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Anderson Video - Transformers

Professor Anderson
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Alright, let's go back to this idea that coils can talk to each other, right? If I run current through one coil it's gonna generate a magnetic field, If I put another coil next to it, I can pick up that magnetic field, generate an EMF in that secondary coil. And let's do it with a particular configuration, and if you do it in this configuration it's called a transformer. So it looks a little bit like this- you're going to take an iron core, and now you're going to take coil and wrap it around this side of that iron, and that is our primary coil. And we run IP through it. On the other side you wrap another wire around and this develops a current in it, I sub s, and that's our secondary coil. Okay, the purpose of the iron core is to trap the B field lines, so B fields that are generated there end up over there, and B fields that are generated here and up over there. Okay, so it's just a simple way to sort of trap those B field lines. There's another way which is put the coils right on top of each other, or wrap them around on top of each other, but that gets a little confusing when you're looking at in a picture. So this thing is called a transformer, and let's see if we can write down some properties. There is an EMF in the primary side and that EMF is the number of terms of the primary coil times delta phi over delta t There is, of course, an EMF in the secondary coil, which is minus N sub s delta phi over delta t I can divide by N sub p, and I get epsilon p over N sub p equals minus delta phi over delta t. And I can do the same over here. Epsilon s over N sub s equals minus delta phi over delta t. And now here's the thing, the iron core traps the B field lines. so the B fields that are coming through this one end up going through the other one. And so on either side you in fact have the same delta phi over delta t on each side. Delta phi over delta t on the left side is exactly the same as delta phi over delta t on the right side because all the field lines go through and they do it in the same amount of time delta t. So now this whole thing simplifies to what, epsilon p over Np equals epsilon s over Ns. And this is typically written like this, epsilon s over epsilon p, I had to divide by an epsilon P and so I've gotta multiply back up by N sub s is equal to Ns over Np. And once you hook this stuff up to a circuit and there is some resistance in it then these things become voltages. Voltage of s over voltage of P is just N sub s over N sub P. And this thing right here is known as the transformer equation. More than meets the eye. Transformers? Robots in Disguise? No? You guys were like five years old or something right? No? Okay I guess they're still pretty popular right, because they're making like those Transformer movies but transformers was like just this little toy, you know, a robot that turns into a car back and forth. And it's kind of named appropriately right? Because what are we doing? We're taking one voltage, V sub s and we're turning it into a different voltage, V sub p or vice versa. Typically you call V sub p the primary, so by putting a voltage on this side of the transformer I can get a totally different voltage on the other side of the transformer and all it depends on is how many coils. Now if I have the same number of coils then I don't change the voltage. That's called a one-to-one transformer. But if I have twice as many loops in the secondary side compared to the primary side then look what happens. Ns is twice Np and I get twice the voltage on the secondary side that I would get on the primary side. That's called a step-up transformer because you have stepped up the voltage. You come in with one voltage, you go out with a bigger voltage. Okay, the opposite is, of course, true. If I come in with a lot of coils and I go out on this side with fewer coils, say, half as many, then it's a step down transformer. I've taken some high voltage and I've transformed it down to some low voltage. Okay, step up increase the voltage, step down decrease the voltage. So where do you see these things? Where do you see transformers? On the power lines, right? Okay, on the power lines you will see transformers, because the high voltage power lines that are going around are too high for your house, okay? They're kilovolts, and you obviously don't want kilovolts in your house because then if you accidentally grab hold of that toaster plug while you're pulling it out, right, you can kill yourself. 110 volts, 120 volts RMS, it'll hurt but it's hard to kill yourself with your household voltage. Okay, you'll definitely feel it but it's really hard to kill yourself. Kilovolts can certainly kill you if there's enough current available. So the voltages that are running around in the power lines are high voltage, and then you want to transform them down to a lower voltage that goes to your house. So you see these things all the time, they're up on the power lines. if you look there's big cans and things up there on the telephone poles, and on the high voltage power lines those are transformers, okay? They are transforming the voltage.