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31. Alternating Current

Phasors for Resistors


Phasors for Resistors

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Hey, guys, in this video, we wanna talk about phasers specifically applied to resistors in a sea circuits. All right, let's get to it. Remember, guys, that the voltage in the current across the resistor at any time T is given by these two equations. Okay, These two functions right here. All right. They're both at the same angle. Omega T. Okay. Remember that the angle for any phaser is Omega T. Because both of these functions, both of these Cozzens have that same angle. They're 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 phase. Er that I drew is the current through the resistor, and it is at some angle omega t Next, I drew the voltage across the resistor, which is at that same angle omega teeth. So when I combine these phasers into a single phaser diagram, I get that the current and the voltage across the resistor lineup because they were both at this omega angle Omega t, They're said to be in faith. They line up. Okay. Any two phasers that air 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. All right. 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 on a C source within 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 fazer and the current phaser. Okay, when the circuits 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're going to be at the angle further phaser is always gonna be Omega t. So this is going to be Omega, which we're told is 20 in seconds times T, which we're told this 200.2 seconds. So this is gonna be four radiance which is equivalent to 229 degrees. If you just convert quickly between radiance and degrees. All right, so now we know how to draw our phasers. 229 degrees places us in the third quadrant because that's greater than 1 80 less than 2. 70. So that's gonna put us somewhere around here. 229 degrees. We're going toe. Have a phaser for the currents. Oh, sorry, guys. A little technical difficulty, a phaser for the current. And we're also going to have a phaser for the voltage. Sorry. 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 could 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. All right, guys, Thanks for watching this video. This wraps up our talk about phasers with respect to resistors in a sea circuits. All right,

A 12 Ω resistor is connected to an AC source. If the resistor’s voltage phasor is initially at 0° , and the figure below shows the phasor after 0.04 s, answer the following: 

a) What is the angular frequency of the source? Assume the phasor is on its first rotation. 

b) What does the current phasor diagram look like? 

c) What is the current in the circuit at this point (t = 0.04 ?)?