Transformers and effect of eddy currents

hello this video follows up the one in the a-level physics revision series on electromagnetism and responds to questions I've received about how eddy currents affect the electromagnetic flux in a core of a transformer so let's just go back to basics and remind ourselves about what goes on if you take a coil of wire which is sometimes called a solenoid and you pass a direct current unchanging direct current through that coil then in the middle of the solenoid there will be a magnetic field and the magnetic field strength which is B is equal to MU 0 which is the permittivity of free sorry the permeability of free space multiplied by the current that's going through the wire multiplied by the number of turns in the solenoid so you can see from that that if you change the current you change the magnetic field if the current is steady then the magnetic field will be steady if on the other hand you have exactly the same setup but this time instead of using a battery to generate a direct current and an unchanging one this time you have an alternating current source then what will happen is that the current if we measure the current in this direction multiplied I'm sorry by time in this direction then that will almost certainly be a sine wave if you use ordinary alternate alternating current which means that the value of the current at any point in time is constantly going up and down up and down in a sine waveform and so there is a constantly changing current it will have a form I equals I naught where I naught is the maximum value times sine Omega T where Omega is 2 pi F and F is the frequency of the wave which is the number of times a crest passes a particular point in one second and that will therefore have a very current because it's constantly going up and down and if you have a varying current then according to this you will have a varying magnetic field now what does all that got to do with it well Faraday says that as far as induced EMFs and induced currents are concerned if you have a steady current and thus a steady magnetic field you don't get any induction at all because Faraday says that an induced EMF is equal to flux change divided by time which is usually written D Phi by DT now if you've got a constant magnetic flux then there isn't the flux change so there will be no induced EMF so if you have this arrangement here where you have your solenoid or your coil of wire and alternating generator generating alternating voltage which produces an alternating current then you will get a variation in the magnetic field and that means that if you bring another coil and this time we'll just put a voltmeter here so there's no power supply in this at all we're simply registering what happens then Faraday's law says that where you have a changing magnetic field you can have an induced EMF and thus an induced current in this in this circuit and which way will the current flow well that's where we have to go to lenses law because lenses law says that the current will always flow in the direction such that it opposes the change that caused it what that basically means is if the current is generated by a magnetic field in that direction that will be a changing magnetic field in that direction so you've got this rate of change here then the current will flow in such a way as to create a magnetic field in that direction opposite to the one that caused it that's what lenses law says by contrast if you were to bring that self same coil that's this coil here this circuit here if you were to bring that next to this circuit then no current would be induced in the second circuit at all because there's no changing magnetic field so let's just have a look and see what we mean let's take a single coil of wire which will make rectangular in shape and underneath it we have a magnet north sails if we just leave that magnet there no current flows in this loop because there is no changing magnetic field there will of course be a magnetic field going for north to south and it will continue right the way around here but there's no change in it therefore no current flows but if you are now to take that magnet and move it up through the center of this loop then you've got a changing magnetic field and as a consequence you'll find that a current will flow in the wire and in my series on electromagnetism I taught how to work out which direction the current would flow we won't worry too much about which direction because that you can work out the key thing is that how do we know which direction the current will flow will it will flow in such a way that it will produce a magnetic field in the opposite direction to this magnetic field so the current will flow in the direction that it needs to flow in order to as it would counter the magnetic field that's moving up through the cable now what we said with transformers was that if you take a coil with a certain number of turns say in one turns and you have a well actually we'll call that NP and VP volts so the voltage supply is V P stands for primary and the number of turns is n in the primary and you then have another circuit with n which is the secondary circuit with n s that's the number in the secondary and you want to know what will the voltage in the secondary be then we developed in the video on electromagnetism the formula that V P equals NP D Phi by DT where D Phi by DT is the change of flux caused by this alternating voltage and we also said that V s is n s D Phi by DT it's the same rate of change of flux because both of these solenoids are experiencing the same rate of change of flux and from that you get that V P divided by V s equals NP / NS so in other words if you have her MP says has a hundred turns and NS has 50 turns then V P water so that MP over NS is 2 then V P over V s will be 2 so whatever your voltage is for in the primary you'll get half of that in the secondary so you can either step up or step down the voltage and we explained this in the video depending on how many turns you have if you have fewer turns then you get a smaller voltage if you have more turns than the primary you get a higher voltage so you can step up or step down as the case may be but you have a problem if you do it like this because whilst in theory and the rate of change of flux is the same in both cases don't forget that the magnetic field is actually being created in the middle of the solenoid here once it gets outside the solenoid once it gets into this region in it and indeed in this region the magnetic field that is varying inside the solenoid is going to be quite different once it gets outside and it's very much more difficult and complex to describe so the idea that these two rates of change of flux are the same is actually theoretically true but in practice it isn't because the rate of change