Hey guys. In this video, we're going to start talking about resistors in AC circuits. Alright? Let's get to it. Just as a reminder, in an AC circuit, the current produced by the source is always going to look like this. Okay. It's always going to be sinusoidal. Alright. Now because of that, Ohm's Law tells us that the voltage across the resistor as a function of time has to be this current as a function of time times the resistance. Right? If we had a basic circuit exactly as above, the voltage across the resistor as a function of time would just be equal to the current traveling through it as a function of time times r the resistance. This means that the voltage across the resistor is Imax∗rcos(ωt). Right? That is simply plugging in this equation into Ohm's Law. Very basic. Let's do an example. A 10 ohm resistor is plugged into an outlet with an RMS voltage of 120 volts. What is the maximum current in the circuit? What about the RMS current?

Okay. We know that the RMS voltage is 120 volts. Now just like we could say that current is equal to the maximum voltage over r, it turns out that the RMS current is also equal to the RMS voltage divided by r. This is something that's really easy to show and you guys can convince yourselves of that on your own. So, this is 120 volts divided by 10 ohms which is 12 amps. Now, what's the maximum current? Well, the maximum current is just going to be the square root of 2 times the RMS current. So that's the square root of 2 times 12 amps, which is about 17 amps. Okay? Resistors in AC circuits are very, very simple problems. Alright?

Now for multiple resistors in an AC circuit, what if you had something like this for instance? All we have to do is combine them into a single equivalent resistor as we would with DC circuits and then we can apply the same equations as we did in the previous example. Alright, guys. This was a little bit of a start with resistors in AC circuits and we'll get to more of that soon. Thanks for watching.