concept

## Power in AC Circuits

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Hey, guys, In this video, we're gonna talk about power in a sea circuits. What elements are emitting power? What elements are not admitting power? What the average power is and things like that. All right, let's get to it in a sea circuits the Onley element to have an average power not equal to zero is what do you guys think it iss? It's the resistor. This is because whatever energy enters a capacitor or an induct, er okay equals the energy that leaves it capacitors and induct Er's are elements that store energy Ah capacitor stores charge to store electric potential energy and a and induct er stores current to store a magnetic potential energy. Okay, but either way, they only store energy. The resistor is what's actually bleeding energy from the circuit. Okay, so if you were the plot, the other elements power as a function of time, you would see that on average, all the peaks would cancel all the valleys and you would have no power on average. Okay, The maximum power of a resistor is going to be that maximum voltage across resistor times the maximum current. Okay, Now, as a function of time you can say that the power equals the current as a function of time squared times the resistance. This gives us the following graph of power and current versus time. You can see that current like we expect is gonna have no average value because anything that's positive any peak above the horizontal cancels with the negative peaks below the horizontal. But power stays above the horizontal. It just bounces above the horizontal. So it's always positive and therefore it has nothing to cancel it out. So on average, it is absolutely not zero. Okay, the average power emitted by an A C circuit is going to be one half off the maximum power. This is because the powers peaks are completely symmetric, so the average is gonna be one half of the maximum. So it's gonna be one half V max times imax. And if you substitute the maximum values for their arms values, you find that this actually equals V rms times I r. M s. So the average power depends upon the RMS voltage in the R. M s current, which is an interesting result, right? We're not talking about the RMS power here. We're talking about the true average of the power and it doesn't depend upon the average of the voltage of the average of the current. It can't because those were zero. But it does, interestingly enough, depend upon the RMS values of the voltage and the RMS value of the current. Okay, let's do a quick example. An A C source operating at a maximum voltage of 120 volts is connected to a 10 ohm resistor. What is the average power emitted by the circuit? Is it equivalent to the RMS power, Which would be I RMS Square times are okay. Don't forget that the average power we're just going to say is one half times the maximum voltage times the maximum current. Okay, so first, what's the maximum current? Well, that's just the maximum voltage which we know divided by R, which is 120 volts. That's the maximum voltage right, divided by 10 homes, which is 12 amps. Okay, so we can say that the average power is one half times 120 volts. Right, which is the maximum power? Sorry. The maximum voltage times 12 amps, which is the maximum current, and that whole thing is gonna equal 720 watts. Now, if I take this maximum current, I can then say that the R. M s current is the maximum current over the square to to which is 12 over the square to to which is going to be 849 amps that I can take and I confined. I r M s squared times are is 849 squared times 10 which is indeed 720 watts. So yes, that does match up. Okay. And this is something we touched upon earlier that the average power depends upon RMS values. So this is a form of power emitted by a resistor. We should absolutely be able to just plug in RMS values for it and get the average power out. Alright, guys, that wraps up for discussion on power in a sea circuits. Thanks for watching