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concept

## Phasors for Inductors

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Hey, guys, in this video, we're gonna talk about phasers and how they apply to the voltages and currents through in doctors. All right, let's get to it. Remember, guys, that there are two functions that are very important regarding conductors in a sea circuits the current through and induct er and the voltage process conductor at any time T thes functions air just given here all right. And remember that they both occur at a different angle. The current occurs at an angle omega T, and the voltage occurs at some different angle. Fate of prime, which is Omega t plus pi over two. Because both functions occur at different angles, they're said to be out of phase. Okay, the current actually lags the voltage in this case. Or you could say the voltage leads the current. Okay. What this means is readily apparent on phaser diagrams. In the first diagram, I plot the current at its angle. Omega T In the second diagram, I plot the voltage at its angle. Omega teeth plus pi over two. Plus that 90 degrees. Okay. Combining these two, we have the voltage ahead of the current by 90 degrees. It's very, very important to remember that the voltage across and induct er leads the current. Okay, this is opposite to capacitors and a C circuits where the voltage lags the current. They're opposites. The voltage leads the current. For in doctors, the voltage lags the current for capacitors. Okay, let's do a quick example about this and a C sources connected to an induct er at a particular instant in time. The current in the circuit is negative and increasing in magnitude. Draw the phasers for the voltage and the current that correspond to this instant in time. Okay, so here's my phaser diagram. Remember, what does it take for phase two to be negative? It has to be on the left side of the graph because it's horizontal. Component has to be negative. What does it take for it to be increasing in magnitude? It has to be moving towards the horizontal axis. Since it rotates counterclockwise, it has to be in the second quadrant. This has to be here so that it's negative, and since it's rotating counter clockwise, it's moving towards the horizontal axis, so it's negative and increasing in magnitude. Okay, this is for the current. Remember that the current across. Sorry, the current through and the doctor lags the voltage. If you look all the above in the green box, the voltage leads the current by 90 degrees. So I would need to draw another phaser 90 degrees ahead. And that would be the voltage across the induct er and that is our phaser diagram for an induct er in in a see circuit. All right, guys, this wraps up our discussion on phasers and how they pertain to induct er's in a sea circuits. Thanks for watching.

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Problem

An AC source operates at a maximum voltage of 75 V and is connected to a 0.4 H inductor. If the current across the inductor is i(t) = i_{MAX} cos[(450 s ^{−1})t],

a) What is i_{MAX}?

b) Draw the phasors for voltage across the inductor and current in the circuit at t = 4.2 ms. Assume that the current phasor begins at 0°.

A

a) i

_{max}= 0.42A b) θ_{iL}= 108^{o}θ_{VL}= 198^{o}B

a) i

_{max}= 0.42A b) θ_{iL}= 108^{o}θ_{VL}= 18^{o}C

a) i

_{max}= 0.42A b) θ_{iL}= 198^{o}θ_{VL}= 108^{o}D

a) i

_{max}= 0.42A b) θ_{iL}= 18^{o}θ_{VL}= 108^{o}