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- [Voiceover] I wanna take a look at our two op amp circuits and make an interesting observation about how this things are behaving when they are working properly. When they're hooked up right, there's something these things do that is really helpful and makes life simple for us. Let's let the gain of our op amp be 10 to the third, or 10 to the sixth. Really high gain, a million. And we're gonna let the output voltage here, V out, let's say six volts. And you remember, what's not shown here in this circuit is the power supply is going to both of these op amps. Plus or minus, let's say it's plus or minus 12 volts. Those power supplies are implicit. They're not shown in the diagram but we know they're there. Alright, now, if V out is six volts and A is 10 to the sixth, then what's V in? V in is the difference between these two voltages here. Let's call this the usual thing. We'll call this V plus. I'm gonna call this V minus. And we know that V in, we know that V in equals V plus minus V minus. And now what the question is what is V in in terms of V out? Well, V in equals V out divided by A. If we fill in the values we had, it's six volts divided by 10 to the sixth, or six microvolts. So this is six microvolts between here and here, okay? So with six volts here, there's six microvolts over here. Okay, this is a really small voltage. In order for this op amp to have an output voltage that stays between plus or minus 12 volts, this voltage over here has to be really small. It has to be down to the microvolts level. So because I'm a practical engineer, I'm just gonna say this is pretty much zero volts. And if I say this is zero, that's pretty much the same thing as saying that V plus approximately equals V minus. So that's a little observation we're gonna make right there. So in this circuit, when it's working right, these two voltages are pretty much the same. So let's take this idea of V plus pretty much equals V minus and apply it to this circuit over here. Now this is our inverting configuration for an op amp. So this is V plus. And this is V minus in this circuit. And let's do the same analysis that we did before. If this is V out, and if V out is six volts, that means that V plus minus V minus divided by 10 to the sixth equals six microvolts, and that says that this is six microvolts in this direction. When we did this over here, because the signs of the inputs are flipped, this was six microvolts this way. So again, because of the enormous gain of this amplifier, this is always gonna be a tiny, tiny number, and so, heck, why not make it zero? So if I treat this as zero, what it means is, I'm gonna go right in here, and I'm gonna change this to zero volts. So let's make a couple more observations, okay? Right now, it says right here, V plus equals zero because it's grounded. So what does that mean V minus is? Well, V minus is also zero. V minus is zero. So that point right there is at zero volts. Okay, so that's pretty cool. So, that point's at zero volts. Now, is it connected to ground? It's not connected to ground. But at zero volts, because of what this op amp is doing it for us, this op amp is making sure, by this feedback path, that this node is always next to this node and that means it's always zero. There's a really cool word that we use for this and the word is virtual. And what does the word virtual mean? Well, virtual means that something is not there but it seems like it is. So in this case, this node is not connected to ground but it seems like it is. So this is referred to as a, a virtual ground. So these two ideas say the same thing. V plus equals V minus is always the situation around the input to an op amp, when it's running properly, and in the case particularly of this op amp configuration, where the plus terminal is connected to ground, we say that the other terminal, V minus, is at a virtual ground, or is a virtual ground. In the next video, I'm gonna go back and do this inverting configuration of the op amp. I'm gonna do the analysis again with this idea of a virtual ground and it's gonna be really easy compared to doing all that algebra.