of flux inside the solenoid is quite different from the rate of change of flux outside the solenoid applying to this coil here so the way people get round that as a problem is they put the coils around a what's called core and it's usually made of something like iron some kind of ferrous material so here we have an iron core and you put the first solenoid round that one and you put the second solenoid round that one and this is then the primary and this is the number of turns in the secondary and the same principle as we head up here applies but why does this work well what happens is that you get a magnetic field in the primary because this has got a an alternating current alternating voltage attached to it once you have a magnetic field in the primary then that magnetic field will magnetize the iron core and once the atoms in the iron core inside the solenoid are magnetized then they will have a magnetic effect on all the atoms right the way around so in fact the effectively the iron core carries the magnetization right the way around and you have the same magnetization and indeed changing magnetization because this this field is constantly changing backwards and forwards and so that's going to have the same effect in the core so that you get broadly the same change of magnetic flux on this side and therefore these two are broadly equal and thus this formula does hold true and what we said in the video on electromagnetism was that the in theory the power from this side should equal the power from that side and power don't forget in electrical terms is always V times I so what you would say is that the voltage in the primary times the current in the primary is equal to the voltage in the secondary times the current in the secondary and that if that were true would suggest that the transformer was 100% efficient because you've got a transfer of power exactly matter the transfer the power in equals the power out but that isn't true of course very rarely true in anything you lose some form of power and you can lose it by a variety of ways this video considers why you lose it through eddy currents in this iron core well let me just start by having a little experiment here's a magnet I'm going to have the south and the north so the field lines are going from south from north to south and what I'm going to do is I'm going to have a kind of pendulum a pendulum which is going to swing that was a forwards through the magnetic field except instead of putting a bob on the end of my pendulum I'm going to have a metal plate so it's just a thin metal disc now what happens as I let that pendulum swing through the magnetic field well imagine it was a wire we know that if you have a magnetic is a magnet north south and here's a wall if you move that wire down quickly that will induce a current to flow in the wire well exactly the same thing happens here as the metallic disc goes through the magnetic field it will induce a current but unlike a wire where the current flows along the wire this is a metal disc so what you actually get is an eddy current a little current flows on the surface of the disk and how do we know which direction that eddy current flows well Lenz's law tells us it flows in a direction such as to oppose the magnetic field that creates it so if the magnetic field is moving from north to south upwards then it the current will flow in the disk you know in such a way as to create a magnetic field downwards to oppose this one here but if a current flows then we know that in terms of power his V times I we just did that up here so and vehicles to IR so if V equals IR then the power is equal to I squared R there's going to be some resistance in this metal disk so there is going to be a power loss as this disk goes through the magnetic field and it's achieved through heating up as that little disc goes through the magnetic field the current flows and it will warm up and so you lose power and what happens when you lose power what happens is as the disc goes through it slows down it's actually called magnetic braking this is a way in which braking can be achieved you have a disc going through a magnetic field instead of just swinging backwards and forwards like a pendulum might it swings and then it goes very very slowly it probably doesn't come out it just stops it's a braking system and the reason it breaks is because you've got this eddy current creating a magnetic field in the opposite direction to this magnetic field generating heat and losing power and the whole thing breaks this pendulum well you can see what's going to happen here you have a magnetic field generated by this solenoid and that magnetic field is gay and that is a changing magnetic field so that magnetic field is going to induce eddy currents in this iron core the iron core is good because it transmits the magnetic field but it's bad because it will have in Joost eddy currents in the core as well as in the secondary in the secondary solenoid and those eddy currents um will have a size and there will also be a resistance in the core so they too will have a power loss and that power loss has to come from somewhere and it has to come out of this power in so if you lose some power through the eddy currents in the core you're not going to have as much power in the secondary and that's why you get or it's one of the reasons why you get power losses in a transformer and why the transformer isn't a hundred percent efficient the way to solve this problem or partially to solve it at any rate is to make the iron core made of layers of iron separated by insulating material so if you make your I am core like that and then wrap your coil around it now because you've got iron and then insulator iron then insulator that's fine as far as transmitting the magnetic field is concerned because these these iron layers will become magnetized and will cause the layers below to become magnetized and therefore will transmit the magnetic field but now given that the the magnetic field created by this primary will say B in that direction it's of course changing the Eddy's will flow in such a way as to cause the magnetic field to oppose it but no current can flow downwards because of course it's not going to get very far before it gets to a piece of insulating material and so consequently you can restrict the extent of the eddy currents that are flowing by having layers of iron separated by insulating material but you can never stop the eddies all together they will flow in the layers they just can't flow between the layers so this is a way of reducing but not eliminating power loss in a transformer

Channel: DrPhysicsA

Views: 71,580

Rating: 4.9205298 out of 5

Keywords: electromagnetism, transformer, core, eddy, current, power, induction

Id: Min9oTvcYX8

Length: 17min 46sec (1066 seconds)

Published: Tue Apr 03 2012