Hey guys, in this video, we want to talk about phasers specifically applied to resistors in AC circuits. Alright, let's get to it. Remember, guys, that the voltage and the current across a resistor at any time t are given by these two equations. Okay? These two functions right here. Alright? They are both at the same angle, ωt. Okay? Remember that the angle for any phaser is ωt. Because both of these functions, both of these cosines, have that same angle, they are said to be in phase. Okay? In phase means identical. Alright and I'll show you what this means in the context of the phasers drawn below. The first phaser that I drew is the current through the resistor, and it is at some angle ωt. Next, I drew the voltage across the resistor, which is at that same angle ωt. So when I combine these phasors into a single phaser diagram, I get that the current and the voltage across the resistor line up because they're both at this omega angle, ωt. They are said to be in phase. They line up. Okay. Any 2 phasers that are in phase will always be lined up as they rotate. Okay? So at any time that you choose to measure, it will always be lined up. Sorry. They will always be lined up. Alright? And this is the conclusion that we're going to take away from this video that the voltage across the resistor is in phase with the current through the resistor. Okay, it's very important to remember that.

Now let's do a quick example. An AC source with an angular frequency of 20 inverse seconds is connected to a resistor with the circuit broken. 0.2 seconds after the circuit is completed, draw the voltage phaser and the current phaser. Okay? When the circuit's broken, nothing is happening. The second it's closed, now time starts. Okay? So the question is if we want to draw those phasers, what is the angle that they are going to be at? The angle for the phaser is always going to be ωt. So, this is going to be ω which we are told is 20 inverse seconds times t which we're told is 0.2 seconds. So this is going to be 4 radians which is equivalent to 229 degrees if you just convert quickly between radians and degrees. Alright, so now we know how to draw our phasors. 229 degrees places us in the 3rd quadrant because that's greater than 180 and less than 270. So that's going to put us somewhere around here, 229 degrees. We're going to have a phaser for the current. Sorry, guys. A little technical difficulty. A phaser for the current, and we are also going to have a phaser for the voltage. Sorry if those colors are the opposite of what I used before, the color itself doesn't really matter. And these are in phase. Okay? And you can draw other angles if you want like this angle or this angle. It doesn't really matter as long as whatever angle you choose, it matches up with this angle of 229 degrees. Alright guys, thanks for watching this video. This wraps up our talk about phasors with respect to resistors and AC circuits. Alright? Alright?