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concept

## Phasors for Capacitors

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Hey, guys, in this video, we're gonna talk about phasers for capacitors in 80 circuits. So the current fazer and the voltage phaser for capacitor in the circuit. All right, let's get to it. Remember, guys that there are two functions that describe the voltage and the current across the capacitor at any time T in an a C circuit. These air given by this Okay, because the angle for each of them is different, right? We have Fada equals omega t here, and we have some other angle which are called data prime equals omega T minus pi over two. Because the coastlines each have a different angle, were saying that they are out of phase. Okay? And in fact, the voltage lags the current. This is very different than the phasers. We saw four resistors which were in phase because both functions had the same angle of mega t. All right, if we look at the three phaser diagrams that I drew the first one, we have the current at an angle. Omega T right. That is the angle of the current in the second one, we have omega T minus pi over two as the angle for the voltage that takes us all the way down into the negatives. Because Omega T itself is we can see is less than pi over two. So that takes us into the negatives. And that also means that these have toe have a 90 degree angles, Right? This is just omega T, which is the angle for the current minus 90 degrees. So they're separated by 90 degrees. So whenever you draw the phaser diagram, which includes both the current and the voltage phases for a capacitor okay, you have to draw it with the voltage lagging, the current okay, or the current leading the voltage. Okay. It's very important that you guys memorize that current leads the voltage or the voltage lags the current for a capacitor, All right. And that is the thing to take away from this that the voltage across capacitor always lags the current in the capacitor circuit. Okay, let's do a quick example. Anay, see sources connected to a capacitor at a particular instant in time, the voltage across the capacitor is positive and increasing in magnitude draw the phasers for the voltage and the current that correspond to this time. Okay, Now Whenever a phaser is increasing in magnitude, it's because as it rotates, it gets closer to a horizontal axis. Okay, As it gets closer and closer to the horizontal axis, its projection onto that axis gets larger and larger and larger. And remember, the projection onto the horizontal axis tells us the value of that phaser. Okay, now, if this phaser is gonna be positive, it needs to be pointing to the right. And if it's gonna be increasing in magnitude, it needs to be pointing to the right and moving towards the X axis. Since phasers always rotate counterclockwise, that means that the voltage phaser has to be here. Okay, and it's rotating like this. So it's positive because it points to the right and it's increasing in magnitude because as it gets closer to that horizontal axis mawr and more and more of it points horizontally until it's on, the horizontal axis now is at a maximum. And then as it moves away from the horizontal access, it decreases and decreases and decreases in value until it's straight up and it's zero. Okay, Now, if the voltage is here, the current is 90 degrees ahead of it, so the current is gonna be here. This is a current through a capacitor. This is the voltage of a capacitor. Okay? And this is a 90 degree angle. So this is what the face or diagram looks like if the voltage is positive and increasing. Alright, guys, that wraps up our discussion on phasers with capacitors. Thanks for watching.

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Problem

An AC source operates at a maximum voltage of 60 V and is connected to a 0.7 mF capacitor. If the current across the capacitor is i(t) = i_{MAX} cos[(100 s^{−1} )t],

a) What is i_{MAX}?

b) Draw the phasors for voltage across the capacitor and current in the circuit at t = 0.02 s. Assume that the current phasor begins at 0°.

A

a) i

_{max}= 4.2A b) θ_{iC}= 115^{o}θ_{VC}= 185^{o}B

a) i

_{max}= 4.2A b) θ_{iC}= 185^{o}θ_{VC}= 115^{o}C

a) i

_{max}= 4.2A b) θ_{iC}= 115^{o}θ_{VC}= 25^{o}D

a) i

_{max}= 4.2A b) θ_{iC}= 25^{o}θ_{VC}= 115^{o}Additional resources for Phasors for Capacitors