of all that business which is going to be R square plus X square L the inductive reactance and inductive reactance how do i define inductive reactance wasn't that just Omega times inductance yeah yeah let's see if we have a bigger inductor we got more reactants and if we have a bigger frequency we have more reactants so this is just I max times the scroot of our square plus Omega square L square and then I can identify this as looking a lot like Ohm's law the maximum voltage is the maximum current times what is the effective resistance I kind of want to say but I can't say resistance so I have to say impedance and I say then impedance for well I call it Z impedance for a resistor and an inductor in a circuit is going to be the scroot of square plus Omega square L square now I'm kind of itching to put an inductor and a capacitor in a resistor at the same time but before we do that we've got to think about how we're going to get maximum current so I'm going to make a graph of current as a function of Omega current as a function of the frequency that I'm using to drive the circuit all right so this is rather complicated first of all the current through a resistor is completely independent so this is a resistors current but if I have a capacitor and I increase the frequency first of all what if the frequency is zero for a capacitor I'm going to do a capacitor in orange if the frequency is zero do I expect the maximum current through the capacitor to be big or small I'm thinking that's probably going to be no current if I just leave a capacitor hooked up to a DC power supply ultimately the current stops rather quickly actually I mean okay it takes infinite time that's not quick but there will be no current in the long term but if I start switching this direction if I cross out this guy and put in an AC and it's going back and forth and back and forth and back and forth and back forth in fact the faster I switch back and forth the more current that I'm going to get here so I get this kind of a behavior oh okay so this guy is my capacitor and if I get myself an inductor now I'm going to say I have an inductor and it's connected to a DC power supply will examine the limits as we often do in physics if I have an inductor hooked up to a DC power supply and am I going to wait for a long time I'm going to get a current through that inductor sure I am in fact it's going to be a really big current so I'm going to say that the inductor starts really big but as soon as I start switching this what if I cross that guy out and put in an AC power supply if I start switching the direction then the inductor gets more and more and more pissy the inductor gives me a graph that looks like this Oh interesting now as we start to compile oh boy as we start to combine these things you can kind of see that there will be a sweet spot in which I can get the maximum current and maximum current square is going to give me the power so there's an ideal situation an ideal relationship between capacitance and inductance that's going to give me a match it's going to give me something really cool but let's first define impedance and then I'll leave this video I think we'll come back and and address that other issue I want to throw it show you all three of my phasers there's my first phaser the resisters phaser where currents in line with voltage and here's the capacitors phasor where I say current leads voltage as we spin counterclockwise and then the inductors phasor says that current lags voltage or voltage leads current and so the cool thing about this is the resistor is easy the resistor you just put the resistor on there's like boom you haven't noticed anything at all so we'll put it over here but if you put the capacitor and the inductor in at the same time you see that they are sort of at cross-purposes to each other they are doing exactly the opposite thing so while the inductance has an effect the capacitance has the opposite effect and we can say what are we going to say about IMAX isn't that V over R but R is it has to be in quotes so IMAX is going to be V over our inductance no our impedance this thing right here impedance the the effective resistance of all these complicated components is called the impedance so I'm going to put this over Z maybe instead I should put I should say IMAX for the capacitor is that over XC and IMAX for my inductor is V over X L all right but notice that these guys are opposite directions and so we're going to have to go over into this equation and define our what we could do it the long way but I just want to show you that this they're in opposite directions P says you got this this is your voltage of the resistor and then you've got your voltage of the capacitor this direction and you've got your vote no sorry your voltage of the capacitor is the heck am i doing sorry the voltage is something that's being controlled by the power supply you've got your current of the resistor here and you've got your current of the capacitor up here and you've got your current of the inductor right here so I have to subtract those two from one another in order to do this problem so watch this the impedance is therefore defined as see if I can put this all under the screw this can be R square plus now it's not going to be all three terms because it's not a three-dimensional problem it's still the two-dimensional problem but I have to take the inductive reactance and subtract the capacitive reactance and then square it and if I expand this I get that the impedance is R square plus Omega L minus 1 over Omega C that quantity square and something beautiful happens when this is minimized if we minimize this sucker then we can get the impedance to be exactly R in fact if these two things are equal something beautiful happens you'll have to wait to find out or maybe you could go find out now

Channel: Doc Schuster

Views: 60,763

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Keywords: problem, AP WGHS, solve, understand, help, tutor

Id: UgoW2d4EidU

Length: 10min 33sec (633 seconds)

Published: Thu Feb 07 2013