Anderson Video - Reactance Example

Professor Anderson
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And they tell us that L is- I'll give you my numbers, it's 28 millihenries. And we want reactance X sub L of 520 ohms. So it's kind of weird that we call reactance the same as resistance, the units are also ohms, it's because it acts like a resistor, it's just that it's out of phase with the current, so you have to be a little bit more careful about it when you include it in a circuit element as we will see in a minute. Alright, what frequency f will L equals 28 millihenries have X L equals 520 ohms? Alright, to do this we just go back to our definition of X L. This is not going to be so bad. We said that X L was equal to omega times L, this is the reactance of an inductor. We don't have omega here, we have f that we're looking for, and so we have to remember the relationship between omega and f, and hopefully you remember it. We know it's got to go up with f, but where does the 2 pi go? Does it go in the bottom or in the top? Well, omega is radians per second, so that means it has to end up in the top. So this is the relationship. Reactance is 2 pi f times L. And now we can just solve this equation for f. f is equal to the reactance divided by 2 pi times L. And now we have all those numbers. So let's plug them in and try it. X L was 520 ohms. Ohms is SI units for resistance so we don't have to write those down. L was 28 millihenries, Milli is 10 to the minus 3. Henries is also SI units so we don't have to write that down. And now punch this into your calculator, tell me what you get and I will approximate it here. We've got a 5.2 times 10 to the 2 up top, 2 pi has got to be very close to 6, 28 is very close to 30, and we've got a 10 to the minus 3. So this is what? I'm going to shift this slightly, let's make it 52 times 10 to the 1 over 6 times 30 is 180 times 10 to the minus 3, and so we get 50 over 180 which is not quite a third. Right, it's right in between a third and a fourth. So we'll say that this is about about 0.27. Sure, why not. Times 10 to the minus 4, oh I'm sorry, this is minus 3, it's going to go up on top so that becomes a 10 to the 4. So I'm gonna say this is about 2.7 times 10 to the 3. Sean did we get a right answer on the phone? 2.9 times 10 to the 3? Ok, so our guess was a little bit off but not too bad.
And they tell us that L is- I'll give you my numbers, it's 28 millihenries. And we want reactance X sub L of 520 ohms. So it's kind of weird that we call reactance the same as resistance, the units are also ohms, it's because it acts like a resistor, it's just that it's out of phase with the current, so you have to be a little bit more careful about it when you include it in a circuit element as we will see in a minute. Alright, what frequency f will L equals 28 millihenries have X L equals 520 ohms? Alright, to do this we just go back to our definition of X L. This is not going to be so bad. We said that X L was equal to omega times L, this is the reactance of an inductor. We don't have omega here, we have f that we're looking for, and so we have to remember the relationship between omega and f, and hopefully you remember it. We know it's got to go up with f, but where does the 2 pi go? Does it go in the bottom or in the top? Well, omega is radians per second, so that means it has to end up in the top. So this is the relationship. Reactance is 2 pi f times L. And now we can just solve this equation for f. f is equal to the reactance divided by 2 pi times L. And now we have all those numbers. So let's plug them in and try it. X L was 520 ohms. Ohms is SI units for resistance so we don't have to write those down. L was 28 millihenries, Milli is 10 to the minus 3. Henries is also SI units so we don't have to write that down. And now punch this into your calculator, tell me what you get and I will approximate it here. We've got a 5.2 times 10 to the 2 up top, 2 pi has got to be very close to 6, 28 is very close to 30, and we've got a 10 to the minus 3. So this is what? I'm going to shift this slightly, let's make it 52 times 10 to the 1 over 6 times 30 is 180 times 10 to the minus 3, and so we get 50 over 180 which is not quite a third. Right, it's right in between a third and a fourth. So we'll say that this is about about 0.27. Sure, why not. Times 10 to the minus 4, oh I'm sorry, this is minus 3, it's going to go up on top so that becomes a 10 to the 4. So I'm gonna say this is about 2.7 times 10 to the 3. Sean did we get a right answer on the phone? 2.9 times 10 to the 3? Ok, so our guess was a little bit off but not too bad.