Professor Anderson

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When we mentioned Ohm's law, we had the following: V equals I R. Voltage is current times resistance. But now with inductors and, indeed, with capacitors, we're not going to use resistance. We're going to use something called reactance. And reactance you write with an X. And this is either the reactance of a capacitor or an inductor. So if we think about our inductor, there is certainly a voltage drop across it, but it is out of phase with the current. And so you cannot just write Ohm's law directly with some resistance, it is called a reactance. So an inductor has a particular reactance to it, and it's that resistance to changes in the current. But we know that has to go like omega, right? If I try to move the current back and forth very quickly, then the effective reactance has to go up. It's going to impede that motion. So there has to be an omega in there, has to go linearly with omega. Also, if I take my solenoid and I just add a whole bunch of coils, it's got to get harder and harder to change the current through there, and so the other factor that we need is L. And so Ohm's law effectively becomes the following: V equals I times X sub L, and that means it's I times Omega times L. This is Ohm's law for an inductor. What's the voltage drop across the inductor? It's that.

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When we mentioned Ohm's law, we had the following: V equals I R. Voltage is current times resistance. But now with inductors and, indeed, with capacitors, we're not going to use resistance. We're going to use something called reactance. And reactance you write with an X. And this is either the reactance of a capacitor or an inductor. So if we think about our inductor, there is certainly a voltage drop across it, but it is out of phase with the current. And so you cannot just write Ohm's law directly with some resistance, it is called a reactance. So an inductor has a particular reactance to it, and it's that resistance to changes in the current. But we know that has to go like omega, right? If I try to move the current back and forth very quickly, then the effective reactance has to go up. It's going to impede that motion. So there has to be an omega in there, has to go linearly with omega. Also, if I take my solenoid and I just add a whole bunch of coils, it's got to get harder and harder to change the current through there, and so the other factor that we need is L. And so Ohm's law effectively becomes the following: V equals I times X sub L, and that means it's I times Omega times L. This is Ohm's law for an inductor. What's the voltage drop across the inductor? It's that.