Hey guys. In this video we're going to talk about these things called RMS values. Since current and voltage are changing continuously in AC circuits, it's helpful to know average quantities of the current and the voltage. But it turns out that it's not actually useful to know the average specifically, but more useful to know a type of average called the RMS. Alright. Let's get started.

A very common question to answer is: in alternating current circuits, what is the average of the current and the average of the voltage? I have above me the two graphs of the voltage versus time and the current versus time. And you guys can see that for every peak I have above the horizontal for voltage which represents a positive voltage or a voltage with a particular polarity, the same thing happens when I look at the current versus time graph above me. For every peak that I have that's above the horizontal axis, which represents a positive current or a current in one direction, I have a symmetric or identical peak below the horizontal which represents a current that's negative or a current in the opposite direction. Okay? And you're going to alternate between these positive and negative peaks forever. So, what do you guys think is the average value of the voltage and the current? It's going to be 0. And it's always going to be 0 because these positive peaks are always going to alternate with the negative peaks and the effect is always going to cancel itself out. Okay?

So, a much better average quantity is called an RMS value. Okay? RMS is an acronym and it stands for the root mean squared. So the RMS value is the root mean squared value. Now, I space these words because there's a little bit missing here so that we really understand what an RMS is. It's the root of the mean of the squared value. That's what RMS means. That's what root mean squared means. It's the root of the mean of the squared. So if I want to know the RMS value of x, for instance, x can be anything it could be voltage, it could be current, it could be power, it could be whatever. To find the RMS value, I first square it, so that's the first step, right, then I average it or I take the mean of it then I take the square root or the root. So it is the root of the mean of the squared, right, the root of the mean of the squared. This is very important that you do it in this order because if, for instance, you were to just average x, that's not going to be the same value as the RMS because, for instance, what's the average of current? 0. So if you then square that average it's still 0 and if they would then take the square root of that average squared it's still 0. Okay? So it has to be the root of the mean of the square. Alright?

Now, luckily, there are very easy relationships between the RMS current and the maximum current and the RMS voltage and the maximum voltage. Or you could rewrite it and say that the maximum value of either is just the square root of 2 times the RMS value. Okay? Let's do a quick example to illustrate this.

If the RMS voltage of an outlet in the US is 120 volts, what is the maximum voltage of an outlet? If you complete a simple circuit with this AC source by connecting a 12 ohm resistor, what is the RMS and the maximum current in this circuit? Okay. So, three questions here. What's the maximum voltage given the RMS voltage? What's the maximum current? And what's the RMS current? So let's take these 1 at a time.

We know that Vrms=120V and we want to figure out what the maximum is. All we need to do is use this equation right here. The maximum voltage is just going to be √2×120V which is about 170 volts. Okay? One question down.

Now we want to know what are the RMS and the maximum currents. I'm going to find the maximum current first. Okay? Now imagine for a second what this circuit looks like. I have an alternating source and I have a resistor. Whatever voltage is across this alternating source is the voltage across the resistor by Kirchhoff's loop rule, right? So when the voltage is V_{max} across the AC source, what's the voltage across the resistor? V_{max}. So what is the maximum current? It's going to be the current when the voltage across the resistor is V_{max}. Okay? So we can just say that the maximum current is going to be Vmax/R. This is just Ohm's law applied to the resistor when the voltage across the resistor is V_{max}. Okay? So this is going to be 170/12, which is about 14.2 amps.

Now that I know the maximum current, I can use this equation to find the RMS current very easily. The RMS current is just going to be the maximum current divided by the square root of 2. That's going to be 14.2/√2, and that is about 10. Okay? That wraps up this discussion on the RMS values for voltages and currents.

Alright, guys, thanks for watching.