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Converting Between a Function and a Phasor

Patrick Ford
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Hey, guys, let's do a phaser example in this case, an example that deals with relating the phasers equation to the phaser diagram. Okay, the current in an a C circuit is given by this equation. Draw. The phase of that corresponds to this current at milliseconds, assuming the phaser begins at zero degrees. So in the beginning, the phaser is going to start here at zero degrees, and it's gonna rotate through some amount of angle to arrive at its final position. We want to figure out what that angle is, so we know where to draw the final position of this phaser. Remember that The angle is just gonna be omega. The angular frequency of the phaser times t. Okay, now we know that tea is just 15 milliseconds. So what's the angular frequency of the phaser? What? We're told that the angular frequency of the current is 3 77 and that's going to be the angular frequency of the phaser. However quickly it's oscillating on a function right. If I were to draw, this is an oscillating graph is gonna be the same rate as how quickly it's oscillating on the face of diagram. Those angular frequencies are the same. So this is just going to be 3 77 times milliseconds. Millions 10 to the negative three. And this equals 566 radiance. We want this to be in degrees because it's easiest to graph degrees for us or sorry to draw degrees on the diagram. Remember, you can convert by dividing this by pie and multiplying it by 180 degrees. This is gonna be 324 degrees. Okay. I'm gonna minimize myself and draw the space with diagram. Yeah, okay. It started from zero degrees. Don't forget, the phaser began at zero. Starting from zero and rotating counter clockwise. This phaser ends up in the fourth quadrant because 24 is greater than 2. 70 but less than 3. 60. Okay, there are two other ways that you can represent this number if you want. This one is 3 24. As the full rotation, you can represent it from the negative y axis if you want, and this would be 54 degrees. Or you can represent it from the positive X axis if you'd like. And this would be 36 degrees Either way, this is correct. But the important thing to remember is that this value 24 is how far it traveled from its initial position. It started at zero degrees, and phasers always rotate counterclockwise. So this is 324 degrees. All right, guys, Thanks for watching